The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions

Majority Judgement Measuring, Ranking and Electing

Rida Laraki CNRS, LAMSADE and École Polytechnique, Paris

(Joint work with Michel Balinski)

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Contents

1 The thesis 2 Traditional Theory of Social Choice Traditional Methods and paradoxs paradoxs in practice Impossibility Theorems 3 Incompatibility Between Electing and Ranking 4 The Method of Majority Judgment Wines Elections Strategy proof in raking 5 The Theory of Majority Judgement Majority Grading Model Strategic Analysis Middlemost SGF Majority Ranking Model Meaningfulness 6 Approval Voting versus Approval Judgment 7 Experimental Evidences 8 Conclusions

Rida Laraki Majority Judgement The methods of voting that are used differ in two ways : (1) how voters express their opinions – the inputs – and (2) how the various opinions are amalgamated – the outputs–. Every one of the methods is meant to be – and is commonly referred to being – a “majority decision.”

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority principle ?

Every democratic country pretends to elect its representatives by a majority principle, though the rules vary.

Rida Laraki Majority Judgement Every one of the methods is meant to be – and is commonly referred to being – a “majority decision.”

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority principle ?

Every democratic country pretends to elect its representatives by a majority principle, though the rules vary. The methods of voting that are used differ in two ways : (1) how voters express their opinions – the inputs – and (2) how the various opinions are amalgamated – the outputs–.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority principle ?

Every democratic country pretends to elect its representatives by a majority principle, though the rules vary. The methods of voting that are used differ in two ways : (1) how voters express their opinions – the inputs – and (2) how the various opinions are amalgamated – the outputs–. Every one of the methods is meant to be – and is commonly referred to being – a “majority decision.”

Rida Laraki Majority Judgement It is our contention to challenge the current philosophical view of what constitutes a majority decision and propose an alternative.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions A challenge

The legitimating force of the majority rule is so pervasive that we often do not notice it and rarely do we question it : We usually take it for granted. [...] It is much too powerful to make it vulnerable to a philosophical challenge.

(Wojciech Sadurski, 2008).

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions A challenge

The legitimating force of the majority rule is so pervasive that we often do not notice it and rarely do we question it : We usually take it for granted. [...] It is much too powerful to make it vulnerable to a philosophical challenge.

(Wojciech Sadurski, 2008).

It is our contention to challenge the current philosophical view of what constitutes a majority decision and propose an alternative.

Rida Laraki Majority Judgement The traditional conception of voting—the underlying theoretical foundation that goes back to 1299—is based on false premises : it is a faulty model of reality. The model leads to an inconsistent theory : real, unacceptable paradoxs are unavoidable (e.g., Arrow’s impossibility theorem, Condorcet’s paradox). So, why continue to use it ?

The traditional methods of voting do not work : they often fail to elect the candidate sought by the voters.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Our objections

More generally, we claim that :

Rida Laraki Majority Judgement The traditional conception of voting—the underlying theoretical foundation that goes back to 1299—is based on false premises : it is a faulty model of reality. The model leads to an inconsistent theory : real, unacceptable paradoxs are unavoidable (e.g., Arrow’s impossibility theorem, Condorcet’s paradox). So, why continue to use it ?

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Our objections

More generally, we claim that : The traditional methods of voting do not work : they often fail to elect the candidate sought by the voters.

Rida Laraki Majority Judgement The model leads to an inconsistent theory : real, unacceptable paradoxs are unavoidable (e.g., Arrow’s impossibility theorem, Condorcet’s paradox). So, why continue to use it ?

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Our objections

More generally, we claim that : The traditional methods of voting do not work : they often fail to elect the candidate sought by the voters. The traditional conception of voting—the underlying theoretical foundation that goes back to 1299—is based on false premises : it is a faulty model of reality.

Rida Laraki Majority Judgement So, why continue to use it ?

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Our objections

More generally, we claim that : The traditional methods of voting do not work : they often fail to elect the candidate sought by the voters. The traditional conception of voting—the underlying theoretical foundation that goes back to 1299—is based on false premises : it is a faulty model of reality. The model leads to an inconsistent theory : real, unacceptable paradoxs are unavoidable (e.g., Arrow’s impossibility theorem, Condorcet’s paradox).

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Our objections

More generally, we claim that : The traditional methods of voting do not work : they often fail to elect the candidate sought by the voters. The traditional conception of voting—the underlying theoretical foundation that goes back to 1299—is based on false premises : it is a faulty model of reality. The model leads to an inconsistent theory : real, unacceptable paradoxs are unavoidable (e.g., Arrow’s impossibility theorem, Condorcet’s paradox). So, why continue to use it ?

Rida Laraki Majority Judgement A more realistic conception of how voters imagine their “preferences”—their likes and dislikes—leads to a new model, a new method of voting : Majority Judgment. It has been tested in voting, committee decisions and wine competitions. Our objective is to show that : Majority Judgment is practical, natural, simple, avoids unacceptable paradoxs, resists manipulations, and—we claim—dominates all known methods for choosing a winner and order of finish in theory and practice.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Our answer

Rida Laraki Majority Judgement It has been tested in voting, committee decisions and wine competitions. Our objective is to show that : Majority Judgment is practical, natural, simple, avoids unacceptable paradoxs, resists manipulations, and—we claim—dominates all known methods for choosing a winner and order of finish in theory and practice.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Our answer

A more realistic conception of how voters imagine their “preferences”—their likes and dislikes—leads to a new model, a new method of voting : Majority Judgment.

Rida Laraki Majority Judgement Our objective is to show that : Majority Judgment is practical, natural, simple, avoids unacceptable paradoxs, resists manipulations, and—we claim—dominates all known methods for choosing a winner and order of finish in theory and practice.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Our answer

A more realistic conception of how voters imagine their “preferences”—their likes and dislikes—leads to a new model, a new method of voting : Majority Judgment. It has been tested in voting, committee decisions and wine competitions.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Our answer

A more realistic conception of how voters imagine their “preferences”—their likes and dislikes—leads to a new model, a new method of voting : Majority Judgment. It has been tested in voting, committee decisions and wine competitions. Our objective is to show that : Majority Judgment is practical, natural, simple, avoids unacceptable paradoxs, resists manipulations, and—we claim—dominates all known methods for choosing a winner and order of finish in theory and practice.

Rida Laraki Majority Judgement messages −→ decisions The traditional model of social choice: voters’ “preferences” −→ society’s “preferences” by which is meant

voters’ rank-orderings −→ society’s rank-ordering

First, this leads to serious inconsistencies. Second, this is an unrealistic vision :

Voters do not have lists of candidates in their minds – the input messages are the wrong ones.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Problem

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs

Rida Laraki Majority Judgement The traditional model of social choice: voters’ “preferences” −→ society’s “preferences” by which is meant

voters’ rank-orderings −→ society’s rank-ordering

First, this leads to serious inconsistencies. Second, this is an unrealistic vision :

Voters do not have lists of candidates in their minds – the input messages are the wrong ones.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Problem

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs messages −→ decisions

Rida Laraki Majority Judgement by which is meant

voters’ rank-orderings −→ society’s rank-ordering

First, this leads to serious inconsistencies. Second, this is an unrealistic vision :

Voters do not have lists of candidates in their minds – the input messages are the wrong ones.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Problem

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs messages −→ decisions The traditional model of social choice: voters’ “preferences” −→ society’s “preferences”

Rida Laraki Majority Judgement First, this leads to serious inconsistencies. Second, this is an unrealistic vision :

Voters do not have lists of candidates in their minds – the input messages are the wrong ones.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Problem

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs messages −→ decisions The traditional model of social choice: voters’ “preferences” −→ society’s “preferences” by which is meant

voters’ rank-orderings −→ society’s rank-ordering

Rida Laraki Majority Judgement Second, this is an unrealistic vision :

Voters do not have lists of candidates in their minds – the input messages are the wrong ones.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Problem

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs messages −→ decisions The traditional model of social choice: voters’ “preferences” −→ society’s “preferences” by which is meant

voters’ rank-orderings −→ society’s rank-ordering

First, this leads to serious inconsistencies.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Problem

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs messages −→ decisions The traditional model of social choice: voters’ “preferences” −→ society’s “preferences” by which is meant

voters’ rank-orderings −→ society’s rank-ordering

First, this leads to serious inconsistencies. Second, this is an unrealistic vision :

Voters do not have lists of candidates in their minds – the input messages are the wrong ones.

Rida Laraki Majority Judgement messages −→ decisions The new model of social choice: voters’ “evaluations” −→ society’s “evaluations” by which is meant

 society’s grades voters’ grades −→ society’s rank-ordering

First, this leads to a consistent theory. Second, this is a much more realistic vision of what voters (and judges) have in mind.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The answer

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs

Rida Laraki Majority Judgement The new model of social choice: voters’ “evaluations” −→ society’s “evaluations” by which is meant

 society’s grades voters’ grades −→ society’s rank-ordering

First, this leads to a consistent theory. Second, this is a much more realistic vision of what voters (and judges) have in mind.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The answer

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs messages −→ decisions

Rida Laraki Majority Judgement by which is meant

 society’s grades voters’ grades −→ society’s rank-ordering

First, this leads to a consistent theory. Second, this is a much more realistic vision of what voters (and judges) have in mind.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The answer

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs messages −→ decisions The new model of social choice: voters’ “evaluations” −→ society’s “evaluations”

Rida Laraki Majority Judgement First, this leads to a consistent theory. Second, this is a much more realistic vision of what voters (and judges) have in mind.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The answer

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs messages −→ decisions The new model of social choice: voters’ “evaluations” −→ society’s “evaluations” by which is meant

 society’s grades voters’ grades −→ society’s rank-ordering

Rida Laraki Majority Judgement Second, this is a much more realistic vision of what voters (and judges) have in mind.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The answer

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs messages −→ decisions The new model of social choice: voters’ “evaluations” −→ society’s “evaluations” by which is meant

 society’s grades voters’ grades −→ society’s rank-ordering

First, this leads to a consistent theory.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The answer

The fundamental problem of electing and ranking : to find a social decision function (SDF) : inputs −→ ouputs messages −→ decisions The new model of social choice: voters’ “evaluations” −→ society’s “evaluations” by which is meant

 society’s grades voters’ grades −→ society’s rank-ordering

First, this leads to a consistent theory. Second, this is a much more realistic vision of what voters (and judges) have in mind.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Contents

1 The thesis 2 Traditional Theory of Social Choice Traditional Methods and paradoxs paradoxs in practice Impossibility Theorems 3 Incompatibility Between Electing and Ranking 4 The Method of Majority Judgment Wines Elections Strategy proof in raking 5 The Theory of Majority Judgement Majority Grading Model Strategic Analysis Middlemost SGF Majority Ranking Model Meaningfulness 6 Approval Voting versus Approval Judgment 7 Experimental Evidences 8 Conclusions

Rida Laraki Majority Judgement The great hope—since Ramun Llull in 1299—has been to choose a Condorcet-winner : a candidate who beats every possible opponent face-to-face. Of course, there may be no Condorcet-winner : 30% 32% 38% ABC ABC A – 68% 30% BCA B 32% – 62% CAB C 70% 38% – because

A(68%) B(62%) C(70%) A

The Condorcet paradox.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Condorcet Paradox (1786)

Traditionally, a voter input is assumed to be—commonly and in the theory of social choice—a list of candidates that is in his/her mind, ordered from best to worst.

Rida Laraki Majority Judgement Of course, there may be no Condorcet-winner : 30% 32% 38% ABC ABC A – 68% 30% BCA B 32% – 62% CAB C 70% 38% – because

A(68%) B(62%) C(70%) A

The Condorcet paradox.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Condorcet Paradox (1786)

Traditionally, a voter input is assumed to be—commonly and in the theory of social choice—a list of candidates that is in his/her mind, ordered from best to worst. The great hope—since Ramun Llull in 1299—has been to choose a Condorcet-winner : a candidate who beats every possible opponent face-to-face.

Rida Laraki Majority Judgement ABC A – 68% 30% B 32% – 62% C 70% 38% – because

A(68%) B(62%) C(70%) A

The Condorcet paradox.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Condorcet Paradox (1786)

Traditionally, a voter input is assumed to be—commonly and in the theory of social choice—a list of candidates that is in his/her mind, ordered from best to worst. The great hope—since Ramun Llull in 1299—has been to choose a Condorcet-winner : a candidate who beats every possible opponent face-to-face. Of course, there may be no Condorcet-winner : 30% 32% 38% ABC BCA CAB

Rida Laraki Majority Judgement because

A(68%) B(62%) C(70%) A

The Condorcet paradox.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Condorcet Paradox (1786)

Traditionally, a voter input is assumed to be—commonly and in the theory of social choice—a list of candidates that is in his/her mind, ordered from best to worst. The great hope—since Ramun Llull in 1299—has been to choose a Condorcet-winner : a candidate who beats every possible opponent face-to-face. Of course, there may be no Condorcet-winner : 30% 32% 38% ABC ABC A – 68% 30% BCA B 32% – 62% CAB C 70% 38% –

Rida Laraki Majority Judgement The Condorcet paradox.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Condorcet Paradox (1786)

Traditionally, a voter input is assumed to be—commonly and in the theory of social choice—a list of candidates that is in his/her mind, ordered from best to worst. The great hope—since Ramun Llull in 1299—has been to choose a Condorcet-winner : a candidate who beats every possible opponent face-to-face. Of course, there may be no Condorcet-winner : 30% 32% 38% ABC ABC A – 68% 30% BCA B 32% – 62% CAB C 70% 38% – because

A(68%) B(62%) C(70%) A

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Condorcet Paradox (1786)

Traditionally, a voter input is assumed to be—commonly and in the theory of social choice—a list of candidates that is in his/her mind, ordered from best to worst. The great hope—since Ramun Llull in 1299—has been to choose a Condorcet-winner : a candidate who beats every possible opponent face-to-face. Of course, there may be no Condorcet-winner : 30% 32% 38% ABC ABC A – 68% 30% BCA B 32% – 62% CAB C 70% 38% – because

A(68%) B(62%) C(70%) A

The Condorcet paradox.

Rida Laraki Majority Judgement Borda score A : 60+38=98 B : 30+64=94 C : 32+76=108

Or, ABC Borda score A – 68% 30% 98 B 32% – 62% 94 C 70% 38% – 108 The Borda-ranking : C A B.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s Method

In 1433, Nicolas Cusanus proposed what is known today as Borda’s method (1780) :

Points 30% 32% 38% 2 ABC 1 BCA 0 CAB

Rida Laraki Majority Judgement Or, ABC Borda score A – 68% 30% 98 B 32% – 62% 94 C 70% 38% – 108 The Borda-ranking : C A B.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s Method

In 1433, Nicolas Cusanus proposed what is known today as Borda’s method (1780) :

Points 30% 32% 38% Borda score 2 ABC A : 60+38=98 1 BCA B : 30+64=94 0 CAB C : 32+76=108

Rida Laraki Majority Judgement The Borda-ranking : C A B.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s Method

In 1433, Nicolas Cusanus proposed what is known today as Borda’s method (1780) :

Points 30% 32% 38% Borda score 2 ABC A : 60+38=98 1 BCA B : 30+64=94 0 CAB C : 32+76=108

Or, ABC Borda score A – 68% 30% 98 B 32% – 62% 94 C 70% 38% – 108

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s Method

In 1433, Nicolas Cusanus proposed what is known today as Borda’s method (1780) :

Points 30% 32% 38% Borda score 2 ABC A : 60+38=98 1 BCA B : 30+64=94 0 CAB C : 32+76=108

Or, ABC Borda score A – 68% 30% 98 B 32% – 62% 94 C 70% 38% – 108 The Borda-ranking : C A B.

Rida Laraki Majority Judgement First-past-the-post (used in UK, USA to elect members of House of representatives ) : A voter names one candidate (the input). The candidate most often named is elected (the output). The question asked to a voter is implicitly : which candidate do you like best ? Two-past-the-post (used in France, Chile to elect the president) : A voter names one candidate. If one candidate is named by more than 50% of the voters, he or she is elected. Otherwise, there is a run-off between the two candidates most often named. Approval Voting (used in many scientific societies) permits a bit more information from voters. The voter may designate as many candidates as she wishes. The candidate most often designated wins. The question asked to a voter is implicitly : who are the acceptable candidates ? AV was formally introduced by Robert Weber in 1977, though it seems to have been practiced in the Sparta of antique Greece...

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions UK’s, USA’s, France’s Methods

Rida Laraki Majority Judgement Two-past-the-post (used in France, Chile to elect the president) : A voter names one candidate. If one candidate is named by more than 50% of the voters, he or she is elected. Otherwise, there is a run-off between the two candidates most often named. Approval Voting (used in many scientific societies) permits a bit more information from voters. The voter may designate as many candidates as she wishes. The candidate most often designated wins. The question asked to a voter is implicitly : who are the acceptable candidates ? AV was formally introduced by Robert Weber in 1977, though it seems to have been practiced in the Sparta of antique Greece...

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions UK’s, USA’s, France’s Methods

First-past-the-post (used in UK, USA to elect members of House of representatives ) : A voter names one candidate (the input). The candidate most often named is elected (the output). The question asked to a voter is implicitly : which candidate do you like best ?

Rida Laraki Majority Judgement Approval Voting (used in many scientific societies) permits a bit more information from voters. The voter may designate as many candidates as she wishes. The candidate most often designated wins. The question asked to a voter is implicitly : who are the acceptable candidates ? AV was formally introduced by Robert Weber in 1977, though it seems to have been practiced in the Sparta of antique Greece...

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions UK’s, USA’s, France’s Methods

First-past-the-post (used in UK, USA to elect members of House of representatives ) : A voter names one candidate (the input). The candidate most often named is elected (the output). The question asked to a voter is implicitly : which candidate do you like best ? Two-past-the-post (used in France, Chile to elect the president) : A voter names one candidate. If one candidate is named by more than 50% of the voters, he or she is elected. Otherwise, there is a run-off between the two candidates most often named.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions UK’s, USA’s, France’s Methods

First-past-the-post (used in UK, USA to elect members of House of representatives ) : A voter names one candidate (the input). The candidate most often named is elected (the output). The question asked to a voter is implicitly : which candidate do you like best ? Two-past-the-post (used in France, Chile to elect the president) : A voter names one candidate. If one candidate is named by more than 50% of the voters, he or she is elected. Otherwise, there is a run-off between the two candidates most often named. Approval Voting (used in many scientific societies) permits a bit more information from voters. The voter may designate as many candidates as she wishes. The candidate most often designated wins. The question asked to a voter is implicitly : who are the acceptable candidates ? AV was formally introduced by Robert Weber in 1977, though it seems to have been practiced in the Sparta of antique Greece...

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions

Borda wrote (in 1780) : I is generally accepted, and to my knowledge never challenged, that in an election the greatest number of votes always designates the will of the electorate... But I will show that this opinion, that is true when the election is between only two candidates , can mislead in all other cases...

Rida Laraki Majority Judgement (2)Two-past-the-post : B A C (3) Borda : C B A (and Condorcet)

If with (1), the 28% vote for B : B wins. If with (2), the 33% vote for C : C wins. If with (3), the 28% vote B C A : B wins.

(1) First-past-the-post : A B C

Strategic manipulation pays:

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s example : the winner depends on the method

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

Rida Laraki Majority Judgement If with (1), the 28% vote for B : B wins. If with (2), the 33% vote for C : C wins. If with (3), the 28% vote B C A : B wins.

(2)Two-past-the-post : B A C (3) Borda : C B A (and Condorcet) Strategic manipulation pays:

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s example : the winner depends on the method

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A B C

Rida Laraki Majority Judgement If with (1), the 28% vote for B : B wins. If with (2), the 33% vote for C : C wins. If with (3), the 28% vote B C A : B wins.

(3) Borda : C B A (and Condorcet) Strategic manipulation pays:

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s example : the winner depends on the method

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A B C (2)Two-past-the-post : B A C

Rida Laraki Majority Judgement If with (1), the 28% vote for B : B wins. If with (2), the 33% vote for C : C wins. If with (3), the 28% vote B C A : B wins.

Strategic manipulation pays:

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s example : the winner depends on the method

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A B C (2)Two-past-the-post : B A C (3) Borda : C B A (and Condorcet)

Rida Laraki Majority Judgement If with (1), the 28% vote for B : B wins. If with (2), the 33% vote for C : C wins. If with (3), the 28% vote B C A : B wins.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s example : the winner depends on the method

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A B C (2)Two-past-the-post : B A C (3) Borda : C B A (and Condorcet) Strategic manipulation pays:

Rida Laraki Majority Judgement If with (2), the 33% vote for C : C wins. If with (3), the 28% vote B C A : B wins.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s example : the winner depends on the method

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A B C (2)Two-past-the-post : B A C (3) Borda : C B A (and Condorcet) Strategic manipulation pays: If with (1), the 28% vote for B : B wins.

Rida Laraki Majority Judgement If with (3), the 28% vote B C A : B wins.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s example : the winner depends on the method

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A B C (2)Two-past-the-post : B A C (3) Borda : C B A (and Condorcet) Strategic manipulation pays: If with (1), the 28% vote for B : B wins. If with (2), the 33% vote for C : C wins.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda’s example : the winner depends on the method

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A B C (2)Two-past-the-post : B A C (3) Borda : C B A (and Condorcet) Strategic manipulation pays: If with (1), the 28% vote for B : B wins. If with (2), the 33% vote for C : C wins. If with (3), the 28% vote B C A : B wins.

Rida Laraki Majority Judgement If with (1), C (a loser) drops out, B wins ; if B (a loser) drops out C wins. If with (2), A (a loser) drops out, C wins.

Arrow’s paradox:

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Arrow’s paradox

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A wins (2)Two-past-the-post : B wins (3) Borda : C wins.

Rida Laraki Majority Judgement If with (1), C (a loser) drops out, B wins ; if B (a loser) drops out C wins. If with (2), A (a loser) drops out, C wins.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Arrow’s paradox

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A wins (2)Two-past-the-post : B wins (3) Borda : C wins. Arrow’s paradox:

Rida Laraki Majority Judgement If with (2), A (a loser) drops out, C wins.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Arrow’s paradox

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A wins (2)Two-past-the-post : B wins (3) Borda : C wins. Arrow’s paradox: If with (1), C (a loser) drops out, B wins ; if B (a loser) drops out C wins.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Arrow’s paradox

5% 33% 34% 28% ABC AABC A – 38% 38% BCCB B 62% – 39% CBAA C 62% 61% –

(1) First-past-the-post : A wins (2)Two-past-the-post : B wins (3) Borda : C wins. Arrow’s paradox: If with (1), C (a loser) drops out, B wins ; if B (a loser) drops out C wins. If with (2), A (a loser) drops out, C wins.

Rida Laraki Majority Judgement The Borda-ranking is A B C. Yet, B is the Condorcet-winner, B A C the Condorcet-ranking.

If C drops out : B is the winner : Arrow’s paradox!

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Arrow’s paradox

33% 3% 16% 18% 30% ABC ABACB A – 49% 79% BCCBA B 51% – 66% CABAC C 21% 34% –

Rida Laraki Majority Judgement Yet, B is the Condorcet-winner, B A C the Condorcet-ranking.

If C drops out : B is the winner : Arrow’s paradox!

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Arrow’s paradox

33% 3% 16% 18% 30% ABC ABACB A – 49% 79% BCCBA B 51% – 66% CABAC C 21% 34% –

The Borda-ranking is A B C.

Rida Laraki Majority Judgement If C drops out : B is the winner : Arrow’s paradox!

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Arrow’s paradox

33% 3% 16% 18% 30% ABC ABACB A – 49% 79% BCCBA B 51% – 66% CABAC C 21% 34% –

The Borda-ranking is A B C. Yet, B is the Condorcet-winner, B A C the Condorcet-ranking.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Arrow’s paradox

33% 3% 16% 18% 30% ABC ABACB A – 49% 79% BCCBA B 51% – 66% CABAC C 21% 34% –

The Borda-ranking is A B C. Yet, B is the Condorcet-winner, B A C the Condorcet-ranking.

If C drops out : B is the winner : Arrow’s paradox!

Rida Laraki Majority Judgement Florida had 25 electoral votes. Most who voted for Nader would have voted for Gore. Without Nader in Florida : 2000 Election Electoral votes George W. Bush 246 Albert Gore 291

Arrow’s paradox : a candidate’s presence (having no chance of winning whatsoever) can change the outcome.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The unacceptable paradoxs are real !

2000 Election Votes Electoral votes Florida votes George W. Bush 50,456,002 271 2,912,790 Albert Gore 50,999,897 266 2,912,253 Ralph Nader 2,882,955 0 97,488

Rida Laraki Majority Judgement Most who voted for Nader would have voted for Gore. Without Nader in Florida : 2000 Election Electoral votes George W. Bush 246 Albert Gore 291

Arrow’s paradox : a candidate’s presence (having no chance of winning whatsoever) can change the outcome.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The unacceptable paradoxs are real !

2000 Election Votes Electoral votes Florida votes George W. Bush 50,456,002 271 2,912,790 Albert Gore 50,999,897 266 2,912,253 Ralph Nader 2,882,955 0 97,488

Florida had 25 electoral votes.

Rida Laraki Majority Judgement 2000 Election Electoral votes George W. Bush 246 Albert Gore 291

Arrow’s paradox : a candidate’s presence (having no chance of winning whatsoever) can change the outcome.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The unacceptable paradoxs are real !

2000 Election Votes Electoral votes Florida votes George W. Bush 50,456,002 271 2,912,790 Albert Gore 50,999,897 266 2,912,253 Ralph Nader 2,882,955 0 97,488

Florida had 25 electoral votes. Most who voted for Nader would have voted for Gore. Without Nader in Florida :

Rida Laraki Majority Judgement Arrow’s paradox : a candidate’s presence (having no chance of winning whatsoever) can change the outcome.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The unacceptable paradoxs are real !

2000 Election Votes Electoral votes Florida votes George W. Bush 50,456,002 271 2,912,790 Albert Gore 50,999,897 266 2,912,253 Ralph Nader 2,882,955 0 97,488

Florida had 25 electoral votes. Most who voted for Nader would have voted for Gore. Without Nader in Florida : 2000 Election Electoral votes George W. Bush 246 Albert Gore 291

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The unacceptable paradoxs are real !

2000 Election Votes Electoral votes Florida votes George W. Bush 50,456,002 271 2,912,790 Albert Gore 50,999,897 266 2,912,253 Ralph Nader 2,882,955 0 97,488

Florida had 25 electoral votes. Most who voted for Nader would have voted for Gore. Without Nader in Florida : 2000 Election Electoral votes George W. Bush 246 Albert Gore 291

Arrow’s paradox : a candidate’s presence (having no chance of winning whatsoever) can change the outcome.

Rida Laraki Majority Judgement Jospin Le Pen > 75% < 25%

First round results 2002 (16 candidates, 72% participation) : Chirac Le Pen Jospin Bayrou Laguiller Chévènement 19,88% 16,86% 16,18% 6,84% 5,72% 5,33%

Mamère Besancenot Saint-Josse Madelin Hue Mégret 5,25% 4,25% 4,23% 3,91% 3,37% 2,34%

(Pasqua) Taubira Lepage Boutin Gluckstein 0% 2,32% 1,88% 1,19% 0,47% Second round results 2002 (80% participation) : Chirac Le Pen Chirac Jospin 82,21% 17,79% < 50% ? > 50% ? Arrow paradox !

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

Rida Laraki Majority Judgement Jospin Le Pen > 75% < 25%

Second round results 2002 (80% participation) : Chirac Le Pen Chirac Jospin 82,21% 17,79% < 50% ? > 50% ? Arrow paradox !

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

First round results 2002 (16 candidates, 72% participation) : Chirac Le Pen Jospin Bayrou Laguiller Chévènement 19,88% 16,86% 16,18% 6,84% 5,72% 5,33%

Mamère Besancenot Saint-Josse Madelin Hue Mégret 5,25% 4,25% 4,23% 3,91% 3,37% 2,34%

(Pasqua) Taubira Lepage Boutin Gluckstein 0% 2,32% 1,88% 1,19% 0,47%

Rida Laraki Majority Judgement Jospin Le Pen > 75% < 25%

Chirac Jospin < 50% ? > 50% ? Arrow paradox !

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

First round results 2002 (16 candidates, 72% participation) : Chirac Le Pen Jospin Bayrou Laguiller Chévènement 19,88% 16,86% 16,18% 6,84% 5,72% 5,33%

Mamère Besancenot Saint-Josse Madelin Hue Mégret 5,25% 4,25% 4,23% 3,91% 3,37% 2,34%

(Pasqua) Taubira Lepage Boutin Gluckstein 0% 2,32% 1,88% 1,19% 0,47% Second round results 2002 (80% participation) : Chirac Le Pen 82,21% 17,79%

Rida Laraki Majority Judgement Jospin Le Pen > 75% < 25% Arrow paradox !

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

First round results 2002 (16 candidates, 72% participation) : Chirac Le Pen Jospin Bayrou Laguiller Chévènement 19,88% 16,86% 16,18% 6,84% 5,72% 5,33%

Mamère Besancenot Saint-Josse Madelin Hue Mégret 5,25% 4,25% 4,23% 3,91% 3,37% 2,34%

(Pasqua) Taubira Lepage Boutin Gluckstein 0% 2,32% 1,88% 1,19% 0,47% Second round results 2002 (80% participation) : Chirac Le Pen Chirac Jospin 82,21% 17,79% < 50% ? > 50% ?

Rida Laraki Majority Judgement Arrow paradox !

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

First round results 2002 (16 candidates, 72% participation) : Chirac Le Pen Jospin Bayrou Laguiller Chévènement 19,88% 16,86% 16,18% 6,84% 5,72% 5,33%

Mamère Besancenot Saint-Josse Madelin Hue Mégret 5,25% 4,25% 4,23% 3,91% 3,37% 2,34%

(Pasqua) Taubira Lepage Boutin Gluckstein 0% 2,32% 1,88% 1,19% 0,47% Second round results 2002 (80% participation) : Chirac Le Pen Chirac Jospin Jospin Le Pen 82,21% 17,79% < 50% ? > 50% ? > 75% < 25%

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

First round results 2002 (16 candidates, 72% participation) : Chirac Le Pen Jospin Bayrou Laguiller Chévènement 19,88% 16,86% 16,18% 6,84% 5,72% 5,33%

Mamère Besancenot Saint-Josse Madelin Hue Mégret 5,25% 4,25% 4,23% 3,91% 3,37% 2,34%

(Pasqua) Taubira Lepage Boutin Gluckstein 0% 2,32% 1,88% 1,19% 0,47% Second round results 2002 (80% participation) : Chirac Le Pen Chirac Jospin Jospin Le Pen 82,21% 17,79% < 50% ? > 50% ? > 75% < 25% Arrow paradox !

Rida Laraki Majority Judgement Minor candidates of the left obtained 27% in 2002, only 11% in 2007. Minor candidates of the right obtained 16% in 2002, only 3% in 2007.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

2007 presidential election.

In response to 2002, 30% of French voters did not vote for their first choices in 2007 : they voted strategically (“le vote utile”).

Rida Laraki Majority Judgement Minor candidates of the right obtained 16% in 2002, only 3% in 2007.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

2007 presidential election.

In response to 2002, 30% of French voters did not vote for their first choices in 2007 : they voted strategically (“le vote utile”). Minor candidates of the left obtained 27% in 2002, only 11% in 2007.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

2007 presidential election.

In response to 2002, 30% of French voters did not vote for their first choices in 2007 : they voted strategically (“le vote utile”). Minor candidates of the left obtained 27% in 2002, only 11% in 2007. Minor candidates of the right obtained 16% in 2002, only 3% in 2007.

Rida Laraki Majority Judgement Sarkozy was the winner with two-past-the-post system : Nicolas Sarkozy 53% Ségoléne Royal 47%

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions 2007 election, first round, 12 candidates

First round results : Sarkozy Royal Bayrou Le Pen Besancenot de Villiers 31,18% 25,87% 18,57% 10,44% 4,08% 2,23%

Buffet Voynet Laguiller Bové Nihous Schivardi 1,93% 1,57% 1,33% 1,32% 1,15% 0,34%

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions 2007 election, first round, 12 candidates

First round results : Sarkozy Royal Bayrou Le Pen Besancenot de Villiers 31,18% 25,87% 18,57% 10,44% 4,08% 2,23%

Buffet Voynet Laguiller Bové Nihous Schivardi 1,93% 1,57% 1,33% 1,32% 1,15% 0,34%

Sarkozy was the winner with two-past-the-post system : Nicolas Sarkozy 53% Ségoléne Royal 47%

Rida Laraki Majority Judgement The same poll stated that among Royal voters, 72% for Bayrou against Sarkozy in the second round, and among Sarkozy voters, 75% for Bayrou against Royal in the second round.

Bayrou was the Condocet-winner and Borda-winner, Sarkozy the first-past-the-post-winner and two-past-the-post winner. What is the true wish of society ?

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

Second round poll of March 20 (TNS-SOFRES) :

Bayrou Le Pen Royal Sarkozy Bayrou — 84% 57% 54% Le Pen 16% — 25% 16% Royal 46% 75% — 46% Sarkozy 46% 84% 54% —

These estimates confirmed by many polls and field experiments.

Rida Laraki Majority Judgement Bayrou was the Condocet-winner and Borda-winner, Sarkozy the first-past-the-post-winner and two-past-the-post winner. What is the true wish of society ?

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

Second round poll of March 20 (TNS-SOFRES) :

Bayrou Le Pen Royal Sarkozy Bayrou — 84% 57% 54% Le Pen 16% — 25% 16% Royal 46% 75% — 46% Sarkozy 46% 84% 54% —

These estimates confirmed by many polls and field experiments. The same poll stated that among Royal voters, 72% for Bayrou against Sarkozy in the second round, and among Sarkozy voters, 75% for Bayrou against Royal in the second round.

Rida Laraki Majority Judgement What is the true wish of society ?

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

Second round poll of March 20 (TNS-SOFRES) :

Bayrou Le Pen Royal Sarkozy Bayrou — 84% 57% 54% Le Pen 16% — 25% 16% Royal 46% 75% — 46% Sarkozy 46% 84% 54% —

These estimates confirmed by many polls and field experiments. The same poll stated that among Royal voters, 72% for Bayrou against Sarkozy in the second round, and among Sarkozy voters, 75% for Bayrou against Royal in the second round.

Bayrou was the Condocet-winner and Borda-winner, Sarkozy the first-past-the-post-winner and two-past-the-post winner.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Are elected Presidents those wished by the voters ?

Second round poll of March 20 (TNS-SOFRES) :

Bayrou Le Pen Royal Sarkozy Bayrou — 84% 57% 54% Le Pen 16% — 25% 16% Royal 46% 75% — 46% Sarkozy 46% 84% 54% —

These estimates confirmed by many polls and field experiments. The same poll stated that among Royal voters, 72% for Bayrou against Sarkozy in the second round, and among Sarkozy voters, 75% for Bayrou against Royal in the second round.

Bayrou was the Condocet-winner and Borda-winner, Sarkozy the first-past-the-post-winner and two-past-the-post winner. What is the true wish of society ?

Rida Laraki Majority Judgement Before the performance of Vlascenko, the order was : 1st Urmanov,2 nd Zagorodniuk, 3rd Candeloro... ! ! !

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Arrow’s paradox : 1997 European Championships, men’s free skating

J1 J2 J3 J4 J5 J6 J7 J8 J9 Mark Place Candeloro 3 2 5 2 3 3 5 6 6 3/5 2nd Kulik 2 4 2 3 6 5 3 4 5 4/6 5th Urmanov 1 1 1 1 1 2 1 1 1 1/8 1st Yagudin 4 3 3 6 4 6 4 3 2 4/7 4th Zagorodniuk 5 5 4 4 2 4 2 2 3 4/7 3rd Vlascenko 6 6 6 5 5 1 6 5 4 5/5 6th

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Arrow’s paradox : 1997 European Championships, men’s free skating

J1 J2 J3 J4 J5 J6 J7 J8 J9 Mark Place Candeloro 3 2 5 2 3 3 5 6 6 3/5 2nd Kulik 2 4 2 3 6 5 3 4 5 4/6 5th Urmanov 1 1 1 1 1 2 1 1 1 1/8 1st Yagudin 4 3 3 6 4 6 4 3 2 4/7 4th Zagorodniuk 5 5 4 4 2 4 2 2 3 4/7 3rd Vlascenko 6 6 6 5 5 1 6 5 4 5/5 6th

Before the performance of Vlascenko, the order was : 1st Urmanov,2 nd Zagorodniuk, 3rd Candeloro... ! ! !

Rida Laraki Majority Judgement This rule was proposed by Dasgupta and Maskin with elaborate theoretical arguments, calling it “the fairest vote of all”.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

The scandal was too big that the rules used for more than half of century were changed. The ISU adopted the OBO rule (“one-by-one”) in 1998 : Rank the competitors by their number of wins (Condorcet’s) ; break any ties by using Borda’s rule.

Rida Laraki Majority Judgement This rule was proposed by Dasgupta and Maskin with elaborate theoretical arguments, calling it “the fairest vote of all”.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

The scandal was too big that the rules used for more than half of century were changed. The ISU adopted the OBO rule (“one-by-one”) in 1998 : Rank the competitors by their number of wins (Condorcet’s) ; break any ties by using Borda’s rule.

Rida Laraki Majority Judgement This rule was proposed by Dasgupta and Maskin with elaborate theoretical arguments, calling it “the fairest vote of all”.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

The scandal was too big that the rules used for more than half of century were changed. The ISU adopted the OBO rule (“one-by-one”) in 1998 : Rank the competitors by their number of wins (Condorcet’s) ; break any ties by using Borda’s rule.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

The scandal was too big that the rules used for more than half of century were changed. The ISU adopted the OBO rule (“one-by-one”) in 1998 : Rank the competitors by their number of wins (Condorcet’s) ; break any ties by using Borda’s rule. This rule was proposed by Dasgupta and Maskin with elaborate theoretical arguments, calling it “the fairest vote of all”.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

Accumulated evidence shows that judges in skating had strong national biases: “The data suggests that countries are divided into two blocs, with the United States, Canada, Germany and Italy on one side and Russia, the Ukraine, France and Poland on the other” (Zitzewitz 2006).

Rida Laraki Majority Judgement The Russian pair first, the Canadian pair second ; the public (and some experts) outraged ; a French judge confessed having favored the Russians (under pressure) . . . then denied it ; the decision amended : both pairs finished first ; deep divisions in the skating world leading to the formulation of a new system (replacing the newly adopted OBO rule). the new system is based only on evaluations was explicitly motivated and designed (without any theoretical support at that time) to avoid Arrow’s paradox and combat strategic manipulations. It does in some extend, but not optimally.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

The big “scandal” of the 2002 Olympic games in Salt Lake City : the first two finishers in the pairs figure skating competition.

Rida Laraki Majority Judgement a French judge confessed having favored the Russians (under pressure) . . . then denied it ; the decision amended : both pairs finished first ; deep divisions in the skating world leading to the formulation of a new system (replacing the newly adopted OBO rule). the new system is based only on evaluations was explicitly motivated and designed (without any theoretical support at that time) to avoid Arrow’s paradox and combat strategic manipulations. It does in some extend, but not optimally.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

The big “scandal” of the 2002 Olympic games in Salt Lake City : the first two finishers in the pairs figure skating competition. The Russian pair first, the Canadian pair second ; the public (and some experts) outraged ;

Rida Laraki Majority Judgement the decision amended : both pairs finished first ; deep divisions in the skating world leading to the formulation of a new system (replacing the newly adopted OBO rule). the new system is based only on evaluations was explicitly motivated and designed (without any theoretical support at that time) to avoid Arrow’s paradox and combat strategic manipulations. It does in some extend, but not optimally.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

The big “scandal” of the 2002 Olympic games in Salt Lake City : the first two finishers in the pairs figure skating competition. The Russian pair first, the Canadian pair second ; the public (and some experts) outraged ; a French judge confessed having favored the Russians (under pressure) . . . then denied it ;

Rida Laraki Majority Judgement deep divisions in the skating world leading to the formulation of a new system (replacing the newly adopted OBO rule). the new system is based only on evaluations was explicitly motivated and designed (without any theoretical support at that time) to avoid Arrow’s paradox and combat strategic manipulations. It does in some extend, but not optimally.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

The big “scandal” of the 2002 Olympic games in Salt Lake City : the first two finishers in the pairs figure skating competition. The Russian pair first, the Canadian pair second ; the public (and some experts) outraged ; a French judge confessed having favored the Russians (under pressure) . . . then denied it ; the decision amended : both pairs finished first ;

Rida Laraki Majority Judgement the new system is based only on evaluations was explicitly motivated and designed (without any theoretical support at that time) to avoid Arrow’s paradox and combat strategic manipulations. It does in some extend, but not optimally.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

The big “scandal” of the 2002 Olympic games in Salt Lake City : the first two finishers in the pairs figure skating competition. The Russian pair first, the Canadian pair second ; the public (and some experts) outraged ; a French judge confessed having favored the Russians (under pressure) . . . then denied it ; the decision amended : both pairs finished first ; deep divisions in the skating world leading to the formulation of a new system (replacing the newly adopted OBO rule).

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategic manipulations in skating

The big “scandal” of the 2002 Olympic games in Salt Lake City : the first two finishers in the pairs figure skating competition. The Russian pair first, the Canadian pair second ; the public (and some experts) outraged ; a French judge confessed having favored the Russians (under pressure) . . . then denied it ; the decision amended : both pairs finished first ; deep divisions in the skating world leading to the formulation of a new system (replacing the newly adopted OBO rule). the new system is based only on evaluations was explicitly motivated and designed (without any theoretical support at that time) to avoid Arrow’s paradox and combat strategic manipulations. It does in some extend, but not optimally.

Rida Laraki Majority Judgement A1) Anonymity : Voters are treated equally. A2) Unanimity : A candidate judged to be the best by all voters is elected. A3) Rationality : If the decision decrees A leads B and B leads C, then it should decrees that A leads C. A4) Independence : Adjoining or withdrawing a candidate does not change the order-of-finish. A5) Strategy Proof : It is a dominant strategy to vote honestly.

A reasonable method of voting should satisfy :

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Natural Axioms

Rida Laraki Majority Judgement A1) Anonymity : Voters are treated equally. A2) Unanimity : A candidate judged to be the best by all voters is elected. A3) Rationality : If the decision decrees A leads B and B leads C, then it should decrees that A leads C. A4) Independence : Adjoining or withdrawing a candidate does not change the order-of-finish. A5) Strategy Proof : It is a dominant strategy to vote honestly.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Natural Axioms

A reasonable method of voting should satisfy :

Rida Laraki Majority Judgement A2) Unanimity : A candidate judged to be the best by all voters is elected. A3) Rationality : If the decision decrees A leads B and B leads C, then it should decrees that A leads C. A4) Independence : Adjoining or withdrawing a candidate does not change the order-of-finish. A5) Strategy Proof : It is a dominant strategy to vote honestly.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Natural Axioms

A reasonable method of voting should satisfy : A1) Anonymity : Voters are treated equally.

Rida Laraki Majority Judgement A3) Rationality : If the decision decrees A leads B and B leads C, then it should decrees that A leads C. A4) Independence : Adjoining or withdrawing a candidate does not change the order-of-finish. A5) Strategy Proof : It is a dominant strategy to vote honestly.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Natural Axioms

A reasonable method of voting should satisfy : A1) Anonymity : Voters are treated equally. A2) Unanimity : A candidate judged to be the best by all voters is elected.

Rida Laraki Majority Judgement A4) Independence : Adjoining or withdrawing a candidate does not change the order-of-finish. A5) Strategy Proof : It is a dominant strategy to vote honestly.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Natural Axioms

A reasonable method of voting should satisfy : A1) Anonymity : Voters are treated equally. A2) Unanimity : A candidate judged to be the best by all voters is elected. A3) Rationality : If the decision decrees A leads B and B leads C, then it should decrees that A leads C.

Rida Laraki Majority Judgement A5) Strategy Proof : It is a dominant strategy to vote honestly.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Natural Axioms

A reasonable method of voting should satisfy : A1) Anonymity : Voters are treated equally. A2) Unanimity : A candidate judged to be the best by all voters is elected. A3) Rationality : If the decision decrees A leads B and B leads C, then it should decrees that A leads C. A4) Independence : Adjoining or withdrawing a candidate does not change the order-of-finish.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Natural Axioms

A reasonable method of voting should satisfy : A1) Anonymity : Voters are treated equally. A2) Unanimity : A candidate judged to be the best by all voters is elected. A3) Rationality : If the decision decrees A leads B and B leads C, then it should decrees that A leads C. A4) Independence : Adjoining or withdrawing a candidate does not change the order-of-finish. A5) Strategy Proof : It is a dominant strategy to vote honestly.

Rida Laraki Majority Judgement Dasgupta and Maskin proved that if voters are restricted in their input rankings (because of some ideological opinions, such as a left right spectra), then their method best avoids Arrow’s paradox and combats strategic manipulations, among all traditional methods. It was disagreed by the ISU federation because of the manipulability scandal in 2002, only 4 years after its adoption ! We prove that this method is subject to Arrow’s paradox in a real recent skating competition (where there is no ideological left-right as in political elections) (see our OR paper). By enlarging the input of voters in the way they express their opinions, majority judgment emerges as the unique method that avoids Arrow paradox and best resist strategic manipulations.

When voters are asked to rank all the candidates, and when all possible rankings are a priori possible as inputs : Theorem (Arrow’s impossibility) No voting method meets A1, A2, A3 and A4.

Theorem (Gibbard/Satterthwaite’s impossibility) No voting method meets A1, A2, A3 and A5.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Unavoidable conundrum of the traditional model

Rida Laraki Majority Judgement Dasgupta and Maskin proved that if voters are restricted in their input rankings (because of some ideological opinions, such as a left right spectra), then their method best avoids Arrow’s paradox and combats strategic manipulations, among all traditional methods. It was disagreed by the ISU federation because of the manipulability scandal in 2002, only 4 years after its adoption ! We prove that this method is subject to Arrow’s paradox in a real recent skating competition (where there is no ideological left-right as in political elections) (see our OR paper). By enlarging the input of voters in the way they express their opinions, majority judgment emerges as the unique method that avoids Arrow paradox and best resist strategic manipulations.

Theorem (Arrow’s impossibility) No voting method meets A1, A2, A3 and A4.

Theorem (Gibbard/Satterthwaite’s impossibility) No voting method meets A1, A2, A3 and A5.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Unavoidable conundrum of the traditional model

When voters are asked to rank all the candidates, and when all possible rankings are a priori possible as inputs :

Rida Laraki Majority Judgement Dasgupta and Maskin proved that if voters are restricted in their input rankings (because of some ideological opinions, such as a left right spectra), then their method best avoids Arrow’s paradox and combats strategic manipulations, among all traditional methods. It was disagreed by the ISU federation because of the manipulability scandal in 2002, only 4 years after its adoption ! We prove that this method is subject to Arrow’s paradox in a real recent skating competition (where there is no ideological left-right as in political elections) (see our OR paper). By enlarging the input of voters in the way they express their opinions, majority judgment emerges as the unique method that avoids Arrow paradox and best resist strategic manipulations.

Theorem (Gibbard/Satterthwaite’s impossibility) No voting method meets A1, A2, A3 and A5.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Unavoidable conundrum of the traditional model

When voters are asked to rank all the candidates, and when all possible rankings are a priori possible as inputs : Theorem (Arrow’s impossibility) No voting method meets A1, A2, A3 and A4.

Rida Laraki Majority Judgement Dasgupta and Maskin proved that if voters are restricted in their input rankings (because of some ideological opinions, such as a left right spectra), then their method best avoids Arrow’s paradox and combats strategic manipulations, among all traditional methods. It was disagreed by the ISU federation because of the manipulability scandal in 2002, only 4 years after its adoption ! We prove that this method is subject to Arrow’s paradox in a real recent skating competition (where there is no ideological left-right as in political elections) (see our OR paper). By enlarging the input of voters in the way they express their opinions, majority judgment emerges as the unique method that avoids Arrow paradox and best resist strategic manipulations.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Unavoidable conundrum of the traditional model

When voters are asked to rank all the candidates, and when all possible rankings are a priori possible as inputs : Theorem (Arrow’s impossibility) No voting method meets A1, A2, A3 and A4.

Theorem (Gibbard/Satterthwaite’s impossibility) No voting method meets A1, A2, A3 and A5.

Rida Laraki Majority Judgement It was disagreed by the ISU federation because of the manipulability scandal in 2002, only 4 years after its adoption ! We prove that this method is subject to Arrow’s paradox in a real recent skating competition (where there is no ideological left-right as in political elections) (see our OR paper). By enlarging the input of voters in the way they express their opinions, majority judgment emerges as the unique method that avoids Arrow paradox and best resist strategic manipulations.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Unavoidable conundrum of the traditional model

When voters are asked to rank all the candidates, and when all possible rankings are a priori possible as inputs : Theorem (Arrow’s impossibility) No voting method meets A1, A2, A3 and A4.

Theorem (Gibbard/Satterthwaite’s impossibility) No voting method meets A1, A2, A3 and A5.

Dasgupta and Maskin proved that if voters are restricted in their input rankings (because of some ideological opinions, such as a left right spectra), then their method best avoids Arrow’s paradox and combats strategic manipulations, among all traditional methods.

Rida Laraki Majority Judgement By enlarging the input of voters in the way they express their opinions, majority judgment emerges as the unique method that avoids Arrow paradox and best resist strategic manipulations.

The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Unavoidable conundrum of the traditional model

When voters are asked to rank all the candidates, and when all possible rankings are a priori possible as inputs : Theorem (Arrow’s impossibility) No voting method meets A1, A2, A3 and A4.

Theorem (Gibbard/Satterthwaite’s impossibility) No voting method meets A1, A2, A3 and A5.

Dasgupta and Maskin proved that if voters are restricted in their input rankings (because of some ideological opinions, such as a left right spectra), then their method best avoids Arrow’s paradox and combats strategic manipulations, among all traditional methods. It was disagreed by the ISU federation because of the manipulability scandal in 2002, only 4 years after its adoption ! We prove that this method is subject to Arrow’s paradox in a real recent skating competition (where there is no ideological left-right as in political elections) (see our OR paper).

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenTraditional Electing Methods and Ranking and paradoxs The Method paradoxs of Majority in practice Judgment Impossibility The Theorems Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Unavoidable conundrum of the traditional model

When voters are asked to rank all the candidates, and when all possible rankings are a priori possible as inputs : Theorem (Arrow’s impossibility) No voting method meets A1, A2, A3 and A4.

Theorem (Gibbard/Satterthwaite’s impossibility) No voting method meets A1, A2, A3 and A5.

Dasgupta and Maskin proved that if voters are restricted in their input rankings (because of some ideological opinions, such as a left right spectra), then their method best avoids Arrow’s paradox and combats strategic manipulations, among all traditional methods. It was disagreed by the ISU federation because of the manipulability scandal in 2002, only 4 years after its adoption ! We prove that this method is subject to Arrow’s paradox in a real recent skating competition (where there is no ideological left-right as in political elections) (see our OR paper). By enlarging the input of voters in the way they express their opinions, majority judgment emerges as the unique method that avoids Arrow paradox and best resist strategic manipulations. Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Contents

1 The thesis 2 Traditional Theory of Social Choice Traditional Methods and paradoxs paradoxs in practice Impossibility Theorems 3 Incompatibility Between Electing and Ranking 4 The Method of Majority Judgment Wines Elections Strategy proof in raking 5 The Theory of Majority Judgement Majority Grading Model Strategic Analysis Middlemost SGF Majority Ranking Model Meaningfulness 6 Approval Voting versus Approval Judgment 7 Experimental Evidences 8 Conclusions

Rida Laraki Majority Judgement The Condorcet-ranking is the ranking that maximizes the Condorcet-score.

Property 1 : the method is Condorcet consistent : the Condorcet-winner —(when he exists)—is always the first-ranked by the Condorcet-ranking.

A voter contributes k Condorcet-points to a rank-ordering if his input agrees in k pair-by-pair comparisons. The Condorcet-score of a rank-ordering is the sum of its Condorcet-points over all voters.

Equivalently—letting v(Ai Ak ) be the number of voters that rank candidate Ai ahead of Ak —the Condorcet-score of a rank-ordering A1 A2 · · · An is

n−1 n X X v(Ai Ak ). i=1 k>i

Property 2 : computing a Condorcet-Kemeny ranking is NP-hard (Bartholdi, Tovey, and Trick, 1989).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet’s method

In 1789, the Marquis the Condorcet proposed the Condorcet-ranking. It is known as Kemeny’s rule. It associates a score to each possible rank ordering.

Rida Laraki Majority Judgement The Condorcet-ranking is the ranking that maximizes the Condorcet-score.

Property 1 : the method is Condorcet consistent : the Condorcet-winner —(when he exists)—is always the first-ranked by the Condorcet-ranking.

The Condorcet-score of a rank-ordering is the sum of its Condorcet-points over all voters.

Equivalently—letting v(Ai Ak ) be the number of voters that rank candidate Ai ahead of Ak —the Condorcet-score of a rank-ordering A1 A2 · · · An is

n−1 n X X v(Ai Ak ). i=1 k>i

Property 2 : computing a Condorcet-Kemeny ranking is NP-hard (Bartholdi, Tovey, and Trick, 1989).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet’s method

In 1789, the Marquis the Condorcet proposed the Condorcet-ranking. It is known as Kemeny’s rule. It associates a score to each possible rank ordering. A voter contributes k Condorcet-points to a rank-ordering if his input agrees in k pair-by-pair comparisons.

Rida Laraki Majority Judgement Property 1 : the method is Condorcet consistent : the Condorcet-winner —(when he exists)—is always the first-ranked by the Condorcet-ranking.

The Condorcet-ranking is the ranking that maximizes the Condorcet-score.

Equivalently—letting v(Ai Ak ) be the number of voters that rank candidate Ai ahead of Ak —the Condorcet-score of a rank-ordering A1 A2 · · · An is

n−1 n X X v(Ai Ak ). i=1 k>i

Property 2 : computing a Condorcet-Kemeny ranking is NP-hard (Bartholdi, Tovey, and Trick, 1989).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet’s method

In 1789, the Marquis the Condorcet proposed the Condorcet-ranking. It is known as Kemeny’s rule. It associates a score to each possible rank ordering. A voter contributes k Condorcet-points to a rank-ordering if his input agrees in k pair-by-pair comparisons. The Condorcet-score of a rank-ordering is the sum of its Condorcet-points over all voters.

Rida Laraki Majority Judgement Property 1 : the method is Condorcet consistent : the Condorcet-winner —(when he exists)—is always the first-ranked by the Condorcet-ranking.

Equivalently—letting v(Ai Ak ) be the number of voters that rank candidate Ai ahead of Ak —the Condorcet-score of a rank-ordering A1 A2 · · · An is

n−1 n X X v(Ai Ak ). i=1 k>i

Property 2 : computing a Condorcet-Kemeny ranking is NP-hard (Bartholdi, Tovey, and Trick, 1989).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet’s method

In 1789, the Marquis the Condorcet proposed the Condorcet-ranking. It is known as Kemeny’s rule. It associates a score to each possible rank ordering. A voter contributes k Condorcet-points to a rank-ordering if his input agrees in k pair-by-pair comparisons. The Condorcet-score of a rank-ordering is the sum of its Condorcet-points over all voters. The Condorcet-ranking is the ranking that maximizes the Condorcet-score.

Rida Laraki Majority Judgement Property 2 : computing a Condorcet-Kemeny ranking is NP-hard (Bartholdi, Tovey, and Trick, 1989).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet’s method

In 1789, the Marquis the Condorcet proposed the Condorcet-ranking. It is known as Kemeny’s rule. It associates a score to each possible rank ordering. A voter contributes k Condorcet-points to a rank-ordering if his input agrees in k pair-by-pair comparisons. The Condorcet-score of a rank-ordering is the sum of its Condorcet-points over all voters. The Condorcet-ranking is the ranking that maximizes the Condorcet-score.

Equivalently—letting v(Ai Ak ) be the number of voters that rank candidate Ai ahead of Ak —the Condorcet-score of a rank-ordering A1 A2 · · · An is

n−1 n X X v(Ai Ak ). i=1 k>i Property 1 : the method is Condorcet consistent : the Condorcet-winner —(when he exists)—is always the first-ranked by the Condorcet-ranking.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet’s method

In 1789, the Marquis the Condorcet proposed the Condorcet-ranking. It is known as Kemeny’s rule. It associates a score to each possible rank ordering. A voter contributes k Condorcet-points to a rank-ordering if his input agrees in k pair-by-pair comparisons. The Condorcet-score of a rank-ordering is the sum of its Condorcet-points over all voters. The Condorcet-ranking is the ranking that maximizes the Condorcet-score.

Equivalently—letting v(Ai Ak ) be the number of voters that rank candidate Ai ahead of Ak —the Condorcet-score of a rank-ordering A1 A2 · · · An is

n−1 n X X v(Ai Ak ). i=1 k>i Property 1 : the method is Condorcet consistent : the Condorcet-winner —(when he exists)—is always the first-ranked by the Condorcet-ranking. Property 2 : computing a Condorcet-Kemeny ranking is NP-hard (Bartholdi, Tovey, and Trick, 1989).

Rida Laraki Majority Judgement The Condorcet-score of the ranking A S C S B S D is 54 + 49 +  + 57 + 51 + 82 + 65 = 358 + 

That of B S A S C S D is 358 − . 1 When  = 2 the Condorcet-ranking is A S C S B S D when  = 0 there is a tie, B S A S C S D is also a Condorcet-ranking.

Both are very different from the Borda-ranking C S B S A S D.

versus ABCD Borda-score A — 49 + % 54% 57% 160 +  B 51 − % — 49% 65% 165 −  C 46% 51% — 82% 179 D 43% 35% 18% — 96

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Example of the Condorcet’s method

Rida Laraki Majority Judgement The Condorcet-score of the ranking A S C S B S D is 54 + 49 +  + 57 + 51 + 82 + 65 = 358 + 

That of B S A S C S D is 358 − . 1 When  = 2 the Condorcet-ranking is A S C S B S D when  = 0 there is a tie, B S A S C S D is also a Condorcet-ranking.

Both are very different from the Borda-ranking C S B S A S D.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Example of the Condorcet’s method

versus ABCD Borda-score A — 49 + % 54% 57% 160 +  B 51 − % — 49% 65% 165 −  C 46% 51% — 82% 179 D 43% 35% 18% — 96

Rida Laraki Majority Judgement That of B S A S C S D is 358 − . 1 When  = 2 the Condorcet-ranking is A S C S B S D when  = 0 there is a tie, B S A S C S D is also a Condorcet-ranking.

Both are very different from the Borda-ranking C S B S A S D.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Example of the Condorcet’s method

versus ABCD Borda-score A — 49 + % 54% 57% 160 +  B 51 − % — 49% 65% 165 −  C 46% 51% — 82% 179 D 43% 35% 18% — 96

The Condorcet-score of the ranking A S C S B S D is 54 + 49 +  + 57 + 51 + 82 + 65 = 358 + 

Rida Laraki Majority Judgement 1 When  = 2 the Condorcet-ranking is A S C S B S D when  = 0 there is a tie, B S A S C S D is also a Condorcet-ranking.

Both are very different from the Borda-ranking C S B S A S D.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Example of the Condorcet’s method

versus ABCD Borda-score A — 49 + % 54% 57% 160 +  B 51 − % — 49% 65% 165 −  C 46% 51% — 82% 179 D 43% 35% 18% — 96

The Condorcet-score of the ranking A S C S B S D is 54 + 49 +  + 57 + 51 + 82 + 65 = 358 + 

That of B S A S C S D is 358 − .

Rida Laraki Majority Judgement when  = 0 there is a tie, B S A S C S D is also a Condorcet-ranking.

Both are very different from the Borda-ranking C S B S A S D.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Example of the Condorcet’s method

versus ABCD Borda-score A — 49 + % 54% 57% 160 +  B 51 − % — 49% 65% 165 −  C 46% 51% — 82% 179 D 43% 35% 18% — 96

The Condorcet-score of the ranking A S C S B S D is 54 + 49 +  + 57 + 51 + 82 + 65 = 358 + 

That of B S A S C S D is 358 − . 1 When  = 2 the Condorcet-ranking is A S C S B S D

Rida Laraki Majority Judgement Both are very different from the Borda-ranking C S B S A S D.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Example of the Condorcet’s method

versus ABCD Borda-score A — 49 + % 54% 57% 160 +  B 51 − % — 49% 65% 165 −  C 46% 51% — 82% 179 D 43% 35% 18% — 96

The Condorcet-score of the ranking A S C S B S D is 54 + 49 +  + 57 + 51 + 82 + 65 = 358 + 

That of B S A S C S D is 358 − . 1 When  = 2 the Condorcet-ranking is A S C S B S D when  = 0 there is a tie, B S A S C S D is also a Condorcet-ranking.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Example of the Condorcet’s method

versus ABCD Borda-score A — 49 + % 54% 57% 160 +  B 51 − % — 49% 65% 165 −  C 46% 51% — 82% 179 D 43% 35% 18% — 96

The Condorcet-score of the ranking A S C S B S D is 54 + 49 +  + 57 + 51 + 82 + 65 = 358 + 

That of B S A S C S D is 358 − . 1 When  = 2 the Condorcet-ranking is A S C S B S D when  = 0 there is a tie, B S A S C S D is also a Condorcet-ranking.

Both are very different from the Borda-ranking C S B S A S D.

Rida Laraki Majority Judgement Is Condorcet’s method good for designating a winner, or a ranking, or both ? Intuitively, both: Given a method of ranking, the first-placed candidate is the winner. Given a method of designating a winner (or loser), he is the first-ranked (or last-ranked) ; the second-ranked is the winner among the remaining candidates ; . . .

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners and rankings ?

Is Borda’s method good for designating a winner, or a ranking, or both ?

Rida Laraki Majority Judgement Intuitively, both: Given a method of ranking, the first-placed candidate is the winner. Given a method of designating a winner (or loser), he is the first-ranked (or last-ranked) ; the second-ranked is the winner among the remaining candidates ; . . .

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners and rankings ?

Is Borda’s method good for designating a winner, or a ranking, or both ? Is Condorcet’s method good for designating a winner, or a ranking, or both ?

Rida Laraki Majority Judgement Given a method of ranking, the first-placed candidate is the winner. Given a method of designating a winner (or loser), he is the first-ranked (or last-ranked) ; the second-ranked is the winner among the remaining candidates ; . . .

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners and rankings ?

Is Borda’s method good for designating a winner, or a ranking, or both ? Is Condorcet’s method good for designating a winner, or a ranking, or both ? Intuitively, both:

Rida Laraki Majority Judgement Given a method of designating a winner (or loser), he is the first-ranked (or last-ranked) ; the second-ranked is the winner among the remaining candidates ; . . .

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners and rankings ?

Is Borda’s method good for designating a winner, or a ranking, or both ? Is Condorcet’s method good for designating a winner, or a ranking, or both ? Intuitively, both: Given a method of ranking, the first-placed candidate is the winner.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners and rankings ?

Is Borda’s method good for designating a winner, or a ranking, or both ? Is Condorcet’s method good for designating a winner, or a ranking, or both ? Intuitively, both: Given a method of ranking, the first-placed candidate is the winner. Given a method of designating a winner (or loser), he is the first-ranked (or last-ranked) ; the second-ranked is the winner among the remaining candidates ; . . .

Rida Laraki Majority Judgement It should : (1) assign a 0 to the worst possible candidate : give a 0 to a candidate last on every voter’s list ; (2) correctly reward a minimal improvement : when a voter inverts two successive candidates of his list, the score of the candidate who moves up increases by 1.

Theorem Borda-score characterization. The Borda-score is the unique candidate-scoring method that assigns a 0 to the worst possible candidate and correctly rewards minimal improvements.

Moral : The Borda-score concerns winners.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda for winners

Given a profile of preferences, a candidate-scoring method assigns a nonnegative score to every candidate.

Rida Laraki Majority Judgement (1) assign a 0 to the worst possible candidate : give a 0 to a candidate last on every voter’s list ; (2) correctly reward a minimal improvement : when a voter inverts two successive candidates of his list, the score of the candidate who moves up increases by 1.

Theorem Borda-score characterization. The Borda-score is the unique candidate-scoring method that assigns a 0 to the worst possible candidate and correctly rewards minimal improvements.

Moral : The Borda-score concerns winners.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda for winners

Given a profile of preferences, a candidate-scoring method assigns a nonnegative score to every candidate. It should :

Rida Laraki Majority Judgement (2) correctly reward a minimal improvement : when a voter inverts two successive candidates of his list, the score of the candidate who moves up increases by 1.

Theorem Borda-score characterization. The Borda-score is the unique candidate-scoring method that assigns a 0 to the worst possible candidate and correctly rewards minimal improvements.

Moral : The Borda-score concerns winners.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda for winners

Given a profile of preferences, a candidate-scoring method assigns a nonnegative score to every candidate. It should : (1) assign a 0 to the worst possible candidate : give a 0 to a candidate last on every voter’s list ;

Rida Laraki Majority Judgement Theorem Borda-score characterization. The Borda-score is the unique candidate-scoring method that assigns a 0 to the worst possible candidate and correctly rewards minimal improvements.

Moral : The Borda-score concerns winners.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda for winners

Given a profile of preferences, a candidate-scoring method assigns a nonnegative score to every candidate. It should : (1) assign a 0 to the worst possible candidate : give a 0 to a candidate last on every voter’s list ; (2) correctly reward a minimal improvement : when a voter inverts two successive candidates of his list, the score of the candidate who moves up increases by 1.

Rida Laraki Majority Judgement Moral : The Borda-score concerns winners.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda for winners

Given a profile of preferences, a candidate-scoring method assigns a nonnegative score to every candidate. It should : (1) assign a 0 to the worst possible candidate : give a 0 to a candidate last on every voter’s list ; (2) correctly reward a minimal improvement : when a voter inverts two successive candidates of his list, the score of the candidate who moves up increases by 1.

Theorem Borda-score characterization. The Borda-score is the unique candidate-scoring method that assigns a 0 to the worst possible candidate and correctly rewards minimal improvements.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Borda for winners

Given a profile of preferences, a candidate-scoring method assigns a nonnegative score to every candidate. It should : (1) assign a 0 to the worst possible candidate : give a 0 to a candidate last on every voter’s list ; (2) correctly reward a minimal improvement : when a voter inverts two successive candidates of his list, the score of the candidate who moves up increases by 1.

Theorem Borda-score characterization. The Borda-score is the unique candidate-scoring method that assigns a 0 to the worst possible candidate and correctly rewards minimal improvements.

Moral : The Borda-score concerns winners.

Rida Laraki Majority Judgement The opposite of a ranking A B C D ... is A ≺ B ≺ C ≺ D ≺ .... A rank-scoring method should : (1) assign a 0 to the worst possible ranking : give a 0 to a ranking if every voter’s preference is the opposite ranking ; (2) correctly reward a minimal improvement : when one voter inverts two successive candidates of his list, the score of every order that agrees with the change increases by 1.

Theorem Condorcet-score characterization. The Condorcet-score is the unique rank-scoring method that assigns a 0 to the worst possible order and correctly rewards minimal improvements.

Moral : The Condorcet-score concerns rankings.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet for rankings

Given a profile of preferences, a rank-scoring method assigns a nonnegative score to every ranking.

Rida Laraki Majority Judgement A rank-scoring method should : (1) assign a 0 to the worst possible ranking : give a 0 to a ranking if every voter’s preference is the opposite ranking ; (2) correctly reward a minimal improvement : when one voter inverts two successive candidates of his list, the score of every order that agrees with the change increases by 1.

Theorem Condorcet-score characterization. The Condorcet-score is the unique rank-scoring method that assigns a 0 to the worst possible order and correctly rewards minimal improvements.

Moral : The Condorcet-score concerns rankings.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet for rankings

Given a profile of preferences, a rank-scoring method assigns a nonnegative score to every ranking. The opposite of a ranking A B C D ... is A ≺ B ≺ C ≺ D ≺ ....

Rida Laraki Majority Judgement (1) assign a 0 to the worst possible ranking : give a 0 to a ranking if every voter’s preference is the opposite ranking ; (2) correctly reward a minimal improvement : when one voter inverts two successive candidates of his list, the score of every order that agrees with the change increases by 1.

Theorem Condorcet-score characterization. The Condorcet-score is the unique rank-scoring method that assigns a 0 to the worst possible order and correctly rewards minimal improvements.

Moral : The Condorcet-score concerns rankings.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet for rankings

Given a profile of preferences, a rank-scoring method assigns a nonnegative score to every ranking. The opposite of a ranking A B C D ... is A ≺ B ≺ C ≺ D ≺ .... A rank-scoring method should :

Rida Laraki Majority Judgement (2) correctly reward a minimal improvement : when one voter inverts two successive candidates of his list, the score of every order that agrees with the change increases by 1.

Theorem Condorcet-score characterization. The Condorcet-score is the unique rank-scoring method that assigns a 0 to the worst possible order and correctly rewards minimal improvements.

Moral : The Condorcet-score concerns rankings.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet for rankings

Given a profile of preferences, a rank-scoring method assigns a nonnegative score to every ranking. The opposite of a ranking A B C D ... is A ≺ B ≺ C ≺ D ≺ .... A rank-scoring method should : (1) assign a 0 to the worst possible ranking : give a 0 to a ranking if every voter’s preference is the opposite ranking ;

Rida Laraki Majority Judgement Theorem Condorcet-score characterization. The Condorcet-score is the unique rank-scoring method that assigns a 0 to the worst possible order and correctly rewards minimal improvements.

Moral : The Condorcet-score concerns rankings.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet for rankings

Given a profile of preferences, a rank-scoring method assigns a nonnegative score to every ranking. The opposite of a ranking A B C D ... is A ≺ B ≺ C ≺ D ≺ .... A rank-scoring method should : (1) assign a 0 to the worst possible ranking : give a 0 to a ranking if every voter’s preference is the opposite ranking ; (2) correctly reward a minimal improvement : when one voter inverts two successive candidates of his list, the score of every order that agrees with the change increases by 1.

Rida Laraki Majority Judgement Moral : The Condorcet-score concerns rankings.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet for rankings

Given a profile of preferences, a rank-scoring method assigns a nonnegative score to every ranking. The opposite of a ranking A B C D ... is A ≺ B ≺ C ≺ D ≺ .... A rank-scoring method should : (1) assign a 0 to the worst possible ranking : give a 0 to a ranking if every voter’s preference is the opposite ranking ; (2) correctly reward a minimal improvement : when one voter inverts two successive candidates of his list, the score of every order that agrees with the change increases by 1.

Theorem Condorcet-score characterization. The Condorcet-score is the unique rank-scoring method that assigns a 0 to the worst possible order and correctly rewards minimal improvements.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Condorcet for rankings

Given a profile of preferences, a rank-scoring method assigns a nonnegative score to every ranking. The opposite of a ranking A B C D ... is A ≺ B ≺ C ≺ D ≺ .... A rank-scoring method should : (1) assign a 0 to the worst possible ranking : give a 0 to a ranking if every voter’s preference is the opposite ranking ; (2) correctly reward a minimal improvement : when one voter inverts two successive candidates of his list, the score of every order that agrees with the change increases by 1.

Theorem Condorcet-score characterization. The Condorcet-score is the unique rank-scoring method that assigns a 0 to the worst possible order and correctly rewards minimal improvements.

Moral : The Condorcet-score concerns rankings.

Rida Laraki Majority Judgement A is the winner, B the loser : reasonable Thus, society’s order is A S C S B : unreasonable

A S B S C and C S A S B tied for first : reasonable

333 : A B C 333 : B C A 333 : C A B

1 : A C B.

By Borda :

By Condorcet :

No reasonable ranking function must choose A C B. Any reasonable choice function must choose A C B.. A fundamental incompatibility between electing and ranking.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners or rankings ?

Are ranking and designating winners two sides of one coin ?

Rida Laraki Majority Judgement A is the winner, B the loser : reasonable Thus, society’s order is A S C S B : unreasonable

A S B S C and C S A S B tied for first : reasonable

1 : A C B.

By Borda :

By Condorcet :

No reasonable ranking function must choose A C B. Any reasonable choice function must choose A C B.. A fundamental incompatibility between electing and ranking.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners or rankings ?

Are ranking and designating winners two sides of one coin ?

333 : A B C 333 : B C A 333 : C A B

Rida Laraki Majority Judgement A is the winner, B the loser : reasonable Thus, society’s order is A S C S B : unreasonable

A S B S C and C S A S B tied for first : reasonable

By Borda :

By Condorcet :

No reasonable ranking function must choose A C B. Any reasonable choice function must choose A C B.. A fundamental incompatibility between electing and ranking.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners or rankings ?

Are ranking and designating winners two sides of one coin ?

333 : A B C 333 : B C A 333 : C A B

1 : A C B.

Rida Laraki Majority Judgement A S B S C and C S A S B tied for first : reasonable

A is the winner, B the loser : reasonable Thus, society’s order is A S C S B : unreasonable By Condorcet :

No reasonable ranking function must choose A C B. Any reasonable choice function must choose A C B.. A fundamental incompatibility between electing and ranking.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners or rankings ?

Are ranking and designating winners two sides of one coin ?

333 : A B C 333 : B C A 333 : C A B

1 : A C B.

By Borda :

Rida Laraki Majority Judgement A S B S C and C S A S B tied for first : reasonable

Thus, society’s order is A S C S B : unreasonable By Condorcet :

No reasonable ranking function must choose A C B. Any reasonable choice function must choose A C B.. A fundamental incompatibility between electing and ranking.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners or rankings ?

Are ranking and designating winners two sides of one coin ?

333 : A B C 333 : B C A 333 : C A B

1 : A C B.

By Borda : A is the winner, B the loser : reasonable

Rida Laraki Majority Judgement A S B S C and C S A S B tied for first : reasonable

By Condorcet :

No reasonable ranking function must choose A C B. Any reasonable choice function must choose A C B.. A fundamental incompatibility between electing and ranking.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners or rankings ?

Are ranking and designating winners two sides of one coin ?

333 : A B C 333 : B C A 333 : C A B

1 : A C B.

By Borda : A is the winner, B the loser : reasonable Thus, society’s order is A S C S B : unreasonable

Rida Laraki Majority Judgement No reasonable ranking function must choose A C B. Any reasonable choice function must choose A C B.. A fundamental incompatibility between electing and ranking.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners or rankings ?

Are ranking and designating winners two sides of one coin ?

333 : A B C 333 : B C A 333 : C A B

1 : A C B.

By Borda : A is the winner, B the loser : reasonable Thus, society’s order is A S C S B : unreasonable By Condorcet : A S B S C and C S A S B tied for first : reasonable

Rida Laraki Majority Judgement Any reasonable choice function must choose A C B.. A fundamental incompatibility between electing and ranking.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners or rankings ?

Are ranking and designating winners two sides of one coin ?

333 : A B C 333 : B C A 333 : C A B

1 : A C B.

By Borda : A is the winner, B the loser : reasonable Thus, society’s order is A S C S B : unreasonable By Condorcet : A S B S C and C S A S B tied for first : reasonable No reasonable ranking function must choose A C B.

Rida Laraki Majority Judgement A fundamental incompatibility between electing and ranking.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners or rankings ?

Are ranking and designating winners two sides of one coin ?

333 : A B C 333 : B C A 333 : C A B

1 : A C B.

By Borda : A is the winner, B the loser : reasonable Thus, society’s order is A S C S B : unreasonable By Condorcet : A S B S C and C S A S B tied for first : reasonable No reasonable ranking function must choose A C B. Any reasonable choice function must choose A C B..

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Winners or rankings ?

Are ranking and designating winners two sides of one coin ?

333 : A B C 333 : B C A 333 : C A B

1 : A C B.

By Borda : A is the winner, B the loser : reasonable Thus, society’s order is A S C S B : unreasonable By Condorcet : A S B S C and C S A S B tied for first : reasonable No reasonable ranking function must choose A C B. Any reasonable choice function must choose A C B.. A fundamental incompatibility between electing and ranking.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Contents

1 The thesis 2 Traditional Theory of Social Choice Traditional Methods and paradoxs paradoxs in practice Impossibility Theorems 3 Incompatibility Between Electing and Ranking 4 The Method of Majority Judgment Wines Elections Strategy proof in raking 5 The Theory of Majority Judgement Majority Grading Model Strategic Analysis Middlemost SGF Majority Ranking Model Meaningfulness 6 Approval Voting versus Approval Judgment 7 Experimental Evidences 8 Conclusions

Rida Laraki Majority Judgement Anjou Bourgogne Chablis Very good Excellent Excellent Very good Very good Excellent Good Good Passable Passable Mediocre Mediocre

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority judgement : ranking three wines

Anjou Bourgogne Chablis Very good Excellent Excellent Very good Very good Excellent Good Good Good Good Good Passable Passable Mediocre Mediocre

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority judgement : ranking three wines

Anjou Bourgogne Chablis Very good Excellent Excellent Very good Very good Excellent Good Good Good Good Good Passable Passable Mediocre Mediocre

Anjou Bourgogne Chablis Very good Excellent Excellent Very good Very good Excellent Good Good Passable Passable Mediocre Mediocre

Rida Laraki Majority Judgement Anjou Bourgogne Very good Excellent Passable Mediocre

Therefore : Anjou Bourgogne Chablis

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority judgement : ranking three wines

Anjou Bourgogne Very good Excellent Very good Very good Passable Mediocre

Rida Laraki Majority Judgement Therefore : Anjou Bourgogne Chablis

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority judgement : ranking three wines

Anjou Bourgogne Very good Excellent Very good Very good Passable Mediocre

Anjou Bourgogne Very good Excellent Passable Mediocre

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority judgement : ranking three wines

Anjou Bourgogne Very good Excellent Very good Very good Passable Mediocre

Anjou Bourgogne Very good Excellent Passable Mediocre

Therefore : Anjou Bourgogne Chablis

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority judgement : voters judge each candidate

Ballot : Election of the President of France 2007 To be president of France, having taken into account all considerations, I judge, in conscience, that this candidate would be :

Excellent Very Good Good Acceptable Poor to Reject Olivier Besancenot Marie-George Buffet Gérard Schivardi François Bayrou José Bové Dominique Voynet Philippe de Villiers Ségolène Royal Frédéric Nihous Jean-Marie Le Pen Arlette Laguiller Nicolas Sarkozy

Check one single grade in the line of each candidate. No grade checked in the line of a candidate means to Reject the candidate.

Rida Laraki Majority Judgement Voters do not vote : they judge candidates in a common language of grades. With 12 candidates, first- or two-past-the-vote allows a voter 13 or 39 (= 13 × 3) possible messages ; the majority judgement with a common language of 6 grades allows a voter 612, i.e., over 2 billion possible messages : voters can really express their opinions. A candidate’s set of grades determines his/her majority-grade : it is the “final-grade” conferred upon the candidate by the electorate. The candidates are ranked according to their majority-grades : the first among them is the winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The new point of view

Rida Laraki Majority Judgement With 12 candidates, first- or two-past-the-vote allows a voter 13 or 39 (= 13 × 3) possible messages ; the majority judgement with a common language of 6 grades allows a voter 612, i.e., over 2 billion possible messages : voters can really express their opinions. A candidate’s set of grades determines his/her majority-grade : it is the “final-grade” conferred upon the candidate by the electorate. The candidates are ranked according to their majority-grades : the first among them is the winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The new point of view

Voters do not vote : they judge candidates in a common language of grades.

Rida Laraki Majority Judgement A candidate’s set of grades determines his/her majority-grade : it is the “final-grade” conferred upon the candidate by the electorate. The candidates are ranked according to their majority-grades : the first among them is the winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The new point of view

Voters do not vote : they judge candidates in a common language of grades. With 12 candidates, first- or two-past-the-vote allows a voter 13 or 39 (= 13 × 3) possible messages ; the majority judgement with a common language of 6 grades allows a voter 612, i.e., over 2 billion possible messages : voters can really express their opinions.

Rida Laraki Majority Judgement The candidates are ranked according to their majority-grades : the first among them is the winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The new point of view

Voters do not vote : they judge candidates in a common language of grades. With 12 candidates, first- or two-past-the-vote allows a voter 13 or 39 (= 13 × 3) possible messages ; the majority judgement with a common language of 6 grades allows a voter 612, i.e., over 2 billion possible messages : voters can really express their opinions. A candidate’s set of grades determines his/her majority-grade : it is the “final-grade” conferred upon the candidate by the electorate.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The new point of view

Voters do not vote : they judge candidates in a common language of grades. With 12 candidates, first- or two-past-the-vote allows a voter 13 or 39 (= 13 × 3) possible messages ; the majority judgement with a common language of 6 grades allows a voter 612, i.e., over 2 billion possible messages : voters can really express their opinions. A candidate’s set of grades determines his/her majority-grade : it is the “final-grade” conferred upon the candidate by the electorate. The candidates are ranked according to their majority-grades : the first among them is the winner.

Rida Laraki Majority Judgement By and large people—in particular, voters and judges—try to answer the question posed. A common language of grades is essential. In our new theory Arrow’s impossibility theorem says : without a common language there can be no consistent collective decision. Common languages definitely do exist in practice (e.g., diving, gymnastic and figure skating competitions, wine competitions, students’ grades, . . . ). The words used in the French experiment constitute—for France—a common language. This is proven by extensive statistical analyses of the majority judgement ballots cast in the “2007 Orsay experiment.”

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The charge to voters, and the common language

It is important to pose a clear and solemn question.

Rida Laraki Majority Judgement A common language of grades is essential. In our new theory Arrow’s impossibility theorem says : without a common language there can be no consistent collective decision. Common languages definitely do exist in practice (e.g., diving, gymnastic and figure skating competitions, wine competitions, students’ grades, . . . ). The words used in the French experiment constitute—for France—a common language. This is proven by extensive statistical analyses of the majority judgement ballots cast in the “2007 Orsay experiment.”

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The charge to voters, and the common language

It is important to pose a clear and solemn question. By and large people—in particular, voters and judges—try to answer the question posed.

Rida Laraki Majority Judgement In our new theory Arrow’s impossibility theorem says : without a common language there can be no consistent collective decision. Common languages definitely do exist in practice (e.g., diving, gymnastic and figure skating competitions, wine competitions, students’ grades, . . . ). The words used in the French experiment constitute—for France—a common language. This is proven by extensive statistical analyses of the majority judgement ballots cast in the “2007 Orsay experiment.”

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The charge to voters, and the common language

It is important to pose a clear and solemn question. By and large people—in particular, voters and judges—try to answer the question posed. A common language of grades is essential.

Rida Laraki Majority Judgement Common languages definitely do exist in practice (e.g., diving, gymnastic and figure skating competitions, wine competitions, students’ grades, . . . ). The words used in the French experiment constitute—for France—a common language. This is proven by extensive statistical analyses of the majority judgement ballots cast in the “2007 Orsay experiment.”

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The charge to voters, and the common language

It is important to pose a clear and solemn question. By and large people—in particular, voters and judges—try to answer the question posed. A common language of grades is essential. In our new theory Arrow’s impossibility theorem says : without a common language there can be no consistent collective decision.

Rida Laraki Majority Judgement The words used in the French experiment constitute—for France—a common language. This is proven by extensive statistical analyses of the majority judgement ballots cast in the “2007 Orsay experiment.”

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The charge to voters, and the common language

It is important to pose a clear and solemn question. By and large people—in particular, voters and judges—try to answer the question posed. A common language of grades is essential. In our new theory Arrow’s impossibility theorem says : without a common language there can be no consistent collective decision. Common languages definitely do exist in practice (e.g., diving, gymnastic and figure skating competitions, wine competitions, students’ grades, . . . ).

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The charge to voters, and the common language

It is important to pose a clear and solemn question. By and large people—in particular, voters and judges—try to answer the question posed. A common language of grades is essential. In our new theory Arrow’s impossibility theorem says : without a common language there can be no consistent collective decision. Common languages definitely do exist in practice (e.g., diving, gymnastic and figure skating competitions, wine competitions, students’ grades, . . . ). The words used in the French experiment constitute—for France—a common language. This is proven by extensive statistical analyses of the majority judgement ballots cast in the “2007 Orsay experiment.”

Rida Laraki Majority Judgement A majority of voters have assigned the candidate at least this grade, 8% + 23% + 27% = 58% of voters assign at least “Good” A majority of voters have assigned the candidate at most this grade, 27% + 12% + 19% + 11% = 69% of voters assign at most “Good”

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority-grade

A candidate’s majority-grade is the middlemost (or median) of his or her grades :

Excellent Very Good Good Acceptable Poor To Reject 8% 23% 27% 12% 19% 11%

Rida Laraki Majority Judgement A majority of voters have assigned the candidate at most this grade, 27% + 12% + 19% + 11% = 69% of voters assign at most “Good”

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority-grade

A candidate’s majority-grade is the middlemost (or median) of his or her grades :

Excellent Very Good Good Acceptable Poor To Reject 8% 23% 27% 12% 19% 11% A majority of voters have assigned the candidate at least this grade, 8% + 23% + 27% = 58% of voters assign at least “Good”

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority-grade

A candidate’s majority-grade is the middlemost (or median) of his or her grades :

Excellent Very Good Good Acceptable Poor To Reject 8% 23% 27% 12% 19% 11% A majority of voters have assigned the candidate at least this grade, 8% + 23% + 27% = 58% of voters assign at least “Good” A majority of voters have assigned the candidate at most this grade, 27% + 12% + 19% + 11% = 69% of voters assign at most “Good”

Rida Laraki Majority Judgement Suppose a voter or bloc of voters judged this candidate “Very Good” : he/she or they have no reason to exaggerate the grade by giving an “Excellent.” Suppose a voter or bloc of voters judged this candidate “Acceptable” : he/she or they have no reason to exaggerate the grade by giving a “Poor” or “to Reject.”

Theorem The majority-grade is strategy-proof-in-grading

The majority-grade respects a majority opinion : If a majority gives a grade of (say) “Acceptable” then that is the majority-grade. The majority-grade uniquely satisfies these and other properties.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy Proof in Grading

Excellent Very Good Good Acceptable Poor To Reject 8% 23% 27% 12% 19% 11%

Rida Laraki Majority Judgement Suppose a voter or bloc of voters judged this candidate “Acceptable” : he/she or they have no reason to exaggerate the grade by giving a “Poor” or “to Reject.”

Theorem The majority-grade is strategy-proof-in-grading

The majority-grade respects a majority opinion : If a majority gives a grade of (say) “Acceptable” then that is the majority-grade. The majority-grade uniquely satisfies these and other properties.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy Proof in Grading

Excellent Very Good Good Acceptable Poor To Reject 8% 23% 27% 12% 19% 11% Suppose a voter or bloc of voters judged this candidate “Very Good” : he/she or they have no reason to exaggerate the grade by giving an “Excellent.”

Rida Laraki Majority Judgement Theorem The majority-grade is strategy-proof-in-grading

The majority-grade respects a majority opinion : If a majority gives a grade of (say) “Acceptable” then that is the majority-grade. The majority-grade uniquely satisfies these and other properties.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy Proof in Grading

Excellent Very Good Good Acceptable Poor To Reject 8% 23% 27% 12% 19% 11% Suppose a voter or bloc of voters judged this candidate “Very Good” : he/she or they have no reason to exaggerate the grade by giving an “Excellent.” Suppose a voter or bloc of voters judged this candidate “Acceptable” : he/she or they have no reason to exaggerate the grade by giving a “Poor” or “to Reject.”

Rida Laraki Majority Judgement The majority-grade respects a majority opinion : If a majority gives a grade of (say) “Acceptable” then that is the majority-grade. The majority-grade uniquely satisfies these and other properties.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy Proof in Grading

Excellent Very Good Good Acceptable Poor To Reject 8% 23% 27% 12% 19% 11% Suppose a voter or bloc of voters judged this candidate “Very Good” : he/she or they have no reason to exaggerate the grade by giving an “Excellent.” Suppose a voter or bloc of voters judged this candidate “Acceptable” : he/she or they have no reason to exaggerate the grade by giving a “Poor” or “to Reject.”

Theorem The majority-grade is strategy-proof-in-grading

Rida Laraki Majority Judgement The majority-grade uniquely satisfies these and other properties.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy Proof in Grading

Excellent Very Good Good Acceptable Poor To Reject 8% 23% 27% 12% 19% 11% Suppose a voter or bloc of voters judged this candidate “Very Good” : he/she or they have no reason to exaggerate the grade by giving an “Excellent.” Suppose a voter or bloc of voters judged this candidate “Acceptable” : he/she or they have no reason to exaggerate the grade by giving a “Poor” or “to Reject.”

Theorem The majority-grade is strategy-proof-in-grading

The majority-grade respects a majority opinion : If a majority gives a grade of (say) “Acceptable” then that is the majority-grade.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy Proof in Grading

Excellent Very Good Good Acceptable Poor To Reject 8% 23% 27% 12% 19% 11% Suppose a voter or bloc of voters judged this candidate “Very Good” : he/she or they have no reason to exaggerate the grade by giving an “Excellent.” Suppose a voter or bloc of voters judged this candidate “Acceptable” : he/she or they have no reason to exaggerate the grade by giving a “Poor” or “to Reject.”

Theorem The majority-grade is strategy-proof-in-grading

The majority-grade respects a majority opinion : If a majority gives a grade of (say) “Acceptable” then that is the majority-grade. The majority-grade uniquely satisfies these and other properties.

Rida Laraki Majority Judgement Experiment conducted in 3 of Orsay’s 12 voting bureaux. These three are not representative of France. Potential participants informed by mailings, local publications and posters with active participation of the Mayor’s office. After casting their official ballots, voters invited to cast majority judgment ballots (at adjacent tables and booths). Carried out under identical conditions : ballots filled out in booths, inserted in envelopes and deposited in transparent urns. 2,360 voted officially, 1,752 (74%) participated in experiment, 1,733 ballots valid. 1,705 were different. Television interviews prove the satisfaction of voters.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions French President elections experiment at Orsay, April 23, 2007

Rida Laraki Majority Judgement These three are not representative of France. Potential participants informed by mailings, local publications and posters with active participation of the Mayor’s office. After casting their official ballots, voters invited to cast majority judgment ballots (at adjacent tables and booths). Carried out under identical conditions : ballots filled out in booths, inserted in envelopes and deposited in transparent urns. 2,360 voted officially, 1,752 (74%) participated in experiment, 1,733 ballots valid. 1,705 were different. Television interviews prove the satisfaction of voters.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions French President elections experiment at Orsay, April 23, 2007

Experiment conducted in 3 of Orsay’s 12 voting bureaux.

Rida Laraki Majority Judgement Potential participants informed by mailings, local publications and posters with active participation of the Mayor’s office. After casting their official ballots, voters invited to cast majority judgment ballots (at adjacent tables and booths). Carried out under identical conditions : ballots filled out in booths, inserted in envelopes and deposited in transparent urns. 2,360 voted officially, 1,752 (74%) participated in experiment, 1,733 ballots valid. 1,705 were different. Television interviews prove the satisfaction of voters.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions French President elections experiment at Orsay, April 23, 2007

Experiment conducted in 3 of Orsay’s 12 voting bureaux. These three are not representative of France.

Rida Laraki Majority Judgement After casting their official ballots, voters invited to cast majority judgment ballots (at adjacent tables and booths). Carried out under identical conditions : ballots filled out in booths, inserted in envelopes and deposited in transparent urns. 2,360 voted officially, 1,752 (74%) participated in experiment, 1,733 ballots valid. 1,705 were different. Television interviews prove the satisfaction of voters.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions French President elections experiment at Orsay, April 23, 2007

Experiment conducted in 3 of Orsay’s 12 voting bureaux. These three are not representative of France. Potential participants informed by mailings, local publications and posters with active participation of the Mayor’s office.

Rida Laraki Majority Judgement Carried out under identical conditions : ballots filled out in booths, inserted in envelopes and deposited in transparent urns. 2,360 voted officially, 1,752 (74%) participated in experiment, 1,733 ballots valid. 1,705 were different. Television interviews prove the satisfaction of voters.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions French President elections experiment at Orsay, April 23, 2007

Experiment conducted in 3 of Orsay’s 12 voting bureaux. These three are not representative of France. Potential participants informed by mailings, local publications and posters with active participation of the Mayor’s office. After casting their official ballots, voters invited to cast majority judgment ballots (at adjacent tables and booths).

Rida Laraki Majority Judgement 2,360 voted officially, 1,752 (74%) participated in experiment, 1,733 ballots valid. 1,705 were different. Television interviews prove the satisfaction of voters.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions French President elections experiment at Orsay, April 23, 2007

Experiment conducted in 3 of Orsay’s 12 voting bureaux. These three are not representative of France. Potential participants informed by mailings, local publications and posters with active participation of the Mayor’s office. After casting their official ballots, voters invited to cast majority judgment ballots (at adjacent tables and booths). Carried out under identical conditions : ballots filled out in booths, inserted in envelopes and deposited in transparent urns.

Rida Laraki Majority Judgement Television interviews prove the satisfaction of voters.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions French President elections experiment at Orsay, April 23, 2007

Experiment conducted in 3 of Orsay’s 12 voting bureaux. These three are not representative of France. Potential participants informed by mailings, local publications and posters with active participation of the Mayor’s office. After casting their official ballots, voters invited to cast majority judgment ballots (at adjacent tables and booths). Carried out under identical conditions : ballots filled out in booths, inserted in envelopes and deposited in transparent urns. 2,360 voted officially, 1,752 (74%) participated in experiment, 1,733 ballots valid. 1,705 were different.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions French President elections experiment at Orsay, April 23, 2007

Experiment conducted in 3 of Orsay’s 12 voting bureaux. These three are not representative of France. Potential participants informed by mailings, local publications and posters with active participation of the Mayor’s office. After casting their official ballots, voters invited to cast majority judgment ballots (at adjacent tables and booths). Carried out under identical conditions : ballots filled out in booths, inserted in envelopes and deposited in transparent urns. 2,360 voted officially, 1,752 (74%) participated in experiment, 1,733 ballots valid. 1,705 were different. Television interviews prove the satisfaction of voters.

Rida Laraki Majority Judgement Bayrou Royal Sarkozy

Le Pen

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Results French Presidential elections, Orsay 3 Bureaux

A politically aware observer of France is able to fill in the blanks. Excel. V.Good Good Accpt. Poor Rej. Blank 13.6% 30.7% 25.1% 14.8 8.4% 4.5% 2.9% 16.7% 22.7% 19.1% 16.8% 12.2% 10.8% 1.8% 19.1% 19.8% 14.3% 11.5% 7.1% 26.5% 1.7% Voynet 2.9% 9.3% 17.5% 23.7% 26.1% 16.2% 4.3% Besancenot 4.1% 9.9% 16.3% 16.0% 22.6% 27.9% 3.2% Buffet 2.5% 7.6% 12.5% 20.6% 26.4% 26.1% 4.3% Bové 1.5% 6.0% 11.4% 16.0% 25.7% 35.3% 4.2% Laguiller 2.1% 5.3% 10.2% 16.6% 25.9% 34.8% 5.3% Nihous 0.3% 1.8% 5.3% 11.0% 26.7% 47.8% 7.2% Villiers 2.4% 6.4% 8.7% 11.3% 15.8% 51.2% 4.3% Schivardi 0.5% 1.0% 3.9% 9.5% 24.9% 54.6% 5.8% 3.0% 4.6% 6.2% 6.5% 5.4% 71.7% 2.7% Red indicates the majority-grade.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Results French Presidential elections, Orsay 3 Bureaux

A politically aware observer of France is able to fill in the blanks. Excel. V.Good Good Accpt. Poor Rej. Blank Bayrou 13.6% 30.7% 25.1% 14.8 8.4% 4.5% 2.9% Royal 16.7% 22.7% 19.1% 16.8% 12.2% 10.8% 1.8% Sarkozy 19.1% 19.8% 14.3% 11.5% 7.1% 26.5% 1.7% Voynet 2.9% 9.3% 17.5% 23.7% 26.1% 16.2% 4.3% Besancenot 4.1% 9.9% 16.3% 16.0% 22.6% 27.9% 3.2% Buffet 2.5% 7.6% 12.5% 20.6% 26.4% 26.1% 4.3% Bové 1.5% 6.0% 11.4% 16.0% 25.7% 35.3% 4.2% Laguiller 2.1% 5.3% 10.2% 16.6% 25.9% 34.8% 5.3% Nihous 0.3% 1.8% 5.3% 11.0% 26.7% 47.8% 7.2% Villiers 2.4% 6.4% 8.7% 11.3% 15.8% 51.2% 4.3% Schivardi 0.5% 1.0% 3.9% 9.5% 24.9% 54.6% 5.8% Le Pen 3.0% 4.6% 6.2% 6.5% 5.4% 71.7% 2.7% Red indicates the majority-grade.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-grades, majority-gauges majority-ranking : French Presidential Elections, Orsay : Many voters

Higher The Lower Official Ntnl M-G M-G M-G vote vote 3 Bayrou 44.3% Good+ 30.6% 25.5% 18.6% 2 Royal 39.4% Good- 41.5% 29.9% 25.9% 1 Sarkozy 38.9% Good- 46.9% 29.0% 31.2% 8 Voynet 29.8% Acceptable- 46.6% 1.7% 1.6% 5 Besancenot 46.3% Poor+ 31.2% 2.5% 4.1% 7 Buffet 43.2% Poor+ 30.5% 1.4% 1.9% 10 Bové 34.9% Poor- 39.4% 0.9% 1.3% 9 Laguiller 34.2% Poor- 40.0% 0.8% 1.3% 11 Nihous 45.0% To reject- 0.3% 1.2% 6 Villiers 44.5% To reject- 1.9% 2.2% 12 Schivardi 39.7% To reject- 0.2% 0.3% 4 Le Pen 25.7% To reject- 5.9% 10.4%

Majority-gauge (p,α ±, q)

Rida Laraki Majority Judgement Bayrou : (44.3%,Good+,30.6%) Royal : (39.4%,Good−,41.5) How could a voter who graded Royal above Bayrou manipulate ? By lowering Bayrou’s majority-gauge and raising Royal’s. Among voters who rated Royal above Bayrou : one who can lower Bayrou’s majority-gauge cannot raise Royal’s ; one who can raise Royal’s cannot lower Bayrou’s.

Theorem No method is strategy-proof-in-ranking. The majority judgement is partially strategy-proof-in-ranking.

Can exaggeration change the outcome ? Yes, if many voters manipulate. But if only some 30% of those who can do so—and polls estimated that 30% of French voters cast votes not in accord with their convictions—they would have failed.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Could strategic voting have made Royal the winner ?

Rida Laraki Majority Judgement Among voters who rated Royal above Bayrou : one who can lower Bayrou’s majority-gauge cannot raise Royal’s ; one who can raise Royal’s cannot lower Bayrou’s.

Theorem No method is strategy-proof-in-ranking. The majority judgement is partially strategy-proof-in-ranking.

Can exaggeration change the outcome ? Yes, if many voters manipulate. But if only some 30% of those who can do so—and polls estimated that 30% of French voters cast votes not in accord with their convictions—they would have failed.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Could strategic voting have made Royal the winner ?

Bayrou : (44.3%,Good+,30.6%) Royal : (39.4%,Good−,41.5) How could a voter who graded Royal above Bayrou manipulate ? By lowering Bayrou’s majority-gauge and raising Royal’s.

Rida Laraki Majority Judgement Theorem No method is strategy-proof-in-ranking. The majority judgement is partially strategy-proof-in-ranking.

Can exaggeration change the outcome ? Yes, if many voters manipulate. But if only some 30% of those who can do so—and polls estimated that 30% of French voters cast votes not in accord with their convictions—they would have failed.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Could strategic voting have made Royal the winner ?

Bayrou : (44.3%,Good+,30.6%) Royal : (39.4%,Good−,41.5) How could a voter who graded Royal above Bayrou manipulate ? By lowering Bayrou’s majority-gauge and raising Royal’s. Among voters who rated Royal above Bayrou : one who can lower Bayrou’s majority-gauge cannot raise Royal’s ; one who can raise Royal’s cannot lower Bayrou’s.

Rida Laraki Majority Judgement Can exaggeration change the outcome ? Yes, if many voters manipulate. But if only some 30% of those who can do so—and polls estimated that 30% of French voters cast votes not in accord with their convictions—they would have failed.

The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Could strategic voting have made Royal the winner ?

Bayrou : (44.3%,Good+,30.6%) Royal : (39.4%,Good−,41.5) How could a voter who graded Royal above Bayrou manipulate ? By lowering Bayrou’s majority-gauge and raising Royal’s. Among voters who rated Royal above Bayrou : one who can lower Bayrou’s majority-gauge cannot raise Royal’s ; one who can raise Royal’s cannot lower Bayrou’s.

Theorem No method is strategy-proof-in-ranking. The majority judgement is partially strategy-proof-in-ranking.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenWines Electing Elections and Strategy Ranking proofThe in Method raking of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Could strategic voting have made Royal the winner ?

Bayrou : (44.3%,Good+,30.6%) Royal : (39.4%,Good−,41.5) How could a voter who graded Royal above Bayrou manipulate ? By lowering Bayrou’s majority-gauge and raising Royal’s. Among voters who rated Royal above Bayrou : one who can lower Bayrou’s majority-gauge cannot raise Royal’s ; one who can raise Royal’s cannot lower Bayrou’s.

Theorem No method is strategy-proof-in-ranking. The majority judgement is partially strategy-proof-in-ranking.

Can exaggeration change the outcome ? Yes, if many voters manipulate. But if only some 30% of those who can do so—and polls estimated that 30% of French voters cast votes not in accord with their convictions—they would have failed.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Contents

1 The thesis 2 Traditional Theory of Social Choice Traditional Methods and paradoxs paradoxs in practice Impossibility Theorems 3 Incompatibility Between Electing and Ranking 4 The Method of Majority Judgment Wines Elections Strategy proof in raking 5 The Theory of Majority Judgement Majority Grading Model Strategic Analysis Middlemost SGF Majority Ranking Model Meaningfulness 6 Approval Voting versus Approval Judgment 7 Experimental Evidences 8 Conclusions

Rida Laraki Majority Judgement in figure skating, diving and gymnastics competitions ; in piano, flute and orchestra competitions ; in classifying wines at wine competitions ; in ranking university students ; in classifying hotels and restaurants, e.g.,the Ritz Hotel is a *****, the Michelin’s *** to the Tour d’Argent restaurant.

Indeed, the decision mechanism used to operate markets itself uses a measure : money.

Money plays the role of Language in the economy. Language plays the role of Money in the new theory of social choice.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Why grading ?

Practical people use measures or grades that are well defined absolute common languages of evaluation to define decision mechanisms :

Rida Laraki Majority Judgement in piano, flute and orchestra competitions ; in classifying wines at wine competitions ; in ranking university students ; in classifying hotels and restaurants, e.g.,the Ritz Hotel is a *****, the Michelin’s *** to the Tour d’Argent restaurant.

Indeed, the decision mechanism used to operate markets itself uses a measure : money.

Money plays the role of Language in the economy. Language plays the role of Money in the new theory of social choice.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Why grading ?

Practical people use measures or grades that are well defined absolute common languages of evaluation to define decision mechanisms : in figure skating, diving and gymnastics competitions ;

Rida Laraki Majority Judgement in classifying wines at wine competitions ; in ranking university students ; in classifying hotels and restaurants, e.g.,the Ritz Hotel is a *****, the Michelin’s *** to the Tour d’Argent restaurant.

Indeed, the decision mechanism used to operate markets itself uses a measure : money.

Money plays the role of Language in the economy. Language plays the role of Money in the new theory of social choice.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Why grading ?

Practical people use measures or grades that are well defined absolute common languages of evaluation to define decision mechanisms : in figure skating, diving and gymnastics competitions ; in piano, flute and orchestra competitions ;

Rida Laraki Majority Judgement in ranking university students ; in classifying hotels and restaurants, e.g.,the Ritz Hotel is a *****, the Michelin’s *** to the Tour d’Argent restaurant.

Indeed, the decision mechanism used to operate markets itself uses a measure : money.

Money plays the role of Language in the economy. Language plays the role of Money in the new theory of social choice.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Why grading ?

Practical people use measures or grades that are well defined absolute common languages of evaluation to define decision mechanisms : in figure skating, diving and gymnastics competitions ; in piano, flute and orchestra competitions ; in classifying wines at wine competitions ;

Rida Laraki Majority Judgement in classifying hotels and restaurants, e.g.,the Ritz Hotel is a *****, the Michelin’s *** to the Tour d’Argent restaurant.

Indeed, the decision mechanism used to operate markets itself uses a measure : money.

Money plays the role of Language in the economy. Language plays the role of Money in the new theory of social choice.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Why grading ?

Practical people use measures or grades that are well defined absolute common languages of evaluation to define decision mechanisms : in figure skating, diving and gymnastics competitions ; in piano, flute and orchestra competitions ; in classifying wines at wine competitions ; in ranking university students ;

Rida Laraki Majority Judgement Indeed, the decision mechanism used to operate markets itself uses a measure : money.

Money plays the role of Language in the economy. Language plays the role of Money in the new theory of social choice.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Why grading ?

Practical people use measures or grades that are well defined absolute common languages of evaluation to define decision mechanisms : in figure skating, diving and gymnastics competitions ; in piano, flute and orchestra competitions ; in classifying wines at wine competitions ; in ranking university students ; in classifying hotels and restaurants, e.g.,the Ritz Hotel is a *****, the Michelin’s *** to the Tour d’Argent restaurant.

Rida Laraki Majority Judgement Money plays the role of Language in the economy. Language plays the role of Money in the new theory of social choice.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Why grading ?

Practical people use measures or grades that are well defined absolute common languages of evaluation to define decision mechanisms : in figure skating, diving and gymnastics competitions ; in piano, flute and orchestra competitions ; in classifying wines at wine competitions ; in ranking university students ; in classifying hotels and restaurants, e.g.,the Ritz Hotel is a *****, the Michelin’s *** to the Tour d’Argent restaurant.

Indeed, the decision mechanism used to operate markets itself uses a measure : money.

Rida Laraki Majority Judgement Language plays the role of Money in the new theory of social choice.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Why grading ?

Practical people use measures or grades that are well defined absolute common languages of evaluation to define decision mechanisms : in figure skating, diving and gymnastics competitions ; in piano, flute and orchestra competitions ; in classifying wines at wine competitions ; in ranking university students ; in classifying hotels and restaurants, e.g.,the Ritz Hotel is a *****, the Michelin’s *** to the Tour d’Argent restaurant.

Indeed, the decision mechanism used to operate markets itself uses a measure : money.

Money plays the role of Language in the economy.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Why grading ?

Practical people use measures or grades that are well defined absolute common languages of evaluation to define decision mechanisms : in figure skating, diving and gymnastics competitions ; in piano, flute and orchestra competitions ; in classifying wines at wine competitions ; in ranking university students ; in classifying hotels and restaurants, e.g.,the Ritz Hotel is a *****, the Michelin’s *** to the Tour d’Argent restaurant.

Indeed, the decision mechanism used to operate markets itself uses a measure : money.

Money plays the role of Language in the economy. Language plays the role of Money in the new theory of social choice.

Rida Laraki Majority Judgement A common language Λ, a set of strictly ordered grades : α, β, γ, . . . ; A finite set of m competitors (alternatives, candidates, performances, competing goods) C = {A, B,..., I ,..., Z} ; and A finite set of n judges J = {1,..., j,..., n}.

A problem is specified by a profile Φ = Φ(C, J ) : an m by n matrix of grades assigned to the competitors (rows) by the judges (columns).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Basic model

There are :

Rida Laraki Majority Judgement A finite set of m competitors (alternatives, candidates, performances, competing goods) C = {A, B,..., I ,..., Z} ; and A finite set of n judges J = {1,..., j,..., n}.

A problem is specified by a profile Φ = Φ(C, J ) : an m by n matrix of grades assigned to the competitors (rows) by the judges (columns).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Basic model

There are : A common language Λ, a set of strictly ordered grades : α, β, γ, . . . ;

Rida Laraki Majority Judgement A finite set of n judges J = {1,..., j,..., n}.

A problem is specified by a profile Φ = Φ(C, J ) : an m by n matrix of grades assigned to the competitors (rows) by the judges (columns).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Basic model

There are : A common language Λ, a set of strictly ordered grades : α, β, γ, . . . ; A finite set of m competitors (alternatives, candidates, performances, competing goods) C = {A, B,..., I ,..., Z} ; and

Rida Laraki Majority Judgement A problem is specified by a profile Φ = Φ(C, J ) : an m by n matrix of grades assigned to the competitors (rows) by the judges (columns).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Basic model

There are : A common language Λ, a set of strictly ordered grades : α, β, γ, . . . ; A finite set of m competitors (alternatives, candidates, performances, competing goods) C = {A, B,..., I ,..., Z} ; and A finite set of n judges J = {1,..., j,..., n}.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Basic model

There are : A common language Λ, a set of strictly ordered grades : α, β, γ, . . . ; A finite set of m competitors (alternatives, candidates, performances, competing goods) C = {A, B,..., I ,..., Z} ; and A finite set of n judges J = {1,..., j,..., n}.

A problem is specified by a profile Φ = Φ(C, J ) : an m by n matrix of grades assigned to the competitors (rows) by the judges (columns).

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Method of grading

A method of grading is a function

F :Λm×n → Λm

profile −→ grade to each competitor

 v. good good good mediocre good   good  F  exc. good good poor v. good  =  v. good  . mediocre exc. poor good bad mediocre

Rida Laraki Majority Judgement if two profiles Φ and Φ0 coincide except one or more judges grade a candidate A higher in Φ than Φ0 then F (Φ)(A)  F (Φ0)(A) ; moreover, if all judges grade a candidate A strictly higher in Φ than Φ0 then F (Φ)(A) F (Φ0)(A).

F is neutral : F (ρΦ) = ρF (Φ), for any permutation ρ of the competitors (or rows) ; F is anonymous : F (Φρ) = F (Φ), for any permutation of the judges (or columns). F is unanimous : F assigns α if every judge assigns α. F is monotonic :

F is independent of irrelevant alternatives (IIA) : if grades assigned to A are the same in Φ and Φ0 then F (Φ)(A) = F (Φ0)(A).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Axioms

A method of grading F should satisfy certain properties :

Rida Laraki Majority Judgement if two profiles Φ and Φ0 coincide except one or more judges grade a candidate A higher in Φ than Φ0 then F (Φ)(A)  F (Φ0)(A) ; moreover, if all judges grade a candidate A strictly higher in Φ than Φ0 then F (Φ)(A) F (Φ0)(A).

F is anonymous : F (Φρ) = F (Φ), for any permutation of the judges (or columns). F is unanimous : F assigns α if every judge assigns α. F is monotonic :

F is independent of irrelevant alternatives (IIA) : if grades assigned to A are the same in Φ and Φ0 then F (Φ)(A) = F (Φ0)(A).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Axioms

A method of grading F should satisfy certain properties : F is neutral : F (ρΦ) = ρF (Φ), for any permutation ρ of the competitors (or rows) ;

Rida Laraki Majority Judgement if two profiles Φ and Φ0 coincide except one or more judges grade a candidate A higher in Φ than Φ0 then F (Φ)(A)  F (Φ0)(A) ; moreover, if all judges grade a candidate A strictly higher in Φ than Φ0 then F (Φ)(A) F (Φ0)(A).

F is unanimous : F assigns α if every judge assigns α. F is monotonic :

F is independent of irrelevant alternatives (IIA) : if grades assigned to A are the same in Φ and Φ0 then F (Φ)(A) = F (Φ0)(A).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Axioms

A method of grading F should satisfy certain properties : F is neutral : F (ρΦ) = ρF (Φ), for any permutation ρ of the competitors (or rows) ; F is anonymous : F (Φρ) = F (Φ), for any permutation of the judges (or columns).

Rida Laraki Majority Judgement if two profiles Φ and Φ0 coincide except one or more judges grade a candidate A higher in Φ than Φ0 then F (Φ)(A)  F (Φ0)(A) ; moreover, if all judges grade a candidate A strictly higher in Φ than Φ0 then F (Φ)(A) F (Φ0)(A).

F is monotonic :

F is independent of irrelevant alternatives (IIA) : if grades assigned to A are the same in Φ and Φ0 then F (Φ)(A) = F (Φ0)(A).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Axioms

A method of grading F should satisfy certain properties : F is neutral : F (ρΦ) = ρF (Φ), for any permutation ρ of the competitors (or rows) ; F is anonymous : F (Φρ) = F (Φ), for any permutation of the judges (or columns). F is unanimous : F assigns α if every judge assigns α.

Rida Laraki Majority Judgement if two profiles Φ and Φ0 coincide except one or more judges grade a candidate A higher in Φ than Φ0 then F (Φ)(A)  F (Φ0)(A) ; moreover, if all judges grade a candidate A strictly higher in Φ than Φ0 then F (Φ)(A) F (Φ0)(A). F is independent of irrelevant alternatives (IIA) : if grades assigned to A are the same in Φ and Φ0 then F (Φ)(A) = F (Φ0)(A).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Axioms

A method of grading F should satisfy certain properties : F is neutral : F (ρΦ) = ρF (Φ), for any permutation ρ of the competitors (or rows) ; F is anonymous : F (Φρ) = F (Φ), for any permutation of the judges (or columns). F is unanimous : F assigns α if every judge assigns α. F is monotonic :

Rida Laraki Majority Judgement moreover, if all judges grade a candidate A strictly higher in Φ than Φ0 then F (Φ)(A) F (Φ0)(A). F is independent of irrelevant alternatives (IIA) : if grades assigned to A are the same in Φ and Φ0 then F (Φ)(A) = F (Φ0)(A).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Axioms

A method of grading F should satisfy certain properties : F is neutral : F (ρΦ) = ρF (Φ), for any permutation ρ of the competitors (or rows) ; F is anonymous : F (Φρ) = F (Φ), for any permutation of the judges (or columns). F is unanimous : F assigns α if every judge assigns α. F is monotonic : if two profiles Φ and Φ0 coincide except one or more judges grade a candidate A higher in Φ than Φ0 then F (Φ)(A)  F (Φ0)(A) ;

Rida Laraki Majority Judgement F is independent of irrelevant alternatives (IIA) : if grades assigned to A are the same in Φ and Φ0 then F (Φ)(A) = F (Φ0)(A).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Axioms

A method of grading F should satisfy certain properties : F is neutral : F (ρΦ) = ρF (Φ), for any permutation ρ of the competitors (or rows) ; F is anonymous : F (Φρ) = F (Φ), for any permutation of the judges (or columns). F is unanimous : F assigns α if every judge assigns α. F is monotonic : if two profiles Φ and Φ0 coincide except one or more judges grade a candidate A higher in Φ than Φ0 then F (Φ)(A)  F (Φ0)(A) ; moreover, if all judges grade a candidate A strictly higher in Φ than Φ0 then F (Φ)(A) F (Φ0)(A).

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Axioms

A method of grading F should satisfy certain properties : F is neutral : F (ρΦ) = ρF (Φ), for any permutation ρ of the competitors (or rows) ; F is anonymous : F (Φρ) = F (Φ), for any permutation of the judges (or columns). F is unanimous : F assigns α if every judge assigns α. F is monotonic : if two profiles Φ and Φ0 coincide except one or more judges grade a candidate A higher in Φ than Φ0 then F (Φ)(A)  F (Φ0)(A) ; moreover, if all judges grade a candidate A strictly higher in Φ than Φ0 then F (Φ)(A) F (Φ0)(A). F is independent of irrelevant alternatives (IIA) : if grades assigned to A are the same in Φ and Φ0 then F (Φ)(A) = F (Φ0)(A).

Rida Laraki Majority Judgement anonymity : f (...,α,...,β,...) = f (. . . , β, . . . , α, . . .) ; unanimity : f (α, α, . . . , α) = α ; and monotonicity :

αj  βj ⇒ f (α1, . . . , αj , . . . , αn)  f (α1, . . . , βj , . . . , αn)

and

(α1, . . . , αn) ≺ (β1, . . . , βn) ⇒ f (α1, . . . , αn) ≺ f (β1, . . . , βn).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Aggregation function

An aggregation function is a function

f :Λn → Λ

judges’ grades of one competitor −→ final grade of competitor f (exc., good, good, poor, v. good) = v.good satisfying :

Rida Laraki Majority Judgement unanimity : f (α, α, . . . , α) = α ; and monotonicity :

αj  βj ⇒ f (α1, . . . , αj , . . . , αn)  f (α1, . . . , βj , . . . , αn)

and

(α1, . . . , αn) ≺ (β1, . . . , βn) ⇒ f (α1, . . . , αn) ≺ f (β1, . . . , βn).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Aggregation function

An aggregation function is a function

f :Λn → Λ

judges’ grades of one competitor −→ final grade of competitor f (exc., good, good, poor, v. good) = v.good satisfying : anonymity : f (...,α,...,β,...) = f (. . . , β, . . . , α, . . .) ;

Rida Laraki Majority Judgement monotonicity :

αj  βj ⇒ f (α1, . . . , αj , . . . , αn)  f (α1, . . . , βj , . . . , αn)

and

(α1, . . . , αn) ≺ (β1, . . . , βn) ⇒ f (α1, . . . , αn) ≺ f (β1, . . . , βn).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Aggregation function

An aggregation function is a function

f :Λn → Λ

judges’ grades of one competitor −→ final grade of competitor f (exc., good, good, poor, v. good) = v.good satisfying : anonymity : f (...,α,...,β,...) = f (. . . , β, . . . , α, . . .) ; unanimity : f (α, α, . . . , α) = α ; and

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Aggregation function

An aggregation function is a function

f :Λn → Λ

judges’ grades of one competitor −→ final grade of competitor f (exc., good, good, poor, v. good) = v.good satisfying : anonymity : f (...,α,...,β,...) = f (. . . , β, . . . , α, . . .) ; unanimity : f (α, α, . . . , α) = α ; and monotonicity :

αj  βj ⇒ f (α1, . . . , αj , . . . , αn)  f (α1, . . . , βj , . . . , αn)

and

(α1, . . . , αn) ≺ (β1, . . . , βn) ⇒ f (α1, . . . , αn) ≺ f (β1, . . . , βn).

Rida Laraki Majority Judgement In practice, the common language is usually parameterized. Small changes in the parametrization or the grades should imply small changes in the outputs. As Laplace suggested, suppose Λ = [0, R], and assume F (so f ) to be continuous.

A social grading function (SGF) F (or f ) is a continuous method of grading that satisfies the five properties.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Possibility theorem

Theorem A method of grading F is neutral, anonymous, unanimous, monotonic and independent of irrelevant alternatives if and only if F (Φ)(A) = f Φ(A)
for every A ∈ C, for some one aggregation function f .

Rida Laraki Majority Judgement As Laplace suggested, suppose Λ = [0, R], and assume F (so f ) to be continuous.

A social grading function (SGF) F (or f ) is a continuous method of grading that satisfies the five properties.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Possibility theorem

Theorem A method of grading F is neutral, anonymous, unanimous, monotonic and independent of irrelevant alternatives if and only if F (Φ)(A) = f Φ(A)
for every A ∈ C, for some one aggregation function f .

In practice, the common language is usually parameterized. Small changes in the parametrization or the grades should imply small changes in the outputs.

Rida Laraki Majority Judgement A social grading function (SGF) F (or f ) is a continuous method of grading that satisfies the five properties.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Possibility theorem

Theorem A method of grading F is neutral, anonymous, unanimous, monotonic and independent of irrelevant alternatives if and only if F (Φ)(A) = f Φ(A)
for every A ∈ C, for some one aggregation function f .

In practice, the common language is usually parameterized. Small changes in the parametrization or the grades should imply small changes in the outputs. As Laplace suggested, suppose Λ = [0, R], and assume F (so f ) to be continuous.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Possibility theorem

Theorem A method of grading F is neutral, anonymous, unanimous, monotonic and independent of irrelevant alternatives if and only if F (Φ)(A) = f Φ(A)
for every A ∈ C, for some one aggregation function f .

In practice, the common language is usually parameterized. Small changes in the parametrization or the grades should imply small changes in the outputs. As Laplace suggested, suppose Λ = [0, R], and assume F (so f ) to be continuous.

A social grading function (SGF) F (or f ) is a continuous method of grading that satisfies the five properties.

Rida Laraki Majority Judgement Utility measures relative satisfaction : in 2002 in France, many voters of the left hated Chirac but were very satisfied with his score (82%) against Le Pen. The same voters would have been very unhappy if Chirac had crushed Jospin by the same score. Grades measure absolute merit : to be president of France, some voters of the left would perhaps judge Chirac Acceptable (or Good) against Le Pen or Jospin or anyone.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Grade versus utility

Grades have nothing to do with utilities.

Rida Laraki Majority Judgement Grades measure absolute merit : to be president of France, some voters of the left would perhaps judge Chirac Acceptable (or Good) against Le Pen or Jospin or anyone.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Grade versus utility

Grades have nothing to do with utilities. Utility measures relative satisfaction : in 2002 in France, many voters of the left hated Chirac but were very satisfied with his score (82%) against Le Pen. The same voters would have been very unhappy if Chirac had crushed Jospin by the same score.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Grade versus utility

Grades have nothing to do with utilities. Utility measures relative satisfaction : in 2002 in France, many voters of the left hated Chirac but were very satisfied with his score (82%) against Le Pen. The same voters would have been very unhappy if Chirac had crushed Jospin by the same score. Grades measure absolute merit : to be president of France, some voters of the left would perhaps judge Chirac Acceptable (or Good) against Le Pen or Jospin or anyone.

Rida Laraki Majority Judgement Given the mechanism and some information, a voter chooses the message that maximizes his (unknown to us) utility function. Majority judgement is proved to be strategy-proof for a large class of utility functions. When it is not, it is shown that it combats manipulations in many well defined senses.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Game of Voting

The utility or satisfaction of a voter may depend on a host of factors (the set of candidates, honesty, the aggregate-message of the decision rule, the set of messages, etc).

Rida Laraki Majority Judgement Majority judgement is proved to be strategy-proof for a large class of utility functions. When it is not, it is shown that it combats manipulations in many well defined senses.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Game of Voting

The utility or satisfaction of a voter may depend on a host of factors (the set of candidates, honesty, the aggregate-message of the decision rule, the set of messages, etc). Given the mechanism and some information, a voter chooses the message that maximizes his (unknown to us) utility function.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Game of Voting

The utility or satisfaction of a voter may depend on a host of factors (the set of candidates, honesty, the aggregate-message of the decision rule, the set of messages, etc). Given the mechanism and some information, a voter chooses the message that maximizes his (unknown to us) utility function. Majority judgement is proved to be strategy-proof for a large class of utility functions. When it is not, it is shown that it combats manipulations in many well defined senses.

Rida Laraki Majority Judgement f is the aggregation function, C is the set of competitors, and Λ the common language which is used.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The utility of a judge

The “utility” of a judge may be imagined to be some function

∗ uj (r , r, f , C, Λ)

where

∗ ∗ (r1 ,..., rn ) are the grades the judges believe are the right ones, and

(r1,..., rn)

are the grades they give,

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The utility of a judge

The “utility” of a judge may be imagined to be some function

∗ uj (r , r, f , C, Λ)

where

∗ ∗ (r1 ,..., rn ) are the grades the judges believe are the right ones, and

(r1,..., rn)

are the grades they give, f is the aggregation function, C is the set of competitors, and Λ the common language which is used.

Rida Laraki Majority Judgement Other’s honesty :

∗ X ∗ uj (r , r, f , C, Λ) = − |ri − ri | + ··· i6=j

Single-peakedness :

∗ ∗ uj (r , r, f , C, Λ) = −|rj − f (r1,..., rn)| + ··· At the extreme, utility may depend solely on who is the winner (a very restrictive assumption, often made by voting theorists).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Some examples

Personal honesty :

∗ ∗ uj (r , r, f , C, Λ) = −|rj − rj | + ···

Rida Laraki Majority Judgement Single-peakedness :

∗ ∗ uj (r , r, f , C, Λ) = −|rj − f (r1,..., rn)| + ··· At the extreme, utility may depend solely on who is the winner (a very restrictive assumption, often made by voting theorists).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Some examples

Personal honesty :

∗ ∗ uj (r , r, f , C, Λ) = −|rj − rj | + ··· Other’s honesty :

∗ X ∗ uj (r , r, f , C, Λ) = − |ri − ri | + ··· i6=j

Rida Laraki Majority Judgement At the extreme, utility may depend solely on who is the winner (a very restrictive assumption, often made by voting theorists).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Some examples

Personal honesty :

∗ ∗ uj (r , r, f , C, Λ) = −|rj − rj | + ··· Other’s honesty :

∗ X ∗ uj (r , r, f , C, Λ) = − |ri − ri | + ··· i6=j

Single-peakedness :

∗ ∗ uj (r , r, f , C, Λ) = −|rj − f (r1,..., rn)| + ···

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Some examples

Personal honesty :

∗ ∗ uj (r , r, f , C, Λ) = −|rj − rj | + ··· Other’s honesty :

∗ X ∗ uj (r , r, f , C, Λ) = − |ri − ri | + ··· i6=j

Single-peakedness :

∗ ∗ uj (r , r, f , C, Λ) = −|rj − f (r1,..., rn)| + ··· At the extreme, utility may depend solely on who is the winner (a very restrictive assumption, often made by voting theorists).

Rida Laraki Majority Judgement when the final grade is r and if a judge’s input grade is some grade r + > r, he cannot increase the final grade ; and if when a judge’s input grade is some grade r − < r, he cannot decrease the final grade.

Strategy-proof-in-grading implies it is a dominant strategy for a judge to honestly assign grades when his utility is single-peaked :

∗ ∗ ∗ uj (r1 ,..., rn , r1,..., rn, f , Λ) = −|rj − f (r1,..., rn)|

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in grading

An aggregation function is strategy-proof-in-grading if

Rida Laraki Majority Judgement and if when a judge’s input grade is some grade r − < r, he cannot decrease the final grade.

Strategy-proof-in-grading implies it is a dominant strategy for a judge to honestly assign grades when his utility is single-peaked :

∗ ∗ ∗ uj (r1 ,..., rn , r1,..., rn, f , Λ) = −|rj − f (r1,..., rn)|

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in grading

An aggregation function is strategy-proof-in-grading if when the final grade is r and if a judge’s input grade is some grade r + > r, he cannot increase the final grade ;

Rida Laraki Majority Judgement Strategy-proof-in-grading implies it is a dominant strategy for a judge to honestly assign grades when his utility is single-peaked :

∗ ∗ ∗ uj (r1 ,..., rn , r1,..., rn, f , Λ) = −|rj − f (r1,..., rn)|

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in grading

An aggregation function is strategy-proof-in-grading if when the final grade is r and if a judge’s input grade is some grade r + > r, he cannot increase the final grade ; and if when a judge’s input grade is some grade r − < r, he cannot decrease the final grade.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in grading

An aggregation function is strategy-proof-in-grading if when the final grade is r and if a judge’s input grade is some grade r + > r, he cannot increase the final grade ; and if when a judge’s input grade is some grade r − < r, he cannot decrease the final grade.

Strategy-proof-in-grading implies it is a dominant strategy for a judge to honestly assign grades when his utility is single-peaked :

∗ ∗ ∗ uj (r1 ,..., rn , r1,..., rn, f , Λ) = −|rj − f (r1,..., rn)|

Rida Laraki Majority Judgement Order functions are clearly strategy-proof-in-grading.

Theorem The unique strategy-proof-in-grading SGFs are the order functions.

The result holds without the continuity assumption. It also holds if the language is finite. Hervé Moulin (1981), proves a related result, in a seminal paper. If the mechanism is a point-summing method (the mean with respect to some parametrization), almost all voters can manipulate.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in grading

The function that associates to a set of grades the kth highest grade is called the kth-order function f k .

Rida Laraki Majority Judgement Theorem The unique strategy-proof-in-grading SGFs are the order functions.

The result holds without the continuity assumption. It also holds if the language is finite. Hervé Moulin (1981), proves a related result, in a seminal paper. If the mechanism is a point-summing method (the mean with respect to some parametrization), almost all voters can manipulate.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in grading

The function that associates to a set of grades the kth highest grade is called the kth-order function f k . Order functions are clearly strategy-proof-in-grading.

Rida Laraki Majority Judgement The result holds without the continuity assumption. It also holds if the language is finite. Hervé Moulin (1981), proves a related result, in a seminal paper. If the mechanism is a point-summing method (the mean with respect to some parametrization), almost all voters can manipulate.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in grading

The function that associates to a set of grades the kth highest grade is called the kth-order function f k . Order functions are clearly strategy-proof-in-grading.

Theorem The unique strategy-proof-in-grading SGFs are the order functions.

Rida Laraki Majority Judgement Hervé Moulin (1981), proves a related result, in a seminal paper. If the mechanism is a point-summing method (the mean with respect to some parametrization), almost all voters can manipulate.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in grading

The function that associates to a set of grades the kth highest grade is called the kth-order function f k . Order functions are clearly strategy-proof-in-grading.

Theorem The unique strategy-proof-in-grading SGFs are the order functions.

The result holds without the continuity assumption. It also holds if the language is finite.

Rida Laraki Majority Judgement If the mechanism is a point-summing method (the mean with respect to some parametrization), almost all voters can manipulate.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in grading

The function that associates to a set of grades the kth highest grade is called the kth-order function f k . Order functions are clearly strategy-proof-in-grading.

Theorem The unique strategy-proof-in-grading SGFs are the order functions.

The result holds without the continuity assumption. It also holds if the language is finite. Hervé Moulin (1981), proves a related result, in a seminal paper.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in grading

The function that associates to a set of grades the kth highest grade is called the kth-order function f k . Order functions are clearly strategy-proof-in-grading.

Theorem The unique strategy-proof-in-grading SGFs are the order functions.

The result holds without the continuity assumption. It also holds if the language is finite. Hervé Moulin (1981), proves a related result, in a seminal paper. If the mechanism is a point-summing method (the mean with respect to some parametrization), almost all voters can manipulate.

Rida Laraki Majority Judgement µ−(f , r) = nbre of judges who can decrease the final grade, µ+(f , r) = nbre of judges who can increase the final grade,

1 1 µ(f , r) = µ−(f , r) + µ+(f , r) 2n 2n

is the neutral-probability that a judge who tries to change the final grade succeed.

The manipulability of f is µ(f ) = maxr=(r1,...,rn) µ(f , r).

Theorem The unique SGFs that minimize manipulability are the order functions. Point-summing methods maximize manipulability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability

Given an aggregation function f and input r = (r1,..., rn), let

Rida Laraki Majority Judgement µ+(f , r) = nbre of judges who can increase the final grade,

1 1 µ(f , r) = µ−(f , r) + µ+(f , r) 2n 2n

is the neutral-probability that a judge who tries to change the final grade succeed.

The manipulability of f is µ(f ) = maxr=(r1,...,rn) µ(f , r).

Theorem The unique SGFs that minimize manipulability are the order functions. Point-summing methods maximize manipulability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability

Given an aggregation function f and input r = (r1,..., rn), let µ−(f , r) = nbre of judges who can decrease the final grade,

Rida Laraki Majority Judgement 1 1 µ(f , r) = µ−(f , r) + µ+(f , r) 2n 2n

is the neutral-probability that a judge who tries to change the final grade succeed.

The manipulability of f is µ(f ) = maxr=(r1,...,rn) µ(f , r).

Theorem The unique SGFs that minimize manipulability are the order functions. Point-summing methods maximize manipulability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability

Given an aggregation function f and input r = (r1,..., rn), let µ−(f , r) = nbre of judges who can decrease the final grade, µ+(f , r) = nbre of judges who can increase the final grade,

Rida Laraki Majority Judgement is the neutral-probability that a judge who tries to change the final grade succeed.

The manipulability of f is µ(f ) = maxr=(r1,...,rn) µ(f , r).

Theorem The unique SGFs that minimize manipulability are the order functions. Point-summing methods maximize manipulability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability

Given an aggregation function f and input r = (r1,..., rn), let µ−(f , r) = nbre of judges who can decrease the final grade, µ+(f , r) = nbre of judges who can increase the final grade,

1 1 µ(f , r) = µ−(f , r) + µ+(f , r) 2n 2n

Rida Laraki Majority Judgement The manipulability of f is µ(f ) = maxr=(r1,...,rn) µ(f , r).

Theorem The unique SGFs that minimize manipulability are the order functions. Point-summing methods maximize manipulability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability

Given an aggregation function f and input r = (r1,..., rn), let µ−(f , r) = nbre of judges who can decrease the final grade, µ+(f , r) = nbre of judges who can increase the final grade,

1 1 µ(f , r) = µ−(f , r) + µ+(f , r) 2n 2n

is the neutral-probability that a judge who tries to change the final grade succeed.

Rida Laraki Majority Judgement Theorem The unique SGFs that minimize manipulability are the order functions. Point-summing methods maximize manipulability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability

Given an aggregation function f and input r = (r1,..., rn), let µ−(f , r) = nbre of judges who can decrease the final grade, µ+(f , r) = nbre of judges who can increase the final grade,

1 1 µ(f , r) = µ−(f , r) + µ+(f , r) 2n 2n

is the neutral-probability that a judge who tries to change the final grade succeed.

The manipulability of f is µ(f ) = maxr=(r1,...,rn) µ(f , r).

Rida Laraki Majority Judgement Point-summing methods maximize manipulability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability

Given an aggregation function f and input r = (r1,..., rn), let µ−(f , r) = nbre of judges who can decrease the final grade, µ+(f , r) = nbre of judges who can increase the final grade,

1 1 µ(f , r) = µ−(f , r) + µ+(f , r) 2n 2n

is the neutral-probability that a judge who tries to change the final grade succeed.

The manipulability of f is µ(f ) = maxr=(r1,...,rn) µ(f , r).

Theorem The unique SGFs that minimize manipulability are the order functions.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability

Given an aggregation function f and input r = (r1,..., rn), let µ−(f , r) = nbre of judges who can decrease the final grade, µ+(f , r) = nbre of judges who can increase the final grade,

1 1 µ(f , r) = µ−(f , r) + µ+(f , r) 2n 2n

is the neutral-probability that a judge who tries to change the final grade succeed.

The manipulability of f is µ(f ) = maxr=(r1,...,rn) µ(f , r).

Theorem The unique SGFs that minimize manipulability are the order functions. Point-summing methods maximize manipulability.

Rida Laraki Majority Judgement judge j cannot decrease B’s final grade ; and judge j cannot increase A’s final grade ;

if the final grade of A is below the final grade of B : r A < r B and if some judge j has A B the opposed ranking : rj > rj ,

Strategy-proof-in-ranking implies it is a dominant strategy for a judge to honestly assign the grades whenever his utility function depends solely on the final ranking (or only on who is the winner).

Theorem (Extending Gibbard-Satterthwaite) There exists no SGF that is strategy-proof-in-ranking.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in ranking

A SGF is strategy-proof-in-ranking if for any two candidates A and B,

Rida Laraki Majority Judgement judge j cannot decrease B’s final grade ; and judge j cannot increase A’s final grade ;

and if some judge j has A B the opposed ranking : rj > rj ,

Strategy-proof-in-ranking implies it is a dominant strategy for a judge to honestly assign the grades whenever his utility function depends solely on the final ranking (or only on who is the winner).

Theorem (Extending Gibbard-Satterthwaite) There exists no SGF that is strategy-proof-in-ranking.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in ranking

A SGF is strategy-proof-in-ranking if for any two candidates A and B, if the final grade of A is below the final grade of B : r A < r B

Rida Laraki Majority Judgement judge j cannot decrease B’s final grade ; and judge j cannot increase A’s final grade ; Strategy-proof-in-ranking implies it is a dominant strategy for a judge to honestly assign the grades whenever his utility function depends solely on the final ranking (or only on who is the winner).

Theorem (Extending Gibbard-Satterthwaite) There exists no SGF that is strategy-proof-in-ranking.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in ranking

A SGF is strategy-proof-in-ranking if for any two candidates A and B, if the final grade of A is below the final grade of B : r A < r B and if some judge j has A B the opposed ranking : rj > rj ,

Rida Laraki Majority Judgement judge j cannot increase A’s final grade ; Strategy-proof-in-ranking implies it is a dominant strategy for a judge to honestly assign the grades whenever his utility function depends solely on the final ranking (or only on who is the winner).

Theorem (Extending Gibbard-Satterthwaite) There exists no SGF that is strategy-proof-in-ranking.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in ranking

A SGF is strategy-proof-in-ranking if for any two candidates A and B, if the final grade of A is below the final grade of B : r A < r B and if some judge j has A B the opposed ranking : rj > rj , judge j cannot decrease B’s final grade ; and

Rida Laraki Majority Judgement Strategy-proof-in-ranking implies it is a dominant strategy for a judge to honestly assign the grades whenever his utility function depends solely on the final ranking (or only on who is the winner).

Theorem (Extending Gibbard-Satterthwaite) There exists no SGF that is strategy-proof-in-ranking.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in ranking

A SGF is strategy-proof-in-ranking if for any two candidates A and B, if the final grade of A is below the final grade of B : r A < r B and if some judge j has A B the opposed ranking : rj > rj , judge j cannot decrease B’s final grade ; and judge j cannot increase A’s final grade ;

Rida Laraki Majority Judgement Theorem (Extending Gibbard-Satterthwaite) There exists no SGF that is strategy-proof-in-ranking.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in ranking

A SGF is strategy-proof-in-ranking if for any two candidates A and B, if the final grade of A is below the final grade of B : r A < r B and if some judge j has A B the opposed ranking : rj > rj , judge j cannot decrease B’s final grade ; and judge j cannot increase A’s final grade ; Strategy-proof-in-ranking implies it is a dominant strategy for a judge to honestly assign the grades whenever his utility function depends solely on the final ranking (or only on who is the winner).

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Strategy in ranking

A SGF is strategy-proof-in-ranking if for any two candidates A and B, if the final grade of A is below the final grade of B : r A < r B and if some judge j has A B the opposed ranking : rj > rj , judge j cannot decrease B’s final grade ; and judge j cannot increase A’s final grade ; Strategy-proof-in-ranking implies it is a dominant strategy for a judge to honestly assign the grades whenever his utility function depends solely on the final ranking (or only on who is the winner).

Theorem (Extending Gibbard-Satterthwaite) There exists no SGF that is strategy-proof-in-ranking.

Rida Laraki Majority Judgement if j can decrease B’s final grade, he cannot increase A’s final grade ; and if j can increase A’s final grade, he cannot decrease B’s final grade.

if the final grade of A is below the final grade of B, and if some judge j believes the opposite then,

Theorem The unique SGFs that are partially strategy-proof-in-ranking are the order functions.

When reporting honestly is not a dominant strategy for all voters, one should study the equilibria of the corresponding Game of Voting. A detailed analysis shows that majority judgement elects at worst the Condorcet-winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Limiting manipulations in ranking

A SGF is partially strategy-proof-in-ranking if : for any two candidates A and B,

Rida Laraki Majority Judgement if j can decrease B’s final grade, he cannot increase A’s final grade ; and if j can increase A’s final grade, he cannot decrease B’s final grade.

and if some judge j believes the opposite then,

Theorem The unique SGFs that are partially strategy-proof-in-ranking are the order functions.

When reporting honestly is not a dominant strategy for all voters, one should study the equilibria of the corresponding Game of Voting. A detailed analysis shows that majority judgement elects at worst the Condorcet-winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Limiting manipulations in ranking

A SGF is partially strategy-proof-in-ranking if : for any two candidates A and B, if the final grade of A is below the final grade of B,

Rida Laraki Majority Judgement if j can decrease B’s final grade, he cannot increase A’s final grade ; and if j can increase A’s final grade, he cannot decrease B’s final grade.

Theorem The unique SGFs that are partially strategy-proof-in-ranking are the order functions.

When reporting honestly is not a dominant strategy for all voters, one should study the equilibria of the corresponding Game of Voting. A detailed analysis shows that majority judgement elects at worst the Condorcet-winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Limiting manipulations in ranking

A SGF is partially strategy-proof-in-ranking if : for any two candidates A and B, if the final grade of A is below the final grade of B, and if some judge j believes the opposite then,

Rida Laraki Majority Judgement if j can increase A’s final grade, he cannot decrease B’s final grade.

Theorem The unique SGFs that are partially strategy-proof-in-ranking are the order functions.

When reporting honestly is not a dominant strategy for all voters, one should study the equilibria of the corresponding Game of Voting. A detailed analysis shows that majority judgement elects at worst the Condorcet-winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Limiting manipulations in ranking

A SGF is partially strategy-proof-in-ranking if : for any two candidates A and B, if the final grade of A is below the final grade of B, and if some judge j believes the opposite then, if j can decrease B’s final grade, he cannot increase A’s final grade ; and

Rida Laraki Majority Judgement Theorem The unique SGFs that are partially strategy-proof-in-ranking are the order functions.

When reporting honestly is not a dominant strategy for all voters, one should study the equilibria of the corresponding Game of Voting. A detailed analysis shows that majority judgement elects at worst the Condorcet-winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Limiting manipulations in ranking

A SGF is partially strategy-proof-in-ranking if : for any two candidates A and B, if the final grade of A is below the final grade of B, and if some judge j believes the opposite then, if j can decrease B’s final grade, he cannot increase A’s final grade ; and if j can increase A’s final grade, he cannot decrease B’s final grade.

Rida Laraki Majority Judgement When reporting honestly is not a dominant strategy for all voters, one should study the equilibria of the corresponding Game of Voting. A detailed analysis shows that majority judgement elects at worst the Condorcet-winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Limiting manipulations in ranking

A SGF is partially strategy-proof-in-ranking if : for any two candidates A and B, if the final grade of A is below the final grade of B, and if some judge j believes the opposite then, if j can decrease B’s final grade, he cannot increase A’s final grade ; and if j can increase A’s final grade, he cannot decrease B’s final grade.

Theorem The unique SGFs that are partially strategy-proof-in-ranking are the order functions.

Rida Laraki Majority Judgement one should study the equilibria of the corresponding Game of Voting. A detailed analysis shows that majority judgement elects at worst the Condorcet-winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Limiting manipulations in ranking

A SGF is partially strategy-proof-in-ranking if : for any two candidates A and B, if the final grade of A is below the final grade of B, and if some judge j believes the opposite then, if j can decrease B’s final grade, he cannot increase A’s final grade ; and if j can increase A’s final grade, he cannot decrease B’s final grade.

Theorem The unique SGFs that are partially strategy-proof-in-ranking are the order functions.

When reporting honestly is not a dominant strategy for all voters,

Rida Laraki Majority Judgement A detailed analysis shows that majority judgement elects at worst the Condorcet-winner.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Limiting manipulations in ranking

A SGF is partially strategy-proof-in-ranking if : for any two candidates A and B, if the final grade of A is below the final grade of B, and if some judge j believes the opposite then, if j can decrease B’s final grade, he cannot increase A’s final grade ; and if j can increase A’s final grade, he cannot decrease B’s final grade.

Theorem The unique SGFs that are partially strategy-proof-in-ranking are the order functions.

When reporting honestly is not a dominant strategy for all voters, one should study the equilibria of the corresponding Game of Voting.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Limiting manipulations in ranking

A SGF is partially strategy-proof-in-ranking if : for any two candidates A and B, if the final grade of A is below the final grade of B, and if some judge j believes the opposite then, if j can decrease B’s final grade, he cannot increase A’s final grade ; and if j can increase A’s final grade, he cannot decrease B’s final grade.

Theorem The unique SGFs that are partially strategy-proof-in-ranking are the order functions.

When reporting honestly is not a dominant strategy for all voters, one should study the equilibria of the corresponding Game of Voting. A detailed analysis shows that majority judgement elects at worst the Condorcet-winner.

Rida Laraki Majority Judgement Theorem The unique aggregation functions that assign a final grade of r when a majority of judges assign r are the middlemost.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Middlemost aggregation functions

The middlemost aggregation functions are (for r1 ≥ ... ≥ rn),

f (r1,..., rn) = r(n+1)/2 when n is odd, and

rn/2 ≥ f (r1,..., rn) ≥ r(n+2)/2 when n is even. f n/2 and f (n+2)/2 are the upper-middlemost and lower-middlemost order functions.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Middlemost aggregation functions

The middlemost aggregation functions are (for r1 ≥ ... ≥ rn),

f (r1,..., rn) = r(n+1)/2 when n is odd, and

rn/2 ≥ f (r1,..., rn) ≥ r(n+2)/2 when n is even. f n/2 and f (n+2)/2 are the upper-middlemost and lower-middlemost order functions. Theorem The unique aggregation functions that assign a final grade of r when a majority of judges assign r are the middlemost.

Rida Laraki Majority Judgement Extreme order-functions are more manipulable than central order functions. More an order function is close to the middle, less it is manipulable.

At the extreme, f 1 allows all the juges to increase the final grade and f n allows all the juges to decrease the final grade :

Let λ = probability a judge wishes to increase the final grade. The probability of effective-manipulability of f is

λµ+(f , r) + (1 − λ)µ−(f , r) EM(f ) = max max . r=(r1,...,rn) 0≤λ≤1 n

Theorem The unique aggregation functions that minimize the probability of effective-manipulability are the middlemost. Point-summing-methods, f 1 and f n maximize this probability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability 2

The k-th order function f k allows n − k + 1 judges to increase the final grade and k judges to decrease it.

Rida Laraki Majority Judgement Extreme order-functions are more manipulable than central order functions. More an order function is close to the middle, less it is manipulable.

Let λ = probability a judge wishes to increase the final grade. The probability of effective-manipulability of f is

λµ+(f , r) + (1 − λ)µ−(f , r) EM(f ) = max max . r=(r1,...,rn) 0≤λ≤1 n

Theorem The unique aggregation functions that minimize the probability of effective-manipulability are the middlemost. Point-summing-methods, f 1 and f n maximize this probability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability 2

The k-th order function f k allows n − k + 1 judges to increase the final grade and k judges to decrease it. At the extreme, f 1 allows all the juges to increase the final grade and f n allows all the juges to decrease the final grade :

Rida Laraki Majority Judgement Let λ = probability a judge wishes to increase the final grade. The probability of effective-manipulability of f is

λµ+(f , r) + (1 − λ)µ−(f , r) EM(f ) = max max . r=(r1,...,rn) 0≤λ≤1 n

Theorem The unique aggregation functions that minimize the probability of effective-manipulability are the middlemost. Point-summing-methods, f 1 and f n maximize this probability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability 2

The k-th order function f k allows n − k + 1 judges to increase the final grade and k judges to decrease it. At the extreme, f 1 allows all the juges to increase the final grade and f n allows all the juges to decrease the final grade : Extreme order-functions are more manipulable than central order functions. More an order function is close to the middle, less it is manipulable.

Rida Laraki Majority Judgement Theorem The unique aggregation functions that minimize the probability of effective-manipulability are the middlemost. Point-summing-methods, f 1 and f n maximize this probability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability 2

The k-th order function f k allows n − k + 1 judges to increase the final grade and k judges to decrease it. At the extreme, f 1 allows all the juges to increase the final grade and f n allows all the juges to decrease the final grade : Extreme order-functions are more manipulable than central order functions. More an order function is close to the middle, less it is manipulable.

Let λ = probability a judge wishes to increase the final grade. The probability of effective-manipulability of f is

λµ+(f , r) + (1 − λ)µ−(f , r) EM(f ) = max max . r=(r1,...,rn) 0≤λ≤1 n

Rida Laraki Majority Judgement Point-summing-methods, f 1 and f n maximize this probability.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability 2

The k-th order function f k allows n − k + 1 judges to increase the final grade and k judges to decrease it. At the extreme, f 1 allows all the juges to increase the final grade and f n allows all the juges to decrease the final grade : Extreme order-functions are more manipulable than central order functions. More an order function is close to the middle, less it is manipulable.

Let λ = probability a judge wishes to increase the final grade. The probability of effective-manipulability of f is

λµ+(f , r) + (1 − λ)µ−(f , r) EM(f ) = max max . r=(r1,...,rn) 0≤λ≤1 n

Theorem The unique aggregation functions that minimize the probability of effective-manipulability are the middlemost.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Minimizing manipulability 2

The k-th order function f k allows n − k + 1 judges to increase the final grade and k judges to decrease it. At the extreme, f 1 allows all the juges to increase the final grade and f n allows all the juges to decrease the final grade : Extreme order-functions are more manipulable than central order functions. More an order function is close to the middle, less it is manipulable.

Let λ = probability a judge wishes to increase the final grade. The probability of effective-manipulability of f is

λµ+(f , r) + (1 − λ)µ−(f , r) EM(f ) = max max . r=(r1,...,rn) 0≤λ≤1 n

Theorem The unique aggregation functions that minimize the probability of effective-manipulability are the middlemost. Point-summing-methods, f 1 and f n maximize this probability.

Rida Laraki Majority Judgement when all of A’s grades belong to the middlemost interval of B’s grades then A’s final grade is at least as high as B’s final grade. The majority-grade f maj is the lower-middlemost function.

Theorem A SGF f respects consensus iff f ≤ f maj . Majority-Grade is the unique middlemost SGF that respects consensus.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-grade

A SGF respects consensus if

Rida Laraki Majority Judgement A’s final grade is at least as high as B’s final grade. The majority-grade f maj is the lower-middlemost function.

Theorem A SGF f respects consensus iff f ≤ f maj . Majority-Grade is the unique middlemost SGF that respects consensus.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-grade

A SGF respects consensus if when all of A’s grades belong to the middlemost interval of B’s grades then

Rida Laraki Majority Judgement The majority-grade f maj is the lower-middlemost function.

Theorem A SGF f respects consensus iff f ≤ f maj . Majority-Grade is the unique middlemost SGF that respects consensus.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-grade

A SGF respects consensus if when all of A’s grades belong to the middlemost interval of B’s grades then A’s final grade is at least as high as B’s final grade.

Rida Laraki Majority Judgement Theorem A SGF f respects consensus iff f ≤ f maj . Majority-Grade is the unique middlemost SGF that respects consensus.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-grade

A SGF respects consensus if when all of A’s grades belong to the middlemost interval of B’s grades then A’s final grade is at least as high as B’s final grade. The majority-grade f maj is the lower-middlemost function.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-grade

A SGF respects consensus if when all of A’s grades belong to the middlemost interval of B’s grades then A’s final grade is at least as high as B’s final grade. The majority-grade f maj is the lower-middlemost function.

Theorem A SGF f respects consensus iff f ≤ f maj . Majority-Grade is the unique middlemost SGF that respects consensus.

Rida Laraki Majority Judgement Axiom I neutral: A S B for the profile Φ implies A S B for the profile σΦ, for σ any permutation of the competitors (or rows).

Axiom II anonymous: A S B for the profile Φ implies A S B for the profile Φσ, for σ any permutation of the judges (or columns).

Axiom III transitive: A S B and B S C implies A S C.

Axiom IV independent of irrelevant alternatives in ranking (IIAR) : if 0 A S B for the profile Φ then A S B for any profile Φ obtained from Φ by eliminating or adjoining some other competitor (or row).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Ranking Model

A method of ranking is a complete binary relation S that, for a given profile Φ, compares any two competitors. It should possess certain minimal properties.

Rida Laraki Majority Judgement Axiom II anonymous: A S B for the profile Φ implies A S B for the profile Φσ, for σ any permutation of the judges (or columns).

Axiom III transitive: A S B and B S C implies A S C.

Axiom IV independent of irrelevant alternatives in ranking (IIAR) : if 0 A S B for the profile Φ then A S B for any profile Φ obtained from Φ by eliminating or adjoining some other competitor (or row).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Ranking Model

A method of ranking is a complete binary relation S that, for a given profile Φ, compares any two competitors. It should possess certain minimal properties.

Axiom I neutral: A S B for the profile Φ implies A S B for the profile σΦ, for σ any permutation of the competitors (or rows).

Rida Laraki Majority Judgement Axiom III transitive: A S B and B S C implies A S C.

Axiom IV independent of irrelevant alternatives in ranking (IIAR) : if 0 A S B for the profile Φ then A S B for any profile Φ obtained from Φ by eliminating or adjoining some other competitor (or row).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Ranking Model

A method of ranking is a complete binary relation S that, for a given profile Φ, compares any two competitors. It should possess certain minimal properties.

Axiom I neutral: A S B for the profile Φ implies A S B for the profile σΦ, for σ any permutation of the competitors (or rows).

Axiom II anonymous: A S B for the profile Φ implies A S B for the profile Φσ, for σ any permutation of the judges (or columns).

Rida Laraki Majority Judgement Axiom IV independent of irrelevant alternatives in ranking (IIAR) : if 0 A S B for the profile Φ then A S B for any profile Φ obtained from Φ by eliminating or adjoining some other competitor (or row).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Ranking Model

A method of ranking is a complete binary relation S that, for a given profile Φ, compares any two competitors. It should possess certain minimal properties.

Axiom I neutral: A S B for the profile Φ implies A S B for the profile σΦ, for σ any permutation of the competitors (or rows).

Axiom II anonymous: A S B for the profile Φ implies A S B for the profile Φσ, for σ any permutation of the judges (or columns).

Axiom III transitive: A S B and B S C implies A S C.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The Ranking Model

A method of ranking is a complete binary relation S that, for a given profile Φ, compares any two competitors. It should possess certain minimal properties.

Axiom I neutral: A S B for the profile Φ implies A S B for the profile σΦ, for σ any permutation of the competitors (or rows).

Axiom II anonymous: A S B for the profile Φ implies A S B for the profile Φσ, for σ any permutation of the judges (or columns).

Axiom III transitive: A S B and B S C implies A S C.

Axiom IV independent of irrelevant alternatives in ranking (IIAR) : if 0 A S B for the profile Φ then A S B for any profile Φ obtained from Φ by eliminating or adjoining some other competitor (or row).

Rida Laraki Majority Judgement Theorem A method of ranking is neutral, anonymous, transitive and independent of irrelevant alternatives in ranking if and only if it is transitive, and respects grades.

A social ranking function (SRF) is a method of ranking that satisfies the four axioms.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Social Ranking Functions

A method of ranking respects grades if the rank-order between two candidates A and B depends only on their sets of grades. Thus, it matters not which judge gave which grade.

Rida Laraki Majority Judgement A social ranking function (SRF) is a method of ranking that satisfies the four axioms.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Social Ranking Functions

A method of ranking respects grades if the rank-order between two candidates A and B depends only on their sets of grades. Thus, it matters not which judge gave which grade.

Theorem A method of ranking is neutral, anonymous, transitive and independent of irrelevant alternatives in ranking if and only if it is transitive, and respects grades.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Social Ranking Functions

A method of ranking respects grades if the rank-order between two candidates A and B depends only on their sets of grades. Thus, it matters not which judge gave which grade.

Theorem A method of ranking is neutral, anonymous, transitive and independent of irrelevant alternatives in ranking if and only if it is transitive, and respects grades.

A social ranking function (SRF) is a method of ranking that satisfies the four axioms.

Rida Laraki Majority Judgement If the preference profile is 30% 10% 10% 25% 25% X : Good Good Pass Pass Bad Y : Pass Bad Good Bad Good X wins with 65% That’s correct. However, if the profile is 5% 35% 35% 25% X : Good Good Pass Bad Y : Pass Bad Good Pass Y wins with 60%. Simple majority rule may fail even with 2 candidates !

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Implications of respecting grades

Suppose an electorate evaluated two candidates as follows : Good Pass Bad X : 40% 35% 25% Y : 35% 30% 35% There is no doubt that X leads Y . What does a majority vote say ?

Rida Laraki Majority Judgement However, if the profile is 5% 35% 35% 25% X : Good Good Pass Bad Y : Pass Bad Good Pass Y wins with 60%. Simple majority rule may fail even with 2 candidates !

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Implications of respecting grades

Suppose an electorate evaluated two candidates as follows : Good Pass Bad X : 40% 35% 25% Y : 35% 30% 35% There is no doubt that X leads Y . What does a majority vote say ? If the preference profile is 30% 10% 10% 25% 25% X : Good Good Pass Pass Bad Y : Pass Bad Good Bad Good X wins with 65% That’s correct.

Rida Laraki Majority Judgement Simple majority rule may fail even with 2 candidates !

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Implications of respecting grades

Suppose an electorate evaluated two candidates as follows : Good Pass Bad X : 40% 35% 25% Y : 35% 30% 35% There is no doubt that X leads Y . What does a majority vote say ? If the preference profile is 30% 10% 10% 25% 25% X : Good Good Pass Pass Bad Y : Pass Bad Good Bad Good X wins with 65% That’s correct. However, if the profile is 5% 35% 35% 25% X : Good Good Pass Bad Y : Pass Bad Good Pass Y wins with 60%.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Implications of respecting grades

Suppose an electorate evaluated two candidates as follows : Good Pass Bad X : 40% 35% 25% Y : 35% 30% 35% There is no doubt that X leads Y . What does a majority vote say ? If the preference profile is 30% 10% 10% 25% 25% X : Good Good Pass Pass Bad Y : Pass Bad Good Bad Good X wins with 65% That’s correct. However, if the profile is 5% 35% 35% 25% X : Good Good Pass Bad Y : Pass Bad Good Pass Y wins with 60%. Simple majority rule may fail even with 2 candidates !

Rida Laraki Majority Judgement Theorem The Majority-ranking is a SRF that always ranks one competitor ahead of another unless the two are assigned an identical set of grades.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-ranking

The majority-ranking ( maj ) between two competitors is determined by : maj maj (1) If f (A) > f (B) then A maj B. (2) If f maj (A) = f maj (B), the majority-grade is dropped from the grades of each of the competitors, and the procedure is repeated.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-ranking

The majority-ranking ( maj ) between two competitors is determined by : maj maj (1) If f (A) > f (B) then A maj B. (2) If f maj (A) = f maj (B), the majority-grade is dropped from the grades of each of the competitors, and the procedure is repeated.

Theorem The Majority-ranking is a SRF that always ranks one competitor ahead of another unless the two are assigned an identical set of grades.

Rida Laraki Majority Judgement Anjou Bourgogne Chablis Very good Excellent Excellent Very good Very good Excellent Good Good Passable Passable Mediocre Mediocre

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions An example : ranking three wines

Anjou Bourgogne Chablis Very good Excellent Excellent Very good Very good Excellent Good Good Good Good Good Passable Passable Mediocre Mediocre

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions An example : ranking three wines

Anjou Bourgogne Chablis Very good Excellent Excellent Very good Very good Excellent Good Good Good Good Good Passable Passable Mediocre Mediocre

Anjou Bourgogne Chablis Very good Excellent Excellent Very good Very good Excellent Good Good Passable Passable Mediocre Mediocre

Rida Laraki Majority Judgement Anjou Bourgogne Very good Excellent Passable Mediocre

Therefore : Anjou Bourgogne Chablis

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority judgement : ranking three wines

Anjou Bourgogne Very good Excellent Very good Very good Passable Mediocre

Rida Laraki Majority Judgement Therefore : Anjou Bourgogne Chablis

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority judgement : ranking three wines

Anjou Bourgogne Very good Excellent Very good Very good Passable Mediocre

Anjou Bourgogne Very good Excellent Passable Mediocre

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority judgement : ranking three wines

Anjou Bourgogne Very good Excellent Very good Very good Passable Mediocre

Anjou Bourgogne Very good Excellent Passable Mediocre

Therefore : Anjou Bourgogne Chablis

Rida Laraki Majority Judgement be choice-monotone : if A S B and one judge raises the grade he gives to A then A S B ; be decisive for the center grades : the ranking between A and B is determined by the center grades, unless that ranking is a tie ; it is then determined by the residual grades ; reward consensus : when all A’s grades belong to the middlemost interval of B’s grades, A is ranked above B.

A social ranking function (SRF) should :

Theorem The majority-ranking is the unique choice-monotone SRF that is decisive for the center and rewards consensus.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-ranking : characterization

The highest and lowest grades are r’s residual grades ; the others are center grades.

Rida Laraki Majority Judgement be choice-monotone : if A S B and one judge raises the grade he gives to A then A S B ; be decisive for the center grades : the ranking between A and B is determined by the center grades, unless that ranking is a tie ; it is then determined by the residual grades ; reward consensus : when all A’s grades belong to the middlemost interval of B’s grades, A is ranked above B.

Theorem The majority-ranking is the unique choice-monotone SRF that is decisive for the center and rewards consensus.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-ranking : characterization

The highest and lowest grades are r’s residual grades ; the others are center grades. A social ranking function (SRF) should :

Rida Laraki Majority Judgement be decisive for the center grades : the ranking between A and B is determined by the center grades, unless that ranking is a tie ; it is then determined by the residual grades ; reward consensus : when all A’s grades belong to the middlemost interval of B’s grades, A is ranked above B.

Theorem The majority-ranking is the unique choice-monotone SRF that is decisive for the center and rewards consensus.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-ranking : characterization

The highest and lowest grades are r’s residual grades ; the others are center grades. A social ranking function (SRF) should :

be choice-monotone : if A S B and one judge raises the grade he gives to A then A S B ;

Rida Laraki Majority Judgement reward consensus : when all A’s grades belong to the middlemost interval of B’s grades, A is ranked above B.

Theorem The majority-ranking is the unique choice-monotone SRF that is decisive for the center and rewards consensus.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-ranking : characterization

The highest and lowest grades are r’s residual grades ; the others are center grades. A social ranking function (SRF) should :

be choice-monotone : if A S B and one judge raises the grade he gives to A then A S B ; be decisive for the center grades : the ranking between A and B is determined by the center grades, unless that ranking is a tie ; it is then determined by the residual grades ;

Rida Laraki Majority Judgement Theorem The majority-ranking is the unique choice-monotone SRF that is decisive for the center and rewards consensus.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-ranking : characterization

The highest and lowest grades are r’s residual grades ; the others are center grades. A social ranking function (SRF) should :

be choice-monotone : if A S B and one judge raises the grade he gives to A then A S B ; be decisive for the center grades : the ranking between A and B is determined by the center grades, unless that ranking is a tie ; it is then determined by the residual grades ; reward consensus : when all A’s grades belong to the middlemost interval of B’s grades, A is ranked above B.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-ranking : characterization

The highest and lowest grades are r’s residual grades ; the others are center grades. A social ranking function (SRF) should :

be choice-monotone : if A S B and one judge raises the grade he gives to A then A S B ; be decisive for the center grades : the ranking between A and B is determined by the center grades, unless that ranking is a tie ; it is then determined by the residual grades ; reward consensus : when all A’s grades belong to the middlemost interval of B’s grades, A is ranked above B.

Theorem The majority-ranking is the unique choice-monotone SRF that is decisive for the center and rewards consensus.

Rida Laraki Majority Judgement p is the number or percentage of the competitor’s grades above the majority-grade,  α+ if p > q, α∗= where α is the competitor’s majority-grade, and α− if p ≤ q, q is the number or percentage of the competitor’s grades below the majority-grade.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority-gauge

The majority-gauge of a competitor is a triple (p, α∗, q), where

Rida Laraki Majority Judgement  α+ if p > q, α∗= where α is the competitor’s majority-grade, and α− if p ≤ q, q is the number or percentage of the competitor’s grades below the majority-grade.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority-gauge

The majority-gauge of a competitor is a triple (p, α∗, q), where p is the number or percentage of the competitor’s grades above the majority-grade,

Rida Laraki Majority Judgement q is the number or percentage of the competitor’s grades below the majority-grade.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority-gauge

The majority-gauge of a competitor is a triple (p, α∗, q), where p is the number or percentage of the competitor’s grades above the majority-grade,  α+ if p > q, α∗= where α is the competitor’s majority-grade, and α− if p ≤ q,

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions The majority-gauge

The majority-gauge of a competitor is a triple (p, α∗, q), where p is the number or percentage of the competitor’s grades above the majority-grade,  α+ if p > q, α∗= where α is the competitor’s majority-grade, and α− if p ≤ q, q is the number or percentage of the competitor’s grades below the majority-grade.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-gauge-ranking

Consider two candidates X and Y with majority-gauges (p, α∗, q) and (r, β∗, s). The majority-gauge-ranking places X ahead of Y , when

α∗ β∗, or α∗ = β∗ = α+ and p > r, or α∗ = β∗ = α− and q < s.

Theorem When the majority-gauge-ranking places a competitor X ahead of another Y , so does the majority-ranking.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority-gauge-ranking : French Elections, 2007

Higher The Lower Official Ntnl M-G M-G M-G vote vote 3 Bayrou 44.3% Good+ 30.6% 25.5% 18.6% 2 Royal 39.4% Good- 41.5% 29.9% 25.9% 1 Sarkozy 38.9% Good- 46.9% 29.0% 31.2% 8 Voynet 29.8% Acceptable- 46.6% 1.7% 1.6% 5 Besancenot 46.3% Poor+ 31.2% 2.5% 4.1% 7 Buffet 43.2% Poor+ 30.5% 1.4% 1.9% 10 Bové 34.9% Poor- 39.4% 0.9% 1.3% 9 Laguiller 34.2% Poor- 40.0% 0.8% 1.3% 11 Nihous 45.0% To reject- 0.3% 1.2% 6 Villiers 44.5% To reject- 1.9% 2.2% 12 Schivardi 39.7% To reject- 0.2% 0.3% 4 Le Pen 25.7% To reject- 5.9% 10.4%

Majority-gauge (p, α±, q)

Rida Laraki Majority Judgement BR-Majoritariane : for any candidate X and any strategy of a minority, the majority has a strategy that elects X . Examples : All reasonable methods : Borda, Condorcet, approval, 1- and 2-past-the-post, transferable-vote, majority-judgement.

Theorem Any candidate could be a Nash-equilibrium winner. If a candidate is a strong-equilibrium winner, it must be a Condorcet-winner.

Theorem No method elects the Condorcet-winner as a Nash equilibrium with the honest grades. With majority judgement, there exists strong-equilibria where the Condorcet winner is elected with his true majority grade and the majority of grades received a candidate are honest.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Nash and Strong Equilibria

Suppose utilities depend only on the winner and the method is :

Rida Laraki Majority Judgement Examples : All reasonable methods : Borda, Condorcet, approval, 1- and 2-past-the-post, transferable-vote, majority-judgement.

Theorem Any candidate could be a Nash-equilibrium winner. If a candidate is a strong-equilibrium winner, it must be a Condorcet-winner.

Theorem No method elects the Condorcet-winner as a Nash equilibrium with the honest grades. With majority judgement, there exists strong-equilibria where the Condorcet winner is elected with his true majority grade and the majority of grades received a candidate are honest.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Nash and Strong Equilibria

Suppose utilities depend only on the winner and the method is : BR-Majoritariane : for any candidate X and any strategy of a minority, the majority has a strategy that elects X .

Rida Laraki Majority Judgement Theorem Any candidate could be a Nash-equilibrium winner. If a candidate is a strong-equilibrium winner, it must be a Condorcet-winner.

Theorem No method elects the Condorcet-winner as a Nash equilibrium with the honest grades. With majority judgement, there exists strong-equilibria where the Condorcet winner is elected with his true majority grade and the majority of grades received a candidate are honest.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Nash and Strong Equilibria

Suppose utilities depend only on the winner and the method is : BR-Majoritariane : for any candidate X and any strategy of a minority, the majority has a strategy that elects X . Examples : All reasonable methods : Borda, Condorcet, approval, 1- and 2-past-the-post, transferable-vote, majority-judgement.

Rida Laraki Majority Judgement If a candidate is a strong-equilibrium winner, it must be a Condorcet-winner.

Theorem No method elects the Condorcet-winner as a Nash equilibrium with the honest grades. With majority judgement, there exists strong-equilibria where the Condorcet winner is elected with his true majority grade and the majority of grades received a candidate are honest.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Nash and Strong Equilibria

Suppose utilities depend only on the winner and the method is : BR-Majoritariane : for any candidate X and any strategy of a minority, the majority has a strategy that elects X . Examples : All reasonable methods : Borda, Condorcet, approval, 1- and 2-past-the-post, transferable-vote, majority-judgement.

Theorem Any candidate could be a Nash-equilibrium winner.

Rida Laraki Majority Judgement Theorem No method elects the Condorcet-winner as a Nash equilibrium with the honest grades. With majority judgement, there exists strong-equilibria where the Condorcet winner is elected with his true majority grade and the majority of grades received a candidate are honest.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Nash and Strong Equilibria

Suppose utilities depend only on the winner and the method is : BR-Majoritariane : for any candidate X and any strategy of a minority, the majority has a strategy that elects X . Examples : All reasonable methods : Borda, Condorcet, approval, 1- and 2-past-the-post, transferable-vote, majority-judgement.

Theorem Any candidate could be a Nash-equilibrium winner. If a candidate is a strong-equilibrium winner, it must be a Condorcet-winner.

Rida Laraki Majority Judgement With majority judgement, there exists strong-equilibria where the Condorcet winner is elected with his true majority grade and the majority of grades received a candidate are honest.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Nash and Strong Equilibria

Suppose utilities depend only on the winner and the method is : BR-Majoritariane : for any candidate X and any strategy of a minority, the majority has a strategy that elects X . Examples : All reasonable methods : Borda, Condorcet, approval, 1- and 2-past-the-post, transferable-vote, majority-judgement.

Theorem Any candidate could be a Nash-equilibrium winner. If a candidate is a strong-equilibrium winner, it must be a Condorcet-winner.

Theorem No method elects the Condorcet-winner as a Nash equilibrium with the honest grades.

Rida Laraki Majority Judgement the Condorcet winner is elected with his true majority grade and the majority of grades received a candidate are honest.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Nash and Strong Equilibria

Suppose utilities depend only on the winner and the method is : BR-Majoritariane : for any candidate X and any strategy of a minority, the majority has a strategy that elects X . Examples : All reasonable methods : Borda, Condorcet, approval, 1- and 2-past-the-post, transferable-vote, majority-judgement.

Theorem Any candidate could be a Nash-equilibrium winner. If a candidate is a strong-equilibrium winner, it must be a Condorcet-winner.

Theorem No method elects the Condorcet-winner as a Nash equilibrium with the honest grades. With majority judgement, there exists strong-equilibria where

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Nash and Strong Equilibria

Suppose utilities depend only on the winner and the method is : BR-Majoritariane : for any candidate X and any strategy of a minority, the majority has a strategy that elects X . Examples : All reasonable methods : Borda, Condorcet, approval, 1- and 2-past-the-post, transferable-vote, majority-judgement.

Theorem Any candidate could be a Nash-equilibrium winner. If a candidate is a strong-equilibrium winner, it must be a Condorcet-winner.

Theorem No method elects the Condorcet-winner as a Nash equilibrium with the honest grades. With majority judgement, there exists strong-equilibria where the Condorcet winner is elected with his true majority grade and the majority of grades received a candidate are honest.

Rida Laraki Majority Judgement Nominal measurement : the meaningful comparisons are “the same” and “different”(e.g., the number of a bus, a person’s blood type, the telephone code of a country). Ordinal measurement : the meaningful comparisons are equality and “above” or “below” (e.g., letter grades on students’ exams, the Mohs scale of mineral hardness, the modified Mercalli Intensity Scale, the several scales of pain). Interval measurement : ordinal comparisons are meaningful, but so too are addition, subtraction and averages (e.g., Gregorian, Hebrew or Moslem calendars, Celsius and Fahrenheit temperatures). Equal intervals have same meaning. Ratio measurement : multiplying and dividing the numbers of the scale makes sense, in addition to what made sense before (e.g., price, length, mass, the Kelvin temperature scale).

The four types of measurement :

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

Rida Laraki Majority Judgement Nominal measurement : the meaningful comparisons are “the same” and “different”(e.g., the number of a bus, a person’s blood type, the telephone code of a country). Ordinal measurement : the meaningful comparisons are equality and “above” or “below” (e.g., letter grades on students’ exams, the Mohs scale of mineral hardness, the modified Mercalli Intensity Scale, the several scales of pain). Interval measurement : ordinal comparisons are meaningful, but so too are addition, subtraction and averages (e.g., Gregorian, Hebrew or Moslem calendars, Celsius and Fahrenheit temperatures). Equal intervals have same meaning. Ratio measurement : multiplying and dividing the numbers of the scale makes sense, in addition to what made sense before (e.g., price, length, mass, the Kelvin temperature scale).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

The four types of measurement :

Rida Laraki Majority Judgement Ordinal measurement : the meaningful comparisons are equality and “above” or “below” (e.g., letter grades on students’ exams, the Mohs scale of mineral hardness, the modified Mercalli Intensity Scale, the several scales of pain). Interval measurement : ordinal comparisons are meaningful, but so too are addition, subtraction and averages (e.g., Gregorian, Hebrew or Moslem calendars, Celsius and Fahrenheit temperatures). Equal intervals have same meaning. Ratio measurement : multiplying and dividing the numbers of the scale makes sense, in addition to what made sense before (e.g., price, length, mass, the Kelvin temperature scale).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

The four types of measurement : Nominal measurement : the meaningful comparisons are “the same” and “different”(e.g., the number of a bus, a person’s blood type, the telephone code of a country).

Rida Laraki Majority Judgement Interval measurement : ordinal comparisons are meaningful, but so too are addition, subtraction and averages (e.g., Gregorian, Hebrew or Moslem calendars, Celsius and Fahrenheit temperatures). Equal intervals have same meaning. Ratio measurement : multiplying and dividing the numbers of the scale makes sense, in addition to what made sense before (e.g., price, length, mass, the Kelvin temperature scale).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

The four types of measurement : Nominal measurement : the meaningful comparisons are “the same” and “different”(e.g., the number of a bus, a person’s blood type, the telephone code of a country). Ordinal measurement : the meaningful comparisons are equality and “above” or “below” (e.g., letter grades on students’ exams, the Mohs scale of mineral hardness, the modified Mercalli Intensity Scale, the several scales of pain).

Rida Laraki Majority Judgement Ratio measurement : multiplying and dividing the numbers of the scale makes sense, in addition to what made sense before (e.g., price, length, mass, the Kelvin temperature scale).

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

The four types of measurement : Nominal measurement : the meaningful comparisons are “the same” and “different”(e.g., the number of a bus, a person’s blood type, the telephone code of a country). Ordinal measurement : the meaningful comparisons are equality and “above” or “below” (e.g., letter grades on students’ exams, the Mohs scale of mineral hardness, the modified Mercalli Intensity Scale, the several scales of pain). Interval measurement : ordinal comparisons are meaningful, but so too are addition, subtraction and averages (e.g., Gregorian, Hebrew or Moslem calendars, Celsius and Fahrenheit temperatures). Equal intervals have same meaning.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

The four types of measurement : Nominal measurement : the meaningful comparisons are “the same” and “different”(e.g., the number of a bus, a person’s blood type, the telephone code of a country). Ordinal measurement : the meaningful comparisons are equality and “above” or “below” (e.g., letter grades on students’ exams, the Mohs scale of mineral hardness, the modified Mercalli Intensity Scale, the several scales of pain). Interval measurement : ordinal comparisons are meaningful, but so too are addition, subtraction and averages (e.g., Gregorian, Hebrew or Moslem calendars, Celsius and Fahrenheit temperatures). Equal intervals have same meaning. Ratio measurement : multiplying and dividing the numbers of the scale makes sense, in addition to what made sense before (e.g., price, length, mass, the Kelvin temperature scale).

Rida Laraki Majority Judgement The “representation problem” : How to assign scale values to empirical observations. The “meaningfulness problem” : What analyses and statements about empirical observations are meaningful given the type of scale values. Common languages of grading are ordinal measures. A scale S is a set of functions from a set which is to be measured X into the real numbers. Each element φ ∈ S is a representation.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

Rida Laraki Majority Judgement The “meaningfulness problem” : What analyses and statements about empirical observations are meaningful given the type of scale values. Common languages of grading are ordinal measures. A scale S is a set of functions from a set which is to be measured X into the real numbers. Each element φ ∈ S is a representation.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

The “representation problem” : How to assign scale values to empirical observations.

Rida Laraki Majority Judgement Common languages of grading are ordinal measures. A scale S is a set of functions from a set which is to be measured X into the real numbers. Each element φ ∈ S is a representation.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

The “representation problem” : How to assign scale values to empirical observations. The “meaningfulness problem” : What analyses and statements about empirical observations are meaningful given the type of scale values.

Rida Laraki Majority Judgement A scale S is a set of functions from a set which is to be measured X into the real numbers. Each element φ ∈ S is a representation.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

The “representation problem” : How to assign scale values to empirical observations. The “meaningfulness problem” : What analyses and statements about empirical observations are meaningful given the type of scale values. Common languages of grading are ordinal measures.

Rida Laraki Majority Judgement Each element φ ∈ S is a representation.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

The “representation problem” : How to assign scale values to empirical observations. The “meaningfulness problem” : What analyses and statements about empirical observations are meaningful given the type of scale values. Common languages of grading are ordinal measures. A scale S is a set of functions from a set which is to be measured X into the real numbers.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

The “representation problem” : How to assign scale values to empirical observations. The “meaningfulness problem” : What analyses and statements about empirical observations are meaningful given the type of scale values. Common languages of grading are ordinal measures. A scale S is a set of functions from a set which is to be measured X into the real numbers. Each element φ ∈ S is a representation.

Rida Laraki Majority Judgement an ordinal scale if for every φ ∈ S the range of φ is an interval of the reals and S = {f (φ): f is a strictly monotonic function of φ onto φ} ; an interval scale if for every φ ∈ S, S = {rφ + s : r > 0 and s real} ; a ratio scale if for every φ ∈ S, S = {rφ : r > 0}.

A scale S is :

If something is claimed for an attribute that is measured by a particular representation of a scale S, then it is meaningful if the same claim is true measured by any other representation of S. Different number grades are not related by a simple change in scale : A school grade of 10 on a scale of [0, 20] in France has an entirely different meaning than a 50 on a scale of [0, 100] in the United States. Yet the particular scale should make no difference in the ultimate outcomes.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

Rida Laraki Majority Judgement an ordinal scale if for every φ ∈ S the range of φ is an interval of the reals and S = {f (φ): f is a strictly monotonic function of φ onto φ} ; an interval scale if for every φ ∈ S, S = {rφ + s : r > 0 and s real} ; a ratio scale if for every φ ∈ S, S = {rφ : r > 0}.

If something is claimed for an attribute that is measured by a particular representation of a scale S, then it is meaningful if the same claim is true measured by any other representation of S. Different number grades are not related by a simple change in scale : A school grade of 10 on a scale of [0, 20] in France has an entirely different meaning than a 50 on a scale of [0, 100] in the United States. Yet the particular scale should make no difference in the ultimate outcomes.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

A scale S is :

Rida Laraki Majority Judgement an interval scale if for every φ ∈ S, S = {rφ + s : r > 0 and s real} ; a ratio scale if for every φ ∈ S, S = {rφ : r > 0}.

If something is claimed for an attribute that is measured by a particular representation of a scale S, then it is meaningful if the same claim is true measured by any other representation of S. Different number grades are not related by a simple change in scale : A school grade of 10 on a scale of [0, 20] in France has an entirely different meaning than a 50 on a scale of [0, 100] in the United States. Yet the particular scale should make no difference in the ultimate outcomes.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

A scale S is : an ordinal scale if for every φ ∈ S the range of φ is an interval of the reals and S = {f (φ): f is a strictly monotonic function of φ onto φ} ;

Rida Laraki Majority Judgement a ratio scale if for every φ ∈ S, S = {rφ : r > 0}.

If something is claimed for an attribute that is measured by a particular representation of a scale S, then it is meaningful if the same claim is true measured by any other representation of S. Different number grades are not related by a simple change in scale : A school grade of 10 on a scale of [0, 20] in France has an entirely different meaning than a 50 on a scale of [0, 100] in the United States. Yet the particular scale should make no difference in the ultimate outcomes.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

A scale S is : an ordinal scale if for every φ ∈ S the range of φ is an interval of the reals and S = {f (φ): f is a strictly monotonic function of φ onto φ} ; an interval scale if for every φ ∈ S, S = {rφ + s : r > 0 and s real} ;

Rida Laraki Majority Judgement If something is claimed for an attribute that is measured by a particular representation of a scale S, then it is meaningful if the same claim is true measured by any other representation of S. Different number grades are not related by a simple change in scale : A school grade of 10 on a scale of [0, 20] in France has an entirely different meaning than a 50 on a scale of [0, 100] in the United States. Yet the particular scale should make no difference in the ultimate outcomes.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

A scale S is : an ordinal scale if for every φ ∈ S the range of φ is an interval of the reals and S = {f (φ): f is a strictly monotonic function of φ onto φ} ; an interval scale if for every φ ∈ S, S = {rφ + s : r > 0 and s real} ; a ratio scale if for every φ ∈ S, S = {rφ : r > 0}.

Rida Laraki Majority Judgement Different number grades are not related by a simple change in scale : A school grade of 10 on a scale of [0, 20] in France has an entirely different meaning than a 50 on a scale of [0, 100] in the United States. Yet the particular scale should make no difference in the ultimate outcomes.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

A scale S is : an ordinal scale if for every φ ∈ S the range of φ is an interval of the reals and S = {f (φ): f is a strictly monotonic function of φ onto φ} ; an interval scale if for every φ ∈ S, S = {rφ + s : r > 0 and s real} ; a ratio scale if for every φ ∈ S, S = {rφ : r > 0}.

If something is claimed for an attribute that is measured by a particular representation of a scale S, then it is meaningful if the same claim is true measured by any other representation of S.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Measurement theory

A scale S is : an ordinal scale if for every φ ∈ S the range of φ is an interval of the reals and S = {f (φ): f is a strictly monotonic function of φ onto φ} ; an interval scale if for every φ ∈ S, S = {rφ + s : r > 0 and s real} ; a ratio scale if for every φ ∈ S, S = {rφ : r > 0}.

If something is claimed for an attribute that is measured by a particular representation of a scale S, then it is meaningful if the same claim is true measured by any other representation of S. Different number grades are not related by a simple change in scale : A school grade of 10 on a scale of [0, 20] in France has an entirely different meaning than a 50 on a scale of [0, 100] in the United States. Yet the particular scale should make no difference in the ultimate outcomes.

Rida Laraki Majority Judgement Theorem The unique language-consistent SGFs are the order functions.

Recall : The function that associates to a set of grades the kth highest grade is the kth-order function f k . The majority-grade is the lower-middlemost order function.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

An aggregation function f is language-consistent if

f φ(r1), . . . , φ(rn) = φ(f (r1,..., rn)

for all increasing, continuous functions

φ :[0, R] → [R, R], φ(0) = R, φ(R) = R

Rida Laraki Majority Judgement Recall : The function that associates to a set of grades the kth highest grade is the kth-order function f k . The majority-grade is the lower-middlemost order function.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

An aggregation function f is language-consistent if

f φ(r1), . . . , φ(rn) = φ(f (r1,..., rn)

for all increasing, continuous functions

φ :[0, R] → [R, R], φ(0) = R, φ(R) = R

Theorem The unique language-consistent SGFs are the order functions.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

An aggregation function f is language-consistent if

f φ(r1), . . . , φ(rn) = φ(f (r1,..., rn)

for all increasing, continuous functions

φ :[0, R] → [R, R], φ(0) = R, φ(R) = R

Theorem The unique language-consistent SGFs are the order functions.

Recall : The function that associates to a set of grades the kth highest grade is the kth-order function f k . The majority-grade is the lower-middlemost order function.

Rida Laraki Majority Judgement An aggregation function f is order-consistent if

f (r1,..., rn) ≥ f (s1,..., sn) implies

f φ(r1), . . . , φ(rn) ≥ f φ(s1), . . . , φ(sn) , for all increasing, continuous functions

φ :[0, R] → [R, R], φ(0) = R, φ(R) = R.

Theorem The unique SGFs that are order-consistent are the order functions.

For point-summing methods to be meaningful the parametrization of the language must induce a scale that is an interval measure. This is impossible in elections.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

Rida Laraki Majority Judgement Theorem The unique SGFs that are order-consistent are the order functions.

For point-summing methods to be meaningful the parametrization of the language must induce a scale that is an interval measure. This is impossible in elections.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

An aggregation function f is order-consistent if

f (r1,..., rn) ≥ f (s1,..., sn) implies

f φ(r1), . . . , φ(rn) ≥ f φ(s1), . . . , φ(sn) , for all increasing, continuous functions

φ :[0, R] → [R, R], φ(0) = R, φ(R) = R.

Rida Laraki Majority Judgement For point-summing methods to be meaningful the parametrization of the language must induce a scale that is an interval measure. This is impossible in elections.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

An aggregation function f is order-consistent if

f (r1,..., rn) ≥ f (s1,..., sn) implies

f φ(r1), . . . , φ(rn) ≥ f φ(s1), . . . , φ(sn) , for all increasing, continuous functions

φ :[0, R] → [R, R], φ(0) = R, φ(R) = R.

Theorem The unique SGFs that are order-consistent are the order functions.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

An aggregation function f is order-consistent if

f (r1,..., rn) ≥ f (s1,..., sn) implies

f φ(r1), . . . , φ(rn) ≥ f φ(s1), . . . , φ(sn) , for all increasing, continuous functions

φ :[0, R] → [R, R], φ(0) = R, φ(R) = R.

Theorem The unique SGFs that are order-consistent are the order functions.

For point-summing methods to be meaningful the parametrization of the language must induce a scale that is an interval measure. This is impossible in elections.

Rida Laraki Majority Judgement When each judge uses her/his own language, the only meaningful information is the order of his preferences. A SGF f is preference-consistent if

f (r1,..., rn) ≥ f (s1,..., sn) implies

f φ1(r1), . . . , φn(rn) ≥ f φ1(s1), . . . , φn(sn) , for all increasing, continuous functions

φj :[0, R] → [R, R], φj (0) = R, φj (R) = R.

Theorem (Arrow’s impossibility) There exists no preference-consistent SGF.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

Measuring competitors to compare them depends crucially on judges using a common language in assigning grades.

Rida Laraki Majority Judgement A SGF f is preference-consistent if

f (r1,..., rn) ≥ f (s1,..., sn) implies

f φ1(r1), . . . , φn(rn) ≥ f φ1(s1), . . . , φn(sn) , for all increasing, continuous functions

φj :[0, R] → [R, R], φj (0) = R, φj (R) = R.

Theorem (Arrow’s impossibility) There exists no preference-consistent SGF.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

Measuring competitors to compare them depends crucially on judges using a common language in assigning grades. When each judge uses her/his own language, the only meaningful information is the order of his preferences.

Rida Laraki Majority Judgement Theorem (Arrow’s impossibility) There exists no preference-consistent SGF.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

Measuring competitors to compare them depends crucially on judges using a common language in assigning grades. When each judge uses her/his own language, the only meaningful information is the order of his preferences. A SGF f is preference-consistent if

f (r1,..., rn) ≥ f (s1,..., sn) implies

f φ1(r1), . . . , φn(rn) ≥ f φ1(s1), . . . , φn(sn) , for all increasing, continuous functions

φj :[0, R] → [R, R], φj (0) = R, φj (R) = R.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Meaningfulness in the new model

Measuring competitors to compare them depends crucially on judges using a common language in assigning grades. When each judge uses her/his own language, the only meaningful information is the order of his preferences. A SGF f is preference-consistent if

f (r1,..., rn) ≥ f (s1,..., sn) implies

f φ1(r1), . . . , φn(rn) ≥ f φ1(s1), . . . , φn(sn) , for all increasing, continuous functions

φj :[0, R] → [R, R], φj (0) = R, φj (R) = R.

Theorem (Arrow’s impossibility) There exists no preference-consistent SGF.

Rida Laraki Majority Judgement Theorem The majority ranking is the unique choice-monotone, meaningful SRF that minimizes the probability of cheating and rewards consensus.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority Judgment Second Characterization

A SRF is choice-monotone if A S B and one judge raises the grade he gives to A then A S B. This is a natural idea that helps to resolve potential ties.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Majority Judgment Second Characterization

A SRF is choice-monotone if A S B and one judge raises the grade he gives to A then A S B. This is a natural idea that helps to resolve potential ties.

Theorem The majority ranking is the unique choice-monotone, meaningful SRF that minimizes the probability of cheating and rewards consensus.

Rida Laraki Majority Judgement Average numbers of each grade per ballot show the language was common :

3 1st 6th 12th Samples of 100 Dsjt samples of 50 prcts. prct. prct. prct. Avg. (σ) Rg Avg. (σ) Rg Excll 0.7 0.7 0.7 0.7 0.7 (.07) 0.6/0.8 0.7 (.12) 0.5/0.9 V.Good 1.3 1.2 1.2 1.4 1.2 (.13) 1.1/1.5 1.3 (.16) 1.1/1.5 Good 1.5 1.5 1.4 1.6 1.5 (.13) 1.4/1.7 1.5 (.27) 0.9/1.8 Accp 1.7 1.7 1.7 1.8 1.8 (.15) 1.7/2.1 1.7 (.27) 2.1/2.6 Poor 2.3 2.3 2.3 2.2 2.3 (.19) 2.1/2.7 2.3 (.19) 2.1/2.6 Rjct 4.6 4.8 4.6 4.3 4.5 (.29) 4.1/4.8 4.5 (.41) 4.1/5.3

Yet, the majority judgement winner not the same in all 3 precincts.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Was the language common to French voters ?

Rida Laraki Majority Judgement 3 1st 6th 12th Samples of 100 Dsjt samples of 50 prcts. prct. prct. prct. Avg. (σ) Rg Avg. (σ) Rg Excll 0.7 0.7 0.7 0.7 0.7 (.07) 0.6/0.8 0.7 (.12) 0.5/0.9 V.Good 1.3 1.2 1.2 1.4 1.2 (.13) 1.1/1.5 1.3 (.16) 1.1/1.5 Good 1.5 1.5 1.4 1.6 1.5 (.13) 1.4/1.7 1.5 (.27) 0.9/1.8 Accp 1.7 1.7 1.7 1.8 1.8 (.15) 1.7/2.1 1.7 (.27) 2.1/2.6 Poor 2.3 2.3 2.3 2.2 2.3 (.19) 2.1/2.7 2.3 (.19) 2.1/2.6 Rjct 4.6 4.8 4.6 4.3 4.5 (.29) 4.1/4.8 4.5 (.41) 4.1/5.3

Yet, the majority judgement winner not the same in all 3 precincts.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Was the language common to French voters ?

Average numbers of each grade per ballot show the language was common :

Rida Laraki Majority Judgement Yet, the majority judgement winner not the same in all 3 precincts.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Was the language common to French voters ?

Average numbers of each grade per ballot show the language was common :

3 1st 6th 12th Samples of 100 Dsjt samples of 50 prcts. prct. prct. prct. Avg. (σ) Rg Avg. (σ) Rg Excll 0.7 0.7 0.7 0.7 0.7 (.07) 0.6/0.8 0.7 (.12) 0.5/0.9 V.Good 1.3 1.2 1.2 1.4 1.2 (.13) 1.1/1.5 1.3 (.16) 1.1/1.5 Good 1.5 1.5 1.4 1.6 1.5 (.13) 1.4/1.7 1.5 (.27) 0.9/1.8 Accp 1.7 1.7 1.7 1.8 1.8 (.15) 1.7/2.1 1.7 (.27) 2.1/2.6 Poor 2.3 2.3 2.3 2.2 2.3 (.19) 2.1/2.7 2.3 (.19) 2.1/2.6 Rjct 4.6 4.8 4.6 4.3 4.5 (.29) 4.1/4.8 4.5 (.41) 4.1/5.3

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Was the language common to French voters ?

Average numbers of each grade per ballot show the language was common :

3 1st 6th 12th Samples of 100 Dsjt samples of 50 prcts. prct. prct. prct. Avg. (σ) Rg Avg. (σ) Rg Excll 0.7 0.7 0.7 0.7 0.7 (.07) 0.6/0.8 0.7 (.12) 0.5/0.9 V.Good 1.3 1.2 1.2 1.4 1.2 (.13) 1.1/1.5 1.3 (.16) 1.1/1.5 Good 1.5 1.5 1.4 1.6 1.5 (.13) 1.4/1.7 1.5 (.27) 0.9/1.8 Accp 1.7 1.7 1.7 1.8 1.8 (.15) 1.7/2.1 1.7 (.27) 2.1/2.6 Poor 2.3 2.3 2.3 2.2 2.3 (.19) 2.1/2.7 2.3 (.19) 2.1/2.6 Rjct 4.6 4.8 4.6 4.3 4.5 (.29) 4.1/4.8 4.5 (.41) 4.1/5.3

Yet, the majority judgement winner not the same in all 3 precincts.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Was the language common to French voters ?

% number of times grades used in a ballot Prct 0 1 2 3 4 5 6 7 +8 1st 47.0 43.1 7.7 1.6 0.2 0.2 0.0 0.0 0.2 Exc 6th 46.6 41.8 8.7 2.0 0.7 0.0 0.2 0.0 0.2 12th 51.1 37.3 7.9 2.3 0.9 0.2 0.0 0.0 0.3 1st 30.2 40.3 19.7 6.8 1.1 1.3 0.5 0.2 0.0 VG 6th 28.8 37.9 22.0 7.2 2.7 0.8 0.3 0.3 0.0 12th 26.0 37.9 20.4 8.2 4.4 2.1 0.7 0.3 0.0 1st 24.3 35.1 22.2 11.4 4.7 1.4 0.7 0.2 0.0 Gd 6th 26.3 35.1 20.5 10.1 5.3 2.2 0.3 0.2 0.0 12th 21.8 30.4 25.5 12.0 7.2 2.3 0.3 0.3 0.2 1st 23.3 29.3 20.0 16.8 6.4 3.6 0.2 0.0 0.4 Acc 6th 22.6 28.8 24.1 13.0 6.5 3.7 0.3 0.5 0.5 12th 22.5 23.0 24.6 17.1 7.3 3.8 0.5 0.9 0.2 1st 16.5 20.0 22.9 15.9 14.0 5.5 2.9 1.4 0.9 Pr 6th 16.3 24.0 19.5 17.0 9.5 5.7 5.8 1.0 1.3 12th 23.2 20.8 18.5 15.2 10.6 6.1 3.1 1.4 1.0 1st 3.0 6.1 10.7 12.0 16.3 17.2 10.4 9.3 15.0 TR 6th 4.7 4.7 9.2 17.0 18.1 14.5 11.0 7.3 13.6 12th 7.0 7.3 14.5 14.0 14.5 13.8 7.3 7.0 14.7

Rida Laraki Majority Judgement Underlying idea : distribution of the students’ grades is uniform in interval [2, 12]. Which of the five passing grades should be assigned to a 5.7 ? The grade {2, 4, 7, 10, 12} closest to 5.7, namely,7 or good. Interval [2, 12] is partitioned into :

2← →4← →7← →10← →12 h z }| { z }| { z }| { z }| { z }| { i [2, 3] [3, 5.5] [5.5, 8.5] [8.5, 11] [11, 12] ,

the five succeeding intervals occupying 10%, 25%, 30%, 25%, 10% of the interval. (This is our explanation !) Can this always be done ?

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Rida Laraki Majority Judgement Which of the five passing grades should be assigned to a 5.7 ? The grade {2, 4, 7, 10, 12} closest to 5.7, namely,7 or good. Interval [2, 12] is partitioned into :

2← →4← →7← →10← →12 h z }| { z }| { z }| { z }| { z }| { i [2, 3] [3, 5.5] [5.5, 8.5] [8.5, 11] [11, 12] ,

the five succeeding intervals occupying 10%, 25%, 30%, 25%, 10% of the interval. (This is our explanation !) Can this always be done ?

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Underlying idea : distribution of the students’ grades is uniform in interval [2, 12].

Rida Laraki Majority Judgement Interval [2, 12] is partitioned into :

2← →4← →7← →10← →12 h z }| { z }| { z }| { z }| { z }| { i [2, 3] [3, 5.5] [5.5, 8.5] [8.5, 11] [11, 12] ,

the five succeeding intervals occupying 10%, 25%, 30%, 25%, 10% of the interval. (This is our explanation !) Can this always be done ?

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Underlying idea : distribution of the students’ grades is uniform in interval [2, 12]. Which of the five passing grades should be assigned to a 5.7 ? The grade {2, 4, 7, 10, 12} closest to 5.7, namely,7 or good.

Rida Laraki Majority Judgement Can this always be done ?

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Underlying idea : distribution of the students’ grades is uniform in interval [2, 12]. Which of the five passing grades should be assigned to a 5.7 ? The grade {2, 4, 7, 10, 12} closest to 5.7, namely,7 or good. Interval [2, 12] is partitioned into :

2← →4← →7← →10← →12 h z }| { z }| { z }| { z }| { z }| { i [2, 3] [3, 5.5] [5.5, 8.5] [8.5, 11] [11, 12] ,

the five succeeding intervals occupying 10%, 25%, 30%, 25%, 10% of the interval. (This is our explanation !)

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Underlying idea : distribution of the students’ grades is uniform in interval [2, 12]. Which of the five passing grades should be assigned to a 5.7 ? The grade {2, 4, 7, 10, 12} closest to 5.7, namely,7 or good. Interval [2, 12] is partitioned into :

2← →4← →7← →10← →12 h z }| { z }| { z }| { z }| { z }| { i [2, 3] [3, 5.5] [5.5, 8.5] [8.5, 11] [11, 12] ,

the five succeeding intervals occupying 10%, 25%, 30%, 25%, 10% of the interval. (This is our explanation !) Can this always be done ?

Rida Laraki Majority Judgement Suppose k number grades, x1 < x2 < ··· < xk , to be given with percentage P distribution (p1, p2,..., pk ), pj = 100. Pi j+1 Let qi = 1(−1) pj for i = 1,..., k.

Theorem

There exist number grades x = (x1,..., xk ) that constitute an interval measure for the percentage distribution (p1,..., pk ) if and only if there exists a δ ≥ 0 that satisfies

max q2i ≤ δ ≤ min q2j+1. i j

When k = 5 and p = (10%, 19%, 42%, 19%, 10%), then q = (10, −9, 33, 14, 24), so max{−9, 14}  min{10, 33, 24} : there is no interval measure. There can be no interval measure for voting in large electorates : point-summing methods make no sense.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Rida Laraki Majority Judgement Pi j+1 Let qi = 1(−1) pj for i = 1,..., k.

Theorem

There exist number grades x = (x1,..., xk ) that constitute an interval measure for the percentage distribution (p1,..., pk ) if and only if there exists a δ ≥ 0 that satisfies

max q2i ≤ δ ≤ min q2j+1. i j

When k = 5 and p = (10%, 19%, 42%, 19%, 10%), then q = (10, −9, 33, 14, 24), so max{−9, 14}  min{10, 33, 24} : there is no interval measure. There can be no interval measure for voting in large electorates : point-summing methods make no sense.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Suppose k number grades, x1 < x2 < ··· < xk , to be given with percentage P distribution (p1, p2,..., pk ), pj = 100.

Rida Laraki Majority Judgement Theorem

There exist number grades x = (x1,..., xk ) that constitute an interval measure for the percentage distribution (p1,..., pk ) if and only if there exists a δ ≥ 0 that satisfies

max q2i ≤ δ ≤ min q2j+1. i j

When k = 5 and p = (10%, 19%, 42%, 19%, 10%), then q = (10, −9, 33, 14, 24), so max{−9, 14}  min{10, 33, 24} : there is no interval measure. There can be no interval measure for voting in large electorates : point-summing methods make no sense.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Suppose k number grades, x1 < x2 < ··· < xk , to be given with percentage P distribution (p1, p2,..., pk ), pj = 100. Pi j+1 Let qi = 1(−1) pj for i = 1,..., k.

Rida Laraki Majority Judgement When k = 5 and p = (10%, 19%, 42%, 19%, 10%), then q = (10, −9, 33, 14, 24), so max{−9, 14}  min{10, 33, 24} : there is no interval measure. There can be no interval measure for voting in large electorates : point-summing methods make no sense.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Suppose k number grades, x1 < x2 < ··· < xk , to be given with percentage P distribution (p1, p2,..., pk ), pj = 100. Pi j+1 Let qi = 1(−1) pj for i = 1,..., k.

Theorem

There exist number grades x = (x1,..., xk ) that constitute an interval measure for the percentage distribution (p1,..., pk ) if and only if there exists a δ ≥ 0 that satisfies

max q2i ≤ δ ≤ min q2j+1. i j

Rida Laraki Majority Judgement There can be no interval measure for voting in large electorates : point-summing methods make no sense.

The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Suppose k number grades, x1 < x2 < ··· < xk , to be given with percentage P distribution (p1, p2,..., pk ), pj = 100. Pi j+1 Let qi = 1(−1) pj for i = 1,..., k.

Theorem

There exist number grades x = (x1,..., xk ) that constitute an interval measure for the percentage distribution (p1,..., pk ) if and only if there exists a δ ≥ 0 that satisfies

max q2i ≤ δ ≤ min q2j+1. i j

When k = 5 and p = (10%, 19%, 42%, 19%, 10%), then q = (10, −9, 33, 14, 24), so max{−9, 14}  min{10, 33, 24} : there is no interval measure.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility BetweenMajority Electing Grading and Model Ranking Strategic The Method Analysis of Middlemost Majority Judgment SGF Majority The Theory Ranking of Majority Model Meaningfulness Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Interval Measures

Suppose k number grades, x1 < x2 < ··· < xk , to be given with percentage P distribution (p1, p2,..., pk ), pj = 100. Pi j+1 Let qi = 1(−1) pj for i = 1,..., k.

Theorem

There exist number grades x = (x1,..., xk ) that constitute an interval measure for the percentage distribution (p1,..., pk ) if and only if there exists a δ ≥ 0 that satisfies

max q2i ≤ δ ≤ min q2j+1. i j

When k = 5 and p = (10%, 19%, 42%, 19%, 10%), then q = (10, −9, 33, 14, 24), so max{−9, 14}  min{10, 33, 24} : there is no interval measure. There can be no interval measure for voting in large electorates : point-summing methods make no sense.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Contents

1 The thesis 2 Traditional Theory of Social Choice Traditional Methods and paradoxs paradoxs in practice Impossibility Theorems 3 Incompatibility Between Electing and Ranking 4 The Method of Majority Judgment Wines Elections Strategy proof in raking 5 The Theory of Majority Judgement Majority Grading Model Strategic Analysis Middlemost SGF Majority Ranking Model Meaningfulness 6 Approval Voting versus Approval Judgment 7 Experimental Evidences 8 Conclusions

Rida Laraki Majority Judgement Each voter either “approves of” a candidate by giving him or her one vote or “disapproves” by giving none, the winner is the candidate with the most votes.

implicitly the vote is relative (not absolute), inviting strategic voting (for which evidence exists), and thus the possibility of Arrow’s paradox.

Approval voting allows each voter to cast as many votes as he or she wishes, but at most one per candidate :

Approval voting may be seen as special case of the majority judgement when the common language consists of two words (which would mean it satisfies IIA). But, then, the two words must have an absolute meaning. As practiced, presented, analyzed and conceived, no words have been used. Consequence :

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

Rida Laraki Majority Judgement implicitly the vote is relative (not absolute), inviting strategic voting (for which evidence exists), and thus the possibility of Arrow’s paradox.

Each voter either “approves of” a candidate by giving him or her one vote or “disapproves” by giving none, the winner is the candidate with the most votes.

Approval voting may be seen as special case of the majority judgement when the common language consists of two words (which would mean it satisfies IIA). But, then, the two words must have an absolute meaning. As practiced, presented, analyzed and conceived, no words have been used. Consequence :

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

Approval voting allows each voter to cast as many votes as he or she wishes, but at most one per candidate :

Rida Laraki Majority Judgement implicitly the vote is relative (not absolute), inviting strategic voting (for which evidence exists), and thus the possibility of Arrow’s paradox.

the winner is the candidate with the most votes.

Approval voting may be seen as special case of the majority judgement when the common language consists of two words (which would mean it satisfies IIA). But, then, the two words must have an absolute meaning. As practiced, presented, analyzed and conceived, no words have been used. Consequence :

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

Approval voting allows each voter to cast as many votes as he or she wishes, but at most one per candidate : Each voter either “approves of” a candidate by giving him or her one vote or “disapproves” by giving none,

Rida Laraki Majority Judgement implicitly the vote is relative (not absolute), inviting strategic voting (for which evidence exists), and thus the possibility of Arrow’s paradox.

Approval voting may be seen as special case of the majority judgement when the common language consists of two words (which would mean it satisfies IIA). But, then, the two words must have an absolute meaning. As practiced, presented, analyzed and conceived, no words have been used. Consequence :

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

Approval voting allows each voter to cast as many votes as he or she wishes, but at most one per candidate : Each voter either “approves of” a candidate by giving him or her one vote or “disapproves” by giving none, the winner is the candidate with the most votes.

Rida Laraki Majority Judgement implicitly the vote is relative (not absolute), inviting strategic voting (for which evidence exists), and thus the possibility of Arrow’s paradox.

As practiced, presented, analyzed and conceived, no words have been used. Consequence :

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

Approval voting allows each voter to cast as many votes as he or she wishes, but at most one per candidate : Each voter either “approves of” a candidate by giving him or her one vote or “disapproves” by giving none, the winner is the candidate with the most votes.

Approval voting may be seen as special case of the majority judgement when the common language consists of two words (which would mean it satisfies IIA). But, then, the two words must have an absolute meaning.

Rida Laraki Majority Judgement implicitly the vote is relative (not absolute), inviting strategic voting (for which evidence exists), and thus the possibility of Arrow’s paradox.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

Approval voting allows each voter to cast as many votes as he or she wishes, but at most one per candidate : Each voter either “approves of” a candidate by giving him or her one vote or “disapproves” by giving none, the winner is the candidate with the most votes.

Approval voting may be seen as special case of the majority judgement when the common language consists of two words (which would mean it satisfies IIA). But, then, the two words must have an absolute meaning. As practiced, presented, analyzed and conceived, no words have been used. Consequence :

Rida Laraki Majority Judgement inviting strategic voting (for which evidence exists), and thus the possibility of Arrow’s paradox.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

Approval voting allows each voter to cast as many votes as he or she wishes, but at most one per candidate : Each voter either “approves of” a candidate by giving him or her one vote or “disapproves” by giving none, the winner is the candidate with the most votes.

Approval voting may be seen as special case of the majority judgement when the common language consists of two words (which would mean it satisfies IIA). But, then, the two words must have an absolute meaning. As practiced, presented, analyzed and conceived, no words have been used. Consequence : implicitly the vote is relative (not absolute),

Rida Laraki Majority Judgement and thus the possibility of Arrow’s paradox.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

Approval voting allows each voter to cast as many votes as he or she wishes, but at most one per candidate : Each voter either “approves of” a candidate by giving him or her one vote or “disapproves” by giving none, the winner is the candidate with the most votes.

Approval voting may be seen as special case of the majority judgement when the common language consists of two words (which would mean it satisfies IIA). But, then, the two words must have an absolute meaning. As practiced, presented, analyzed and conceived, no words have been used. Consequence : implicitly the vote is relative (not absolute), inviting strategic voting (for which evidence exists),

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

Approval voting allows each voter to cast as many votes as he or she wishes, but at most one per candidate : Each voter either “approves of” a candidate by giving him or her one vote or “disapproves” by giving none, the winner is the candidate with the most votes.

Approval voting may be seen as special case of the majority judgement when the common language consists of two words (which would mean it satisfies IIA). But, then, the two words must have an absolute meaning. As practiced, presented, analyzed and conceived, no words have been used. Consequence : implicitly the vote is relative (not absolute), inviting strategic voting (for which evidence exists), and thus the possibility of Arrow’s paradox.

Rida Laraki Majority Judgement The 2007 ballot of the Society for Social Choice and Welfare instructions :

“You can vote for any number of candidates by ticking the appropriate boxes.”

What does a voter have in mind ? 1999 experiment of Social Choice and Welfare Society, three candidates, 52 reported rankings : 1 ballot 2 ticks, 49 ballots 1 tick, 2 ballots 0 ticks. The votes were purely (with perhaps one exception) strategic !

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

Rida Laraki Majority Judgement What does a voter have in mind ? 1999 experiment of Social Choice and Welfare Society, three candidates, 52 reported rankings : 1 ballot 2 ticks, 49 ballots 1 tick, 2 ballots 0 ticks. The votes were purely (with perhaps one exception) strategic !

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

The 2007 ballot of the Society for Social Choice and Welfare instructions :

“You can vote for any number of candidates by ticking the appropriate boxes.”

Rida Laraki Majority Judgement 1999 experiment of Social Choice and Welfare Society, three candidates, 52 reported rankings : 1 ballot 2 ticks, 49 ballots 1 tick, 2 ballots 0 ticks. The votes were purely (with perhaps one exception) strategic !

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

The 2007 ballot of the Society for Social Choice and Welfare instructions :

“You can vote for any number of candidates by ticking the appropriate boxes.”

What does a voter have in mind ?

Rida Laraki Majority Judgement The votes were purely (with perhaps one exception) strategic !

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

The 2007 ballot of the Society for Social Choice and Welfare instructions :

“You can vote for any number of candidates by ticking the appropriate boxes.”

What does a voter have in mind ? 1999 experiment of Social Choice and Welfare Society, three candidates, 52 reported rankings : 1 ballot 2 ticks, 49 ballots 1 tick, 2 ballots 0 ticks.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting

The 2007 ballot of the Society for Social Choice and Welfare instructions :

“You can vote for any number of candidates by ticking the appropriate boxes.”

What does a voter have in mind ? 1999 experiment of Social Choice and Welfare Society, three candidates, 52 reported rankings : 1 ballot 2 ticks, 49 ballots 1 tick, 2 ballots 0 ticks. The votes were purely (with perhaps one exception) strategic !

Rida Laraki Majority Judgement Presidential polling results, March 20, 2007, France (Bva) :

Question : Question : Would each of the these Do you personally wish each of candidates be a good these candidates to win the President of France ? presidential election ? Yes No Yes No Bayrou 60% 36% 33% 48% Sarkozy 59% 38% 29% 56% Royal 49% 48% 36% 49% Le Pen 12% 84% What does a voter have in mind when she/he casts a “tick” ?

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting as practiced is not meaningful

Rida Laraki Majority Judgement Question : Question : Would each of the these Do you personally wish each of candidates be a good these candidates to win the President of France ? presidential election ? Yes No Yes No Bayrou 60% 36% 33% 48% Sarkozy 59% 38% 29% 56% Royal 49% 48% 36% 49% Le Pen 12% 84% What does a voter have in mind when she/he casts a “tick” ?

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting as practiced is not meaningful

Presidential polling results, March 20, 2007, France (Bva) :

Rida Laraki Majority Judgement What does a voter have in mind when she/he casts a “tick” ?

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting as practiced is not meaningful

Presidential polling results, March 20, 2007, France (Bva) :

Question : Question : Would each of the these Do you personally wish each of candidates be a good these candidates to win the President of France ? presidential election ? Yes No Yes No Bayrou 60% 36% 33% 48% Sarkozy 59% 38% 29% 56% Royal 49% 48% 36% 49% Le Pen 12% 84%

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Approval voting as practiced is not meaningful

Presidential polling results, March 20, 2007, France (Bva) :

Question : Question : Would each of the these Do you personally wish each of candidates be a good these candidates to win the President of France ? presidential election ? Yes No Yes No Bayrou 60% 36% 33% 48% Sarkozy 59% 38% 29% 56% Royal 49% 48% 36% 49% Le Pen 12% 84% What does a voter have in mind when she/he casts a “tick” ?

Rida Laraki Majority Judgement Numbers of wins (one of these three candidates always wins), 10,000 sample problems of 101 ballots drawn at random from 501 “representative ballots” of the 2007 Orsay experiment :

Royal Bayrou Sarkozy Tie Approval Voting (Good) 371 8,250 439 940 Majority Judgement (six grades) 1,330 3,953 4,686 31 Approval Voting (Very Good) 1,129 1,132 6,258 1,481

Approval Voting is called Aproval Judgment when a tick has as meaning the answer to a question that has an absolute meaning (such as “Do thing that this candidate is good” or is “acceptable ?” . Thus, there are many approval judgment methods (depending on the question).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions What does a voter have in mind when she/he casts a “tick” ?

Rida Laraki Majority Judgement Royal Bayrou Sarkozy Tie Approval Voting (Good) 371 8,250 439 940 Majority Judgement (six grades) 1,330 3,953 4,686 31 Approval Voting (Very Good) 1,129 1,132 6,258 1,481

Approval Voting is called Aproval Judgment when a tick has as meaning the answer to a question that has an absolute meaning (such as “Do thing that this candidate is good” or is “acceptable ?” . Thus, there are many approval judgment methods (depending on the question).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions What does a voter have in mind when she/he casts a “tick” ?

Numbers of wins (one of these three candidates always wins), 10,000 sample problems of 101 ballots drawn at random from 501 “representative ballots” of the 2007 Orsay experiment :

Rida Laraki Majority Judgement Approval Voting is called Aproval Judgment when a tick has as meaning the answer to a question that has an absolute meaning (such as “Do thing that this candidate is good” or is “acceptable ?” . Thus, there are many approval judgment methods (depending on the question).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions What does a voter have in mind when she/he casts a “tick” ?

Numbers of wins (one of these three candidates always wins), 10,000 sample problems of 101 ballots drawn at random from 501 “representative ballots” of the 2007 Orsay experiment :

Royal Bayrou Sarkozy Tie Approval Voting (Good) 371 8,250 439 940 Majority Judgement (six grades) 1,330 3,953 4,686 31 Approval Voting (Very Good) 1,129 1,132 6,258 1,481

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions What does a voter have in mind when she/he casts a “tick” ?

Numbers of wins (one of these three candidates always wins), 10,000 sample problems of 101 ballots drawn at random from 501 “representative ballots” of the 2007 Orsay experiment :

Royal Bayrou Sarkozy Tie Approval Voting (Good) 371 8,250 439 940 Majority Judgement (six grades) 1,330 3,953 4,686 31 Approval Voting (Very Good) 1,129 1,132 6,258 1,481

Approval Voting is called Aproval Judgment when a tick has as meaning the answer to a question that has an absolute meaning (such as “Do thing that this candidate is good” or is “acceptable ?” . Thus, there are many approval judgment methods (depending on the question).

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Contents

1 The thesis 2 Traditional Theory of Social Choice Traditional Methods and paradoxs paradoxs in practice Impossibility Theorems 3 Incompatibility Between Electing and Ranking 4 The Method of Majority Judgment Wines Elections Strategy proof in raking 5 The Theory of Majority Judgement Majority Grading Model Strategic Analysis Middlemost SGF Majority Ranking Model Meaningfulness 6 Approval Voting versus Approval Judgment 7 Experimental Evidences 8 Conclusions

Rida Laraki Majority Judgement The language is not natural but numerical so abstract. It may not define a common language in a large electorate (15 or 16 is good in math but superb in philosophy). It contains many levels which makes it more difficult to be common. The difference between 11 and 12 may not be meaningful. Words that carry meanings have a greater chance to be absolute than numbers With a numerical scale, voters assume the scores are summed, a clear invitation to manipulate—the greater the spread, the greater the opportunity. It must, in any case, be realized that adding numbers (or computing their averages) makes absolutely no sense unless the numbers belong to an interval measure.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions “Meaningfulness” of the common language

We rejected the usual [0,20] French grades :

Rida Laraki Majority Judgement It may not define a common language in a large electorate (15 or 16 is good in math but superb in philosophy). It contains many levels which makes it more difficult to be common. The difference between 11 and 12 may not be meaningful. Words that carry meanings have a greater chance to be absolute than numbers With a numerical scale, voters assume the scores are summed, a clear invitation to manipulate—the greater the spread, the greater the opportunity. It must, in any case, be realized that adding numbers (or computing their averages) makes absolutely no sense unless the numbers belong to an interval measure.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions “Meaningfulness” of the common language

We rejected the usual [0,20] French grades : The language is not natural but numerical so abstract.

Rida Laraki Majority Judgement It contains many levels which makes it more difficult to be common. The difference between 11 and 12 may not be meaningful. Words that carry meanings have a greater chance to be absolute than numbers With a numerical scale, voters assume the scores are summed, a clear invitation to manipulate—the greater the spread, the greater the opportunity. It must, in any case, be realized that adding numbers (or computing their averages) makes absolutely no sense unless the numbers belong to an interval measure.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions “Meaningfulness” of the common language

We rejected the usual [0,20] French grades : The language is not natural but numerical so abstract. It may not define a common language in a large electorate (15 or 16 is good in math but superb in philosophy).

Rida Laraki Majority Judgement The difference between 11 and 12 may not be meaningful. Words that carry meanings have a greater chance to be absolute than numbers With a numerical scale, voters assume the scores are summed, a clear invitation to manipulate—the greater the spread, the greater the opportunity. It must, in any case, be realized that adding numbers (or computing their averages) makes absolutely no sense unless the numbers belong to an interval measure.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions “Meaningfulness” of the common language

We rejected the usual [0,20] French grades : The language is not natural but numerical so abstract. It may not define a common language in a large electorate (15 or 16 is good in math but superb in philosophy). It contains many levels which makes it more difficult to be common.

Rida Laraki Majority Judgement Words that carry meanings have a greater chance to be absolute than numbers With a numerical scale, voters assume the scores are summed, a clear invitation to manipulate—the greater the spread, the greater the opportunity. It must, in any case, be realized that adding numbers (or computing their averages) makes absolutely no sense unless the numbers belong to an interval measure.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions “Meaningfulness” of the common language

We rejected the usual [0,20] French grades : The language is not natural but numerical so abstract. It may not define a common language in a large electorate (15 or 16 is good in math but superb in philosophy). It contains many levels which makes it more difficult to be common. The difference between 11 and 12 may not be meaningful.

Rida Laraki Majority Judgement With a numerical scale, voters assume the scores are summed, a clear invitation to manipulate—the greater the spread, the greater the opportunity. It must, in any case, be realized that adding numbers (or computing their averages) makes absolutely no sense unless the numbers belong to an interval measure.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions “Meaningfulness” of the common language

We rejected the usual [0,20] French grades : The language is not natural but numerical so abstract. It may not define a common language in a large electorate (15 or 16 is good in math but superb in philosophy). It contains many levels which makes it more difficult to be common. The difference between 11 and 12 may not be meaningful. Words that carry meanings have a greater chance to be absolute than numbers

Rida Laraki Majority Judgement It must, in any case, be realized that adding numbers (or computing their averages) makes absolutely no sense unless the numbers belong to an interval measure.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions “Meaningfulness” of the common language

We rejected the usual [0,20] French grades : The language is not natural but numerical so abstract. It may not define a common language in a large electorate (15 or 16 is good in math but superb in philosophy). It contains many levels which makes it more difficult to be common. The difference between 11 and 12 may not be meaningful. Words that carry meanings have a greater chance to be absolute than numbers With a numerical scale, voters assume the scores are summed, a clear invitation to manipulate—the greater the spread, the greater the opportunity.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions “Meaningfulness” of the common language

We rejected the usual [0,20] French grades : The language is not natural but numerical so abstract. It may not define a common language in a large electorate (15 or 16 is good in math but superb in philosophy). It contains many levels which makes it more difficult to be common. The difference between 11 and 12 may not be meaningful. Words that carry meanings have a greater chance to be absolute than numbers With a numerical scale, voters assume the scores are summed, a clear invitation to manipulate—the greater the spread, the greater the opportunity. It must, in any case, be realized that adding numbers (or computing their averages) makes absolutely no sense unless the numbers belong to an interval measure.

Rida Laraki Majority Judgement Percent of electors who used k (k = 1,..., 6) grades :

No. grades : 1 2 3 4 5 6 percentages : 1% 2% 10% 31% 42% 14%

Average numbers of each grade per ballot show the language was common :

3 1st 6th 12th Samples of 100 Dsjt samples of 50 prcts. prct. prct. prct. Avg. (σ) Rg Avg. (σ) Rg Excll 0.7 0.7 0.7 0.7 0.7 (.07) 0.6/0.8 0.7 (.12) 0.5/0.9 V.Good 1.3 1.2 1.2 1.4 1.2 (.13) 1.1/1.5 1.3 (.16) 1.1/1.5 Good 1.5 1.5 1.4 1.6 1.5 (.13) 1.4/1.7 1.5 (.27) 0.9/1.8 Accp 1.7 1.7 1.7 1.8 1.8 (.15) 1.7/2.1 1.7 (.27) 2.1/2.6 Poor 2.3 2.3 2.3 2.2 2.3 (.19) 2.1/2.7 2.3 (.19) 2.1/2.6 Rjct 4.6 4.8 4.6 4.3 4.5 (.29) 4.1/4.8 4.5 (.41) 4.1/5.3

Yet, the majority judgement winner not the same in all 3 precincts. Extensive statistical analyses of a large number of samples show the same stability.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Voting “behavior”

Rida Laraki Majority Judgement Average numbers of each grade per ballot show the language was common :

3 1st 6th 12th Samples of 100 Dsjt samples of 50 prcts. prct. prct. prct. Avg. (σ) Rg Avg. (σ) Rg Excll 0.7 0.7 0.7 0.7 0.7 (.07) 0.6/0.8 0.7 (.12) 0.5/0.9 V.Good 1.3 1.2 1.2 1.4 1.2 (.13) 1.1/1.5 1.3 (.16) 1.1/1.5 Good 1.5 1.5 1.4 1.6 1.5 (.13) 1.4/1.7 1.5 (.27) 0.9/1.8 Accp 1.7 1.7 1.7 1.8 1.8 (.15) 1.7/2.1 1.7 (.27) 2.1/2.6 Poor 2.3 2.3 2.3 2.2 2.3 (.19) 2.1/2.7 2.3 (.19) 2.1/2.6 Rjct 4.6 4.8 4.6 4.3 4.5 (.29) 4.1/4.8 4.5 (.41) 4.1/5.3

Yet, the majority judgement winner not the same in all 3 precincts. Extensive statistical analyses of a large number of samples show the same stability.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Voting “behavior”

Percent of electors who used k (k = 1,..., 6) grades :

No. grades : 1 2 3 4 5 6 percentages : 1% 2% 10% 31% 42% 14%

Rida Laraki Majority Judgement Yet, the majority judgement winner not the same in all 3 precincts. Extensive statistical analyses of a large number of samples show the same stability.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Voting “behavior”

Percent of electors who used k (k = 1,..., 6) grades :

No. grades : 1 2 3 4 5 6 percentages : 1% 2% 10% 31% 42% 14%

Average numbers of each grade per ballot show the language was common :

3 1st 6th 12th Samples of 100 Dsjt samples of 50 prcts. prct. prct. prct. Avg. (σ) Rg Avg. (σ) Rg Excll 0.7 0.7 0.7 0.7 0.7 (.07) 0.6/0.8 0.7 (.12) 0.5/0.9 V.Good 1.3 1.2 1.2 1.4 1.2 (.13) 1.1/1.5 1.3 (.16) 1.1/1.5 Good 1.5 1.5 1.4 1.6 1.5 (.13) 1.4/1.7 1.5 (.27) 0.9/1.8 Accp 1.7 1.7 1.7 1.8 1.8 (.15) 1.7/2.1 1.7 (.27) 2.1/2.6 Poor 2.3 2.3 2.3 2.2 2.3 (.19) 2.1/2.7 2.3 (.19) 2.1/2.6 Rjct 4.6 4.8 4.6 4.3 4.5 (.29) 4.1/4.8 4.5 (.41) 4.1/5.3

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Voting “behavior”

Percent of electors who used k (k = 1,..., 6) grades :

No. grades : 1 2 3 4 5 6 percentages : 1% 2% 10% 31% 42% 14%

Average numbers of each grade per ballot show the language was common :

3 1st 6th 12th Samples of 100 Dsjt samples of 50 prcts. prct. prct. prct. Avg. (σ) Rg Avg. (σ) Rg Excll 0.7 0.7 0.7 0.7 0.7 (.07) 0.6/0.8 0.7 (.12) 0.5/0.9 V.Good 1.3 1.2 1.2 1.4 1.2 (.13) 1.1/1.5 1.3 (.16) 1.1/1.5 Good 1.5 1.5 1.4 1.6 1.5 (.13) 1.4/1.7 1.5 (.27) 0.9/1.8 Accp 1.7 1.7 1.7 1.8 1.8 (.15) 1.7/2.1 1.7 (.27) 2.1/2.6 Poor 2.3 2.3 2.3 2.2 2.3 (.19) 2.1/2.7 2.3 (.19) 2.1/2.6 Rjct 4.6 4.8 4.6 4.3 4.5 (.29) 4.1/4.8 4.5 (.41) 4.1/5.3

Yet, the majority judgement winner not the same in all 3 precincts. Extensive statistical analyses of a large number of samples show the same stability.

Rida Laraki Majority Judgement 11% of ballots had at least two Excellents, 16% of ballots at least two Very Good, no Excellent, 6% of ballots at least two Goods, no better grade, At least one third of the voters expressed no single preferred candidate ! A same ranking may carry very different meanings, as shown by the distributions of the highest, second highest and third highest grades :

Grades : Exclt V Good Good Accp Poor Rejct Highest 52% 37% 9% 2% 0% 1% Second highest – 35% 41% 16% 5% 3% Third highest – – 26% 40% 22% 13% Input messages that are voters’ rank-orders are meaningless!

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions A proof that the traditional model is not realistic

Rida Laraki Majority Judgement 16% of ballots at least two Very Good, no Excellent, 6% of ballots at least two Goods, no better grade, At least one third of the voters expressed no single preferred candidate ! A same ranking may carry very different meanings, as shown by the distributions of the highest, second highest and third highest grades :

Grades : Exclt V Good Good Accp Poor Rejct Highest 52% 37% 9% 2% 0% 1% Second highest – 35% 41% 16% 5% 3% Third highest – – 26% 40% 22% 13% Input messages that are voters’ rank-orders are meaningless!

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions A proof that the traditional model is not realistic

11% of ballots had at least two Excellents,

Rida Laraki Majority Judgement 6% of ballots at least two Goods, no better grade, At least one third of the voters expressed no single preferred candidate ! A same ranking may carry very different meanings, as shown by the distributions of the highest, second highest and third highest grades :

Grades : Exclt V Good Good Accp Poor Rejct Highest 52% 37% 9% 2% 0% 1% Second highest – 35% 41% 16% 5% 3% Third highest – – 26% 40% 22% 13% Input messages that are voters’ rank-orders are meaningless!

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions A proof that the traditional model is not realistic

11% of ballots had at least two Excellents, 16% of ballots at least two Very Good, no Excellent,

Rida Laraki Majority Judgement At least one third of the voters expressed no single preferred candidate ! A same ranking may carry very different meanings, as shown by the distributions of the highest, second highest and third highest grades :

Grades : Exclt V Good Good Accp Poor Rejct Highest 52% 37% 9% 2% 0% 1% Second highest – 35% 41% 16% 5% 3% Third highest – – 26% 40% 22% 13% Input messages that are voters’ rank-orders are meaningless!

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions A proof that the traditional model is not realistic

11% of ballots had at least two Excellents, 16% of ballots at least two Very Good, no Excellent, 6% of ballots at least two Goods, no better grade,

Rida Laraki Majority Judgement A same ranking may carry very different meanings, as shown by the distributions of the highest, second highest and third highest grades :

Grades : Exclt V Good Good Accp Poor Rejct Highest 52% 37% 9% 2% 0% 1% Second highest – 35% 41% 16% 5% 3% Third highest – – 26% 40% 22% 13% Input messages that are voters’ rank-orders are meaningless!

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions A proof that the traditional model is not realistic

11% of ballots had at least two Excellents, 16% of ballots at least two Very Good, no Excellent, 6% of ballots at least two Goods, no better grade, At least one third of the voters expressed no single preferred candidate !

Rida Laraki Majority Judgement Grades : Exclt V Good Good Accp Poor Rejct Highest 52% 37% 9% 2% 0% 1% Second highest – 35% 41% 16% 5% 3% Third highest – – 26% 40% 22% 13% Input messages that are voters’ rank-orders are meaningless!

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions A proof that the traditional model is not realistic

11% of ballots had at least two Excellents, 16% of ballots at least two Very Good, no Excellent, 6% of ballots at least two Goods, no better grade, At least one third of the voters expressed no single preferred candidate ! A same ranking may carry very different meanings, as shown by the distributions of the highest, second highest and third highest grades :

Rida Laraki Majority Judgement Input messages that are voters’ rank-orders are meaningless!

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions A proof that the traditional model is not realistic

11% of ballots had at least two Excellents, 16% of ballots at least two Very Good, no Excellent, 6% of ballots at least two Goods, no better grade, At least one third of the voters expressed no single preferred candidate ! A same ranking may carry very different meanings, as shown by the distributions of the highest, second highest and third highest grades :

Grades : Exclt V Good Good Accp Poor Rejct Highest 52% 37% 9% 2% 0% 1% Second highest – 35% 41% 16% 5% 3% Third highest – – 26% 40% 22% 13%

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions A proof that the traditional model is not realistic

11% of ballots had at least two Excellents, 16% of ballots at least two Very Good, no Excellent, 6% of ballots at least two Goods, no better grade, At least one third of the voters expressed no single preferred candidate ! A same ranking may carry very different meanings, as shown by the distributions of the highest, second highest and third highest grades :

Grades : Exclt V Good Good Accp Poor Rejct Highest 52% 37% 9% 2% 0% 1% Second highest – 35% 41% 16% 5% 3% Third highest – – 26% 40% 22% 13% Input messages that are voters’ rank-orders are meaningless!

Rida Laraki Majority Judgement From the 1,733 ballots we have been able to deduce a left-right political spectrum along which all 12 candidates are placed, with Bayrou the unique candidate at the center. The principal candidates were Bayrou, Royal and Sarkozy : with every one of the methods we applied, one of these three candidates always is the winner in every random sample of ballots. From the 1,733 ballots, a random sample of 501 was found that is approximately representative of the national vote in France. From these 501 ballots random samples of 201 were drawn and the winners determined according to five different methods.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : favoring the centrist

Rida Laraki Majority Judgement The principal candidates were Bayrou, Royal and Sarkozy : with every one of the methods we applied, one of these three candidates always is the winner in every random sample of ballots. From the 1,733 ballots, a random sample of 501 was found that is approximately representative of the national vote in France. From these 501 ballots random samples of 201 were drawn and the winners determined according to five different methods.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : favoring the centrist

From the 1,733 ballots we have been able to deduce a left-right political spectrum along which all 12 candidates are placed, with Bayrou the unique candidate at the center.

Rida Laraki Majority Judgement From the 1,733 ballots, a random sample of 501 was found that is approximately representative of the national vote in France. From these 501 ballots random samples of 201 were drawn and the winners determined according to five different methods.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : favoring the centrist

From the 1,733 ballots we have been able to deduce a left-right political spectrum along which all 12 candidates are placed, with Bayrou the unique candidate at the center. The principal candidates were Bayrou, Royal and Sarkozy : with every one of the methods we applied, one of these three candidates always is the winner in every random sample of ballots.

Rida Laraki Majority Judgement From these 501 ballots random samples of 201 were drawn and the winners determined according to five different methods.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : favoring the centrist

From the 1,733 ballots we have been able to deduce a left-right political spectrum along which all 12 candidates are placed, with Bayrou the unique candidate at the center. The principal candidates were Bayrou, Royal and Sarkozy : with every one of the methods we applied, one of these three candidates always is the winner in every random sample of ballots. From the 1,733 ballots, a random sample of 501 was found that is approximately representative of the national vote in France.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : favoring the centrist

From the 1,733 ballots we have been able to deduce a left-right political spectrum along which all 12 candidates are placed, with Bayrou the unique candidate at the center. The principal candidates were Bayrou, Royal and Sarkozy : with every one of the methods we applied, one of these three candidates always is the winner in every random sample of ballots. From the 1,733 ballots, a random sample of 501 was found that is approximately representative of the national vote in France. From these 501 ballots random samples of 201 were drawn and the winners determined according to five different methods.

Rida Laraki Majority Judgement 10,000 random samples of 201 from 501 “representative” ballots, among only the three principal candidates, number of wins :

Left ←− −→Right Royal Bayrou Sarkozy Tie Cycle First-past-the-post winner 6560 9,261 83 – Two-past-the-post winner 1,078 172 8,154 596 – Approval Very Good 472 651 7,919 958 – Majority judgement-winner 587 4,402 5,008 3 – Condorcet-winner 138 8,390 954 389 129 Approval Good 36 9,436 30 498 – Point-summing 132 9,444 260 164 – Borda-winner 51 8,659 1,122 168 –

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : (3) favoring the centrist

Rida Laraki Majority Judgement Left ←− −→Right Royal Bayrou Sarkozy Tie Cycle First-past-the-post winner 6560 9,261 83 – Two-past-the-post winner 1,078 172 8,154 596 – Approval Very Good 472 651 7,919 958 – Majority judgement-winner 587 4,402 5,008 3 – Condorcet-winner 138 8,390 954 389 129 Approval Good 36 9,436 30 498 – Point-summing 132 9,444 260 164 – Borda-winner 51 8,659 1,122 168 –

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : (3) favoring the centrist

10,000 random samples of 201 from 501 “representative” ballots, among only the three principal candidates, number of wins :

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : (3) favoring the centrist

10,000 random samples of 201 from 501 “representative” ballots, among only the three principal candidates, number of wins :

Left ←− −→Right Royal Bayrou Sarkozy Tie Cycle First-past-the-post winner 6560 9,261 83 – Two-past-the-post winner 1,078 172 8,154 596 – Approval Very Good 472 651 7,919 958 – Majority judgement-winner 587 4,402 5,008 3 – Condorcet-winner 138 8,390 954 389 129 Approval Good 36 9,436 30 498 – Point-summing 132 9,444 260 164 – Borda-winner 51 8,659 1,122 168 –

Rida Laraki Majority Judgement 10,000 random samples of 201 from 501 “representative” ballots, among the all twelve principal candidates, number of wins :

Left ←− −→Right Royal Bayrou Sarkozy Tie Cycle First-past-the-post winner 9770 9,022 5 – Two-past-the-post winner 1,146 98 8,197 559 – Approval Very Good 467 658 7,947 928 – Majority judgement-winner 606 4,326 5,065 3 – Condorcet-winner 142 8,329 974 441 114 Approval Good 23 9,465 40 472 – Point-summing 139 9,463 239 159 – Borda-winner 12 9,9760 12 –

First- and two-past-the-post (unduly) penalize the centrist, point-summing and Borda (unduly) favor the centrist.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : (4) favoring the centrist

Rida Laraki Majority Judgement Left ←− −→Right Royal Bayrou Sarkozy Tie Cycle First-past-the-post winner 9770 9,022 5 – Two-past-the-post winner 1,146 98 8,197 559 – Approval Very Good 467 658 7,947 928 – Majority judgement-winner 606 4,326 5,065 3 – Condorcet-winner 142 8,329 974 441 114 Approval Good 23 9,465 40 472 – Point-summing 139 9,463 239 159 – Borda-winner 12 9,9760 12 –

First- and two-past-the-post (unduly) penalize the centrist, point-summing and Borda (unduly) favor the centrist.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : (4) favoring the centrist

10,000 random samples of 201 from 501 “representative” ballots, among the all twelve principal candidates, number of wins :

Rida Laraki Majority Judgement First- and two-past-the-post (unduly) penalize the centrist, point-summing and Borda (unduly) favor the centrist.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : (4) favoring the centrist

10,000 random samples of 201 from 501 “representative” ballots, among the all twelve principal candidates, number of wins :

Left ←− −→Right Royal Bayrou Sarkozy Tie Cycle First-past-the-post winner 9770 9,022 5 – Two-past-the-post winner 1,146 98 8,197 559 – Approval Very Good 467 658 7,947 928 – Majority judgement-winner 606 4,326 5,065 3 – Condorcet-winner 142 8,329 974 441 114 Approval Good 23 9,465 40 472 – Point-summing 139 9,463 239 159 – Borda-winner 12 9,9760 12 –

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : (4) favoring the centrist

10,000 random samples of 201 from 501 “representative” ballots, among the all twelve principal candidates, number of wins :

Left ←− −→Right Royal Bayrou Sarkozy Tie Cycle First-past-the-post winner 9770 9,022 5 – Two-past-the-post winner 1,146 98 8,197 559 – Approval Very Good 467 658 7,947 928 – Majority judgement-winner 606 4,326 5,065 3 – Condorcet-winner 142 8,329 974 441 114 Approval Good 23 9,465 40 472 – Point-summing 139 9,463 239 159 – Borda-winner 12 9,9760 12 –

First- and two-past-the-post (unduly) penalize the centrist, point-summing and Borda (unduly) favor the centrist.

Rida Laraki Majority Judgement Strategy 1 : all those voters who gave grade to B two levels above A change to give B highest and A lowest possible grades. Strategy 2 : 30% of those voters who gave higher grade to B than A change to give B highest and A the lowest possible grades.

Numbers of successful strategic manipulations:

Point- Borda First- Approval Approval Cond- Majority sum p-p Good VGood orcet judge Strat 1 9,965 9,313 8,699 8,569 8,407 7,042 6,142 Strat 2 9,769 7,864 4,411 8,849 8,557 4,641 5,313

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : strategic manipulability

Manipulability of methods : 10,000 random samples of 101 from 501 “representative” ballots, given that there is a same unique winner A and same unique runner-up B for every method.

Rida Laraki Majority Judgement Strategy 2 : 30% of those voters who gave higher grade to B than A change to give B highest and A the lowest possible grades.

Numbers of successful strategic manipulations:

Point- Borda First- Approval Approval Cond- Majority sum p-p Good VGood orcet judge Strat 1 9,965 9,313 8,699 8,569 8,407 7,042 6,142 Strat 2 9,769 7,864 4,411 8,849 8,557 4,641 5,313

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : strategic manipulability

Manipulability of methods : 10,000 random samples of 101 from 501 “representative” ballots, given that there is a same unique winner A and same unique runner-up B for every method. Strategy 1 : all those voters who gave grade to B two levels above A change to give B highest and A lowest possible grades.

Rida Laraki Majority Judgement Numbers of successful strategic manipulations:

Point- Borda First- Approval Approval Cond- Majority sum p-p Good VGood orcet judge Strat 1 9,965 9,313 8,699 8,569 8,407 7,042 6,142 Strat 2 9,769 7,864 4,411 8,849 8,557 4,641 5,313

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : strategic manipulability

Manipulability of methods : 10,000 random samples of 101 from 501 “representative” ballots, given that there is a same unique winner A and same unique runner-up B for every method. Strategy 1 : all those voters who gave grade to B two levels above A change to give B highest and A lowest possible grades. Strategy 2 : 30% of those voters who gave higher grade to B than A change to give B highest and A the lowest possible grades.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Statistical comparisons : strategic manipulability

Manipulability of methods : 10,000 random samples of 101 from 501 “representative” ballots, given that there is a same unique winner A and same unique runner-up B for every method. Strategy 1 : all those voters who gave grade to B two levels above A change to give B highest and A lowest possible grades. Strategy 2 : 30% of those voters who gave higher grade to B than A change to give B highest and A the lowest possible grades.

Numbers of successful strategic manipulations:

Point- Borda First- Approval Approval Cond- Majority sum p-p Good VGood orcet judge Strat 1 9,965 9,313 8,699 8,569 8,407 7,042 6,142 Strat 2 9,769 7,864 4,411 8,849 8,557 4,641 5,313

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Pool Opinion Way-Terra Nova, French presidential, April 12-16, 2012

Majority Majority- First-past-the- AV- judgment gauge post score score 1) Hollande (45.1%, Good+, 43.3%) 1 28.6%1 49.4% 2) Bayrou (34.1%, Good−, 40.7%) 5 9.1%3 39.20% 3) Sarkozy (49.3%, Accept+, 39.6%) 2 27.3%2 40.5% 4) Mélenchon (42.5%, Accept+, 40.4%) 4 11.0%4 39.1% 5) Dupont-Aignan (40.6%, Poor+, 33.9%) 7 1.5% 8 10.7% 6) Joly (36.8%, Poor−, 38.5%) 6 2.3% 6 26.7% 7) Poutou (26.2%, Poor−, 45.7%) 8 1.2% 7 13.3% 8) Le Pen (46.1%, Poor−, 47.6%) 3 17.9%5 27.4% 9) Arthaud (24.8%, Poor−, 49.9%) 9 0.7% 9 8.4% 10) Cheminade (48.0%, to Reject, −) 10 0.4% 10 3.2%

Rida Laraki Majority Judgement The MJ-, Condorcet- and Borda-rankings are identical (put Bayrou comfortably ahead of Sarkozy) but differ from first-past-the-post and AV (place Bayrou behind). The margin of victory and ranking are much comfortable with MJ than all other methods. More information is better. Other experiments confirm all results (forthcoming OR paper).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Pool Opinion Way-Terra Nova, French presidential, April 12-16, 2012.

Only the five major candidates were tested.

Condorcet- Borda- ranking Hollande Bayrou Sarkozy Mélenchon Le Pen ranking 1) Hollande – 51.6% 53.9% 68.5% 64.1% 1) 59.5% 2) Bayrou 48.4% – 56.5% 59.4% 70.5% 2) 58.7% 3) Sarkozy 46.1% 43.5% – 50.5% 65.7% 3) 51.4% 4) Mélenchon 31.5% 40.6% 49.5% – 59.7% 4) 45.3% 5) Le Pen 35.9% 29.5% 34.3% 40.3% – 5) 35.0%

Rida Laraki Majority Judgement The margin of victory and ranking are much comfortable with MJ than all other methods. More information is better. Other experiments confirm all results (forthcoming OR paper).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Pool Opinion Way-Terra Nova, French presidential, April 12-16, 2012.

Only the five major candidates were tested.

Condorcet- Borda- ranking Hollande Bayrou Sarkozy Mélenchon Le Pen ranking 1) Hollande – 51.6% 53.9% 68.5% 64.1% 1) 59.5% 2) Bayrou 48.4% – 56.5% 59.4% 70.5% 2) 58.7% 3) Sarkozy 46.1% 43.5% – 50.5% 65.7% 3) 51.4% 4) Mélenchon 31.5% 40.6% 49.5% – 59.7% 4) 45.3% 5) Le Pen 35.9% 29.5% 34.3% 40.3% – 5) 35.0%

The MJ-, Condorcet- and Borda-rankings are identical (put Bayrou comfortably ahead of Sarkozy) but differ from first-past-the-post and AV (place Bayrou behind).

Rida Laraki Majority Judgement Other experiments confirm all results (forthcoming OR paper).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Pool Opinion Way-Terra Nova, French presidential, April 12-16, 2012.

Only the five major candidates were tested.

Condorcet- Borda- ranking Hollande Bayrou Sarkozy Mélenchon Le Pen ranking 1) Hollande – 51.6% 53.9% 68.5% 64.1% 1) 59.5% 2) Bayrou 48.4% – 56.5% 59.4% 70.5% 2) 58.7% 3) Sarkozy 46.1% 43.5% – 50.5% 65.7% 3) 51.4% 4) Mélenchon 31.5% 40.6% 49.5% – 59.7% 4) 45.3% 5) Le Pen 35.9% 29.5% 34.3% 40.3% – 5) 35.0%

The MJ-, Condorcet- and Borda-rankings are identical (put Bayrou comfortably ahead of Sarkozy) but differ from first-past-the-post and AV (place Bayrou behind). The margin of victory and ranking are much comfortable with MJ than all other methods. More information is better.

Rida Laraki Majority Judgement Other experiments confirm all results (forthcoming OR paper).

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Pool Opinion Way-Terra Nova, French presidential, April 12-16, 2012.

Only the five major candidates were tested.

Condorcet- Borda- ranking Hollande Bayrou Sarkozy Mélenchon Le Pen ranking 1) Hollande – 51.6% 53.9% 68.5% 64.1% 1) 59.5% 2) Bayrou 48.4% – 56.5% 59.4% 70.5% 2) 58.7% 3) Sarkozy 46.1% 43.5% – 50.5% 65.7% 3) 51.4% 4) Mélenchon 31.5% 40.6% 49.5% – 59.7% 4) 45.3% 5) Le Pen 35.9% 29.5% 34.3% 40.3% – 5) 35.0%

The MJ-, Condorcet- and Borda-rankings are identical (put Bayrou comfortably ahead of Sarkozy) but differ from first-past-the-post and AV (place Bayrou behind). The margin of victory and ranking are much comfortable with MJ than all other methods. More information is better.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Pool Opinion Way-Terra Nova, French presidential, April 12-16, 2012.

Only the five major candidates were tested.

Condorcet- Borda- ranking Hollande Bayrou Sarkozy Mélenchon Le Pen ranking 1) Hollande – 51.6% 53.9% 68.5% 64.1% 1) 59.5% 2) Bayrou 48.4% – 56.5% 59.4% 70.5% 2) 58.7% 3) Sarkozy 46.1% 43.5% – 50.5% 65.7% 3) 51.4% 4) Mélenchon 31.5% 40.6% 49.5% – 59.7% 4) 45.3% 5) Le Pen 35.9% 29.5% 34.3% 40.3% – 5) 35.0%

The MJ-, Condorcet- and Borda-rankings are identical (put Bayrou comfortably ahead of Sarkozy) but differ from first-past-the-post and AV (place Bayrou behind). The margin of victory and ranking are much comfortable with MJ than all other methods. More information is better. Other experiments confirm all results (forthcoming OR paper).

Rida Laraki Majority Judgement Condorcet- Borda- ranking Aubry Hollande Montebourg Royal Valls Baylet ranking 1 Aubry – 50.2% 68.5% 85.0% 85.9% 95.5% 77.0% 2 Hollande 49.8% – 65.3% 85.4% 87.1% 94.8% 76.5% 3 Montebourg 31.5% 34.7% – 68.3% 69.0% 91.8% 59.1% 4 Royal 15.0% 14.6% 31.7% – 54.7% 78.2% 38.1% 5 Valls 14.1% 12.9% 31.0% 45.3% – 78.9% 36.4% 6 Baylet 4.5% 5.2% 8.2% 21.8% 21.1% – 12.2%

Practice shows what was illustrated in theory : majority voting can elect a candidate who is not judged to be the best according to the evaluations.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Field experiment. French Socialist primaries, Fresnes, 2011

Majority judgment Majority-gauge First-past-the-post 1 Hollande (18.2%, Excellent−, 49.7%) 35.7% 2 Aubry (48.5%, Very Good+, 20.2%) 34.5% 3 Montebourg (33.7%, Very Good−, 39.1%) 18.5% 4 Royal (37.5%, Good−, 38.9%) 6.0% 5 Valls (36.4%, Good−, 40.4%) 5.3% 6 Baylet (27.2%, Acceptable−, 48.2%) 0.0%

Rida Laraki Majority Judgement Practice shows what was illustrated in theory : majority voting can elect a candidate who is not judged to be the best according to the evaluations.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Field experiment. French Socialist primaries, Fresnes, 2011

Majority judgment Majority-gauge First-past-the-post 1 Hollande (18.2%, Excellent−, 49.7%) 35.7% 2 Aubry (48.5%, Very Good+, 20.2%) 34.5% 3 Montebourg (33.7%, Very Good−, 39.1%) 18.5% 4 Royal (37.5%, Good−, 38.9%) 6.0% 5 Valls (36.4%, Good−, 40.4%) 5.3% 6 Baylet (27.2%, Acceptable−, 48.2%) 0.0%

Condorcet- Borda- ranking Aubry Hollande Montebourg Royal Valls Baylet ranking 1 Aubry – 50.2% 68.5% 85.0% 85.9% 95.5% 77.0% 2 Hollande 49.8% – 65.3% 85.4% 87.1% 94.8% 76.5% 3 Montebourg 31.5% 34.7% – 68.3% 69.0% 91.8% 59.1% 4 Royal 15.0% 14.6% 31.7% – 54.7% 78.2% 38.1% 5 Valls 14.1% 12.9% 31.0% 45.3% – 78.9% 36.4% 6 Baylet 4.5% 5.2% 8.2% 21.8% 21.1% – 12.2%

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Field experiment. French Socialist primaries, Fresnes, 2011

Majority judgment Majority-gauge First-past-the-post 1 Hollande (18.2%, Excellent−, 49.7%) 35.7% 2 Aubry (48.5%, Very Good+, 20.2%) 34.5% 3 Montebourg (33.7%, Very Good−, 39.1%) 18.5% 4 Royal (37.5%, Good−, 38.9%) 6.0% 5 Valls (36.4%, Good−, 40.4%) 5.3% 6 Baylet (27.2%, Acceptable−, 48.2%) 0.0%

Condorcet- Borda- ranking Aubry Hollande Montebourg Royal Valls Baylet ranking 1 Aubry – 50.2% 68.5% 85.0% 85.9% 95.5% 77.0% 2 Hollande 49.8% – 65.3% 85.4% 87.1% 94.8% 76.5% 3 Montebourg 31.5% 34.7% – 68.3% 69.0% 91.8% 59.1% 4 Royal 15.0% 14.6% 31.7% – 54.7% 78.2% 38.1% 5 Valls 14.1% 12.9% 31.0% 45.3% – 78.9% 36.4% 6 Baylet 4.5% 5.2% 8.2% 21.8% 21.1% – 12.2%

Practice shows what was illustrated in theory : majority voting can elect a candidate who is not judged to be the best according to the evaluations.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Contents

1 The thesis 2 Traditional Theory of Social Choice Traditional Methods and paradoxs paradoxs in practice Impossibility Theorems 3 Incompatibility Between Electing and Ranking 4 The Method of Majority Judgment Wines Elections Strategy proof in raking 5 The Theory of Majority Judgement Majority Grading Model Strategic Analysis Middlemost SGF Majority Ranking Model Meaningfulness 6 Approval Voting versus Approval Judgment 7 Experimental Evidences 8 Conclusions

Rida Laraki Majority Judgement The scientific community concurs that usual simple majority decision – first-past-the-post – is to be eschewed when there are at least three candidates. However, it concurs that simple majority decision should be the choice when there are but two candidates. We believe and argue, majority decision between two may fail, and has. Jacques Chirac defeated Jean-Marie Le Pen with a crushing 82% of the vote in the run-off of 2002, but that percentage in no way measured his support in the nation. Close scores between two candidates may mean little as well : voters may like both candidates, may like neither, or may like one and not the other. These differences can be captured only with a finer measure of opinions. Close scores occur often to be important : the 2000 U.S. presidential race was decided by an official margin of 537 votes.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to simple majority decision, even for 2 candidates

Rida Laraki Majority Judgement However, it concurs that simple majority decision should be the choice when there are but two candidates. We believe and argue, majority decision between two may fail, and has. Jacques Chirac defeated Jean-Marie Le Pen with a crushing 82% of the vote in the run-off of 2002, but that percentage in no way measured his support in the nation. Close scores between two candidates may mean little as well : voters may like both candidates, may like neither, or may like one and not the other. These differences can be captured only with a finer measure of opinions. Close scores occur often to be important : the 2000 U.S. presidential race was decided by an official margin of 537 votes.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to simple majority decision, even for 2 candidates

The scientific community concurs that usual simple majority decision – first-past-the-post – is to be eschewed when there are at least three candidates.

Rida Laraki Majority Judgement However, it concurs that simple majority decision should be the choice when there are but two candidates. We believe and argue, majority decision between two may fail, and has. Jacques Chirac defeated Jean-Marie Le Pen with a crushing 82% of the vote in the run-off of 2002, but that percentage in no way measured his support in the nation. Close scores between two candidates may mean little as well : voters may like both candidates, may like neither, or may like one and not the other. These differences can be captured only with a finer measure of opinions. Close scores occur often to be important : the 2000 U.S. presidential race was decided by an official margin of 537 votes.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to simple majority decision, even for 2 candidates

The scientific community concurs that usual simple majority decision – first-past-the-post – is to be eschewed when there are at least three candidates.

Rida Laraki Majority Judgement We believe and argue, majority decision between two may fail, and has. Jacques Chirac defeated Jean-Marie Le Pen with a crushing 82% of the vote in the run-off of 2002, but that percentage in no way measured his support in the nation. Close scores between two candidates may mean little as well : voters may like both candidates, may like neither, or may like one and not the other. These differences can be captured only with a finer measure of opinions. Close scores occur often to be important : the 2000 U.S. presidential race was decided by an official margin of 537 votes.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to simple majority decision, even for 2 candidates

The scientific community concurs that usual simple majority decision – first-past-the-post – is to be eschewed when there are at least three candidates. However, it concurs that simple majority decision should be the choice when there are but two candidates.

Rida Laraki Majority Judgement Jacques Chirac defeated Jean-Marie Le Pen with a crushing 82% of the vote in the run-off of 2002, but that percentage in no way measured his support in the nation. Close scores between two candidates may mean little as well : voters may like both candidates, may like neither, or may like one and not the other. These differences can be captured only with a finer measure of opinions. Close scores occur often to be important : the 2000 U.S. presidential race was decided by an official margin of 537 votes.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to simple majority decision, even for 2 candidates

The scientific community concurs that usual simple majority decision – first-past-the-post – is to be eschewed when there are at least three candidates. However, it concurs that simple majority decision should be the choice when there are but two candidates. We believe and argue, majority decision between two may fail, and has.

Rida Laraki Majority Judgement Close scores between two candidates may mean little as well : voters may like both candidates, may like neither, or may like one and not the other. These differences can be captured only with a finer measure of opinions. Close scores occur often to be important : the 2000 U.S. presidential race was decided by an official margin of 537 votes.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to simple majority decision, even for 2 candidates

The scientific community concurs that usual simple majority decision – first-past-the-post – is to be eschewed when there are at least three candidates. However, it concurs that simple majority decision should be the choice when there are but two candidates. We believe and argue, majority decision between two may fail, and has. Jacques Chirac defeated Jean-Marie Le Pen with a crushing 82% of the vote in the run-off of 2002, but that percentage in no way measured his support in the nation.

Rida Laraki Majority Judgement These differences can be captured only with a finer measure of opinions. Close scores occur often to be important : the 2000 U.S. presidential race was decided by an official margin of 537 votes.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to simple majority decision, even for 2 candidates

The scientific community concurs that usual simple majority decision – first-past-the-post – is to be eschewed when there are at least three candidates. However, it concurs that simple majority decision should be the choice when there are but two candidates. We believe and argue, majority decision between two may fail, and has. Jacques Chirac defeated Jean-Marie Le Pen with a crushing 82% of the vote in the run-off of 2002, but that percentage in no way measured his support in the nation. Close scores between two candidates may mean little as well : voters may like both candidates, may like neither, or may like one and not the other.

Rida Laraki Majority Judgement Close scores occur often to be important : the 2000 U.S. presidential race was decided by an official margin of 537 votes.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to simple majority decision, even for 2 candidates

The scientific community concurs that usual simple majority decision – first-past-the-post – is to be eschewed when there are at least three candidates. However, it concurs that simple majority decision should be the choice when there are but two candidates. We believe and argue, majority decision between two may fail, and has. Jacques Chirac defeated Jean-Marie Le Pen with a crushing 82% of the vote in the run-off of 2002, but that percentage in no way measured his support in the nation. Close scores between two candidates may mean little as well : voters may like both candidates, may like neither, or may like one and not the other. These differences can be captured only with a finer measure of opinions.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to simple majority decision, even for 2 candidates

The scientific community concurs that usual simple majority decision – first-past-the-post – is to be eschewed when there are at least three candidates. However, it concurs that simple majority decision should be the choice when there are but two candidates. We believe and argue, majority decision between two may fail, and has. Jacques Chirac defeated Jean-Marie Le Pen with a crushing 82% of the vote in the run-off of 2002, but that percentage in no way measured his support in the nation. Close scores between two candidates may mean little as well : voters may like both candidates, may like neither, or may like one and not the other. These differences can be captured only with a finer measure of opinions. Close scores occur often to be important : the 2000 U.S. presidential race was decided by an official margin of 537 votes.

Rida Laraki Majority Judgement Condorcet’s method may lead to no winner and suffers from the defects of simple majority decision. Borda’s method is open to Arrow’s paradox, highly manipulable, and unduly biased in favor of centrists. Dasgupta-Maskin’s method is a hybrid of Condorcet’s and Borda’s – so in principle deficient for the reasons developed above – It seeks to satisfy the four minimal requirements and to resist manipulation. To prove it satisfies these requirements, instead of enlarging voters’ possible expressions of opinion, it must restrain them (implicitly assuming that voters’ rank-order inputs are naturally expressible along a clear-cut ideological ordering of the candidates). It cannot be the case in most competitions (wine, skating) and there is ample experimental evidence that shows voters do not behave in accord with this restriction.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Borda and Condorcet

Rida Laraki Majority Judgement Borda’s method is open to Arrow’s paradox, highly manipulable, and unduly biased in favor of centrists. Dasgupta-Maskin’s method is a hybrid of Condorcet’s and Borda’s – so in principle deficient for the reasons developed above – It seeks to satisfy the four minimal requirements and to resist manipulation. To prove it satisfies these requirements, instead of enlarging voters’ possible expressions of opinion, it must restrain them (implicitly assuming that voters’ rank-order inputs are naturally expressible along a clear-cut ideological ordering of the candidates). It cannot be the case in most competitions (wine, skating) and there is ample experimental evidence that shows voters do not behave in accord with this restriction.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Borda and Condorcet

Condorcet’s method may lead to no winner and suffers from the defects of simple majority decision.

Rida Laraki Majority Judgement Dasgupta-Maskin’s method is a hybrid of Condorcet’s and Borda’s – so in principle deficient for the reasons developed above – It seeks to satisfy the four minimal requirements and to resist manipulation. To prove it satisfies these requirements, instead of enlarging voters’ possible expressions of opinion, it must restrain them (implicitly assuming that voters’ rank-order inputs are naturally expressible along a clear-cut ideological ordering of the candidates). It cannot be the case in most competitions (wine, skating) and there is ample experimental evidence that shows voters do not behave in accord with this restriction.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Borda and Condorcet

Condorcet’s method may lead to no winner and suffers from the defects of simple majority decision. Borda’s method is open to Arrow’s paradox, highly manipulable, and unduly biased in favor of centrists.

Rida Laraki Majority Judgement It seeks to satisfy the four minimal requirements and to resist manipulation. To prove it satisfies these requirements, instead of enlarging voters’ possible expressions of opinion, it must restrain them (implicitly assuming that voters’ rank-order inputs are naturally expressible along a clear-cut ideological ordering of the candidates). It cannot be the case in most competitions (wine, skating) and there is ample experimental evidence that shows voters do not behave in accord with this restriction.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Borda and Condorcet

Condorcet’s method may lead to no winner and suffers from the defects of simple majority decision. Borda’s method is open to Arrow’s paradox, highly manipulable, and unduly biased in favor of centrists. Dasgupta-Maskin’s method is a hybrid of Condorcet’s and Borda’s – so in principle deficient for the reasons developed above –

Rida Laraki Majority Judgement To prove it satisfies these requirements, instead of enlarging voters’ possible expressions of opinion, it must restrain them (implicitly assuming that voters’ rank-order inputs are naturally expressible along a clear-cut ideological ordering of the candidates). It cannot be the case in most competitions (wine, skating) and there is ample experimental evidence that shows voters do not behave in accord with this restriction.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Borda and Condorcet

Condorcet’s method may lead to no winner and suffers from the defects of simple majority decision. Borda’s method is open to Arrow’s paradox, highly manipulable, and unduly biased in favor of centrists. Dasgupta-Maskin’s method is a hybrid of Condorcet’s and Borda’s – so in principle deficient for the reasons developed above – It seeks to satisfy the four minimal requirements and to resist manipulation.

Rida Laraki Majority Judgement It cannot be the case in most competitions (wine, skating) and there is ample experimental evidence that shows voters do not behave in accord with this restriction.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Borda and Condorcet

Condorcet’s method may lead to no winner and suffers from the defects of simple majority decision. Borda’s method is open to Arrow’s paradox, highly manipulable, and unduly biased in favor of centrists. Dasgupta-Maskin’s method is a hybrid of Condorcet’s and Borda’s – so in principle deficient for the reasons developed above – It seeks to satisfy the four minimal requirements and to resist manipulation. To prove it satisfies these requirements, instead of enlarging voters’ possible expressions of opinion, it must restrain them (implicitly assuming that voters’ rank-order inputs are naturally expressible along a clear-cut ideological ordering of the candidates).

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Borda and Condorcet

Condorcet’s method may lead to no winner and suffers from the defects of simple majority decision. Borda’s method is open to Arrow’s paradox, highly manipulable, and unduly biased in favor of centrists. Dasgupta-Maskin’s method is a hybrid of Condorcet’s and Borda’s – so in principle deficient for the reasons developed above – It seeks to satisfy the four minimal requirements and to resist manipulation. To prove it satisfies these requirements, instead of enlarging voters’ possible expressions of opinion, it must restrain them (implicitly assuming that voters’ rank-order inputs are naturally expressible along a clear-cut ideological ordering of the candidates). It cannot be the case in most competitions (wine, skating) and there is ample experimental evidence that shows voters do not behave in accord with this restriction.

Rida Laraki Majority Judgement Unthinkable system in skating, with 9 judges and so many competitors ! ! !. In polarized elections pitting different ideologies and policies against each other such as a presidential race, often no candidate receives a majority of “approvals” and the results are not sufficiently different to impart legitimacy to the winner. On the other hand, in a non-polarized election such as a primary, often many candidates end with strong “majorities,” so again none has a really clear and distinctive mandate. In both cases experience shows that scores may be close, so the results are all the more manipulable.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Approval Voting

The yes/no or two levels of approval voting are insufficient to judge candidates.

Rida Laraki Majority Judgement In polarized elections pitting different ideologies and policies against each other such as a presidential race, often no candidate receives a majority of “approvals” and the results are not sufficiently different to impart legitimacy to the winner. On the other hand, in a non-polarized election such as a primary, often many candidates end with strong “majorities,” so again none has a really clear and distinctive mandate. In both cases experience shows that scores may be close, so the results are all the more manipulable.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Approval Voting

The yes/no or two levels of approval voting are insufficient to judge candidates. Unthinkable system in skating, with 9 judges and so many competitors ! ! !.

Rida Laraki Majority Judgement On the other hand, in a non-polarized election such as a primary, often many candidates end with strong “majorities,” so again none has a really clear and distinctive mandate. In both cases experience shows that scores may be close, so the results are all the more manipulable.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Approval Voting

The yes/no or two levels of approval voting are insufficient to judge candidates. Unthinkable system in skating, with 9 judges and so many competitors ! ! !. In polarized elections pitting different ideologies and policies against each other such as a presidential race, often no candidate receives a majority of “approvals” and the results are not sufficiently different to impart legitimacy to the winner.

Rida Laraki Majority Judgement In both cases experience shows that scores may be close, so the results are all the more manipulable.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Approval Voting

The yes/no or two levels of approval voting are insufficient to judge candidates. Unthinkable system in skating, with 9 judges and so many competitors ! ! !. In polarized elections pitting different ideologies and policies against each other such as a presidential race, often no candidate receives a majority of “approvals” and the results are not sufficiently different to impart legitimacy to the winner. On the other hand, in a non-polarized election such as a primary, often many candidates end with strong “majorities,” so again none has a really clear and distinctive mandate.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions No to Approval Voting

The yes/no or two levels of approval voting are insufficient to judge candidates. Unthinkable system in skating, with 9 judges and so many competitors ! ! !. In polarized elections pitting different ideologies and policies against each other such as a presidential race, often no candidate receives a majority of “approvals” and the results are not sufficiently different to impart legitimacy to the winner. On the other hand, in a non-polarized election such as a primary, often many candidates end with strong “majorities,” so again none has a really clear and distinctive mandate. In both cases experience shows that scores may be close, so the results are all the more manipulable.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Field experiment. French Socialist primaries, Alfortville, 2011.

Majority Majority- Approval Approval Reported Actual judgment gauge voting judgment votes votes 1 Hollande (40.1%, Good+, 25.4%) 87.3% 87.0% 37.7% 39.7% 2 Aubry (33.1%, Good+, 30.6%) 85.2% 82.0% 29.2% 28.9% 3 Montebourg (39.8%, Accept.+, 36.3%) 64.1% 63.7% 12.5% 12.3% 4 Valls (28.5%, Accept.−, 44.7%) 53.2% 55.3% 10.0% 8.6% 5 Royal (27.1%, Accept.−, 47.2%) 53.5% 52.8% 10.3% 9.7% 6 Baylet (41.7%, Poor+, 28.9%) 25.7% 20.4% 0.4% 0.7%

Rida Laraki Majority Judgement The practice in judging competitions has taken an important first step: instead of comparing it evaluates. A second step needs to be taken too : to change the procedures for amalgamating the different evaluations. Many have taken a small step in this direction by eliminating the top and bottom grades or the top two and bottom two grades. Terra Nova – “an independent progressive think tank whose goal is to produce and diffuse innovative political solutions in France and Europe” – has taken both steps in voting. Terra Nova has included in 2011 majority judgment in its recommendations for reforming the presidential election system of France. Darwin would conclude : for a better democracy, natural selection will lead, in the long term, to majority judgment.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Step by step

Rida Laraki Majority Judgement A second step needs to be taken too : to change the procedures for amalgamating the different evaluations. Many have taken a small step in this direction by eliminating the top and bottom grades or the top two and bottom two grades. Terra Nova – “an independent progressive think tank whose goal is to produce and diffuse innovative political solutions in France and Europe” – has taken both steps in voting. Terra Nova has included in 2011 majority judgment in its recommendations for reforming the presidential election system of France. Darwin would conclude : for a better democracy, natural selection will lead, in the long term, to majority judgment.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Step by step

The practice in judging competitions has taken an important first step: instead of comparing it evaluates.

Rida Laraki Majority Judgement Many have taken a small step in this direction by eliminating the top and bottom grades or the top two and bottom two grades. Terra Nova – “an independent progressive think tank whose goal is to produce and diffuse innovative political solutions in France and Europe” – has taken both steps in voting. Terra Nova has included in 2011 majority judgment in its recommendations for reforming the presidential election system of France. Darwin would conclude : for a better democracy, natural selection will lead, in the long term, to majority judgment.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Step by step

The practice in judging competitions has taken an important first step: instead of comparing it evaluates. A second step needs to be taken too : to change the procedures for amalgamating the different evaluations.

Rida Laraki Majority Judgement Terra Nova – “an independent progressive think tank whose goal is to produce and diffuse innovative political solutions in France and Europe” – has taken both steps in voting. Terra Nova has included in 2011 majority judgment in its recommendations for reforming the presidential election system of France. Darwin would conclude : for a better democracy, natural selection will lead, in the long term, to majority judgment.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Step by step

The practice in judging competitions has taken an important first step: instead of comparing it evaluates. A second step needs to be taken too : to change the procedures for amalgamating the different evaluations. Many have taken a small step in this direction by eliminating the top and bottom grades or the top two and bottom two grades.

Rida Laraki Majority Judgement Terra Nova has included in 2011 majority judgment in its recommendations for reforming the presidential election system of France. Darwin would conclude : for a better democracy, natural selection will lead, in the long term, to majority judgment.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Step by step

The practice in judging competitions has taken an important first step: instead of comparing it evaluates. A second step needs to be taken too : to change the procedures for amalgamating the different evaluations. Many have taken a small step in this direction by eliminating the top and bottom grades or the top two and bottom two grades. Terra Nova – “an independent progressive think tank whose goal is to produce and diffuse innovative political solutions in France and Europe” – has taken both steps in voting.

Rida Laraki Majority Judgement Darwin would conclude : for a better democracy, natural selection will lead, in the long term, to majority judgment.

The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Step by step

The practice in judging competitions has taken an important first step: instead of comparing it evaluates. A second step needs to be taken too : to change the procedures for amalgamating the different evaluations. Many have taken a small step in this direction by eliminating the top and bottom grades or the top two and bottom two grades. Terra Nova – “an independent progressive think tank whose goal is to produce and diffuse innovative political solutions in France and Europe” – has taken both steps in voting. Terra Nova has included in 2011 majority judgment in its recommendations for reforming the presidential election system of France.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions Step by step

The practice in judging competitions has taken an important first step: instead of comparing it evaluates. A second step needs to be taken too : to change the procedures for amalgamating the different evaluations. Many have taken a small step in this direction by eliminating the top and bottom grades or the top two and bottom two grades. Terra Nova – “an independent progressive think tank whose goal is to produce and diffuse innovative political solutions in France and Europe” – has taken both steps in voting. Terra Nova has included in 2011 majority judgment in its recommendations for reforming the presidential election system of France. Darwin would conclude : for a better democracy, natural selection will lead, in the long term, to majority judgment.

Rida Laraki Majority Judgement The thesis Traditional Theory of Social Choice Incompatibility Between Electing and Ranking The Method of Majority Judgment The Theory of Majority Judgement Approval Voting versus Approval Judgment Experimental Evidences Conclusions References

 Michel Balinski and Rida Laraki. 2010. Majority Judgment : Measuring, Ranking, and Electing. MIT Press.

 — and — 2007 ‘A theory of measuring, electing and ranking, PNAS, USA.  — and —. 2012. “Ne votez pas, jugez.” Pour la science, avril : 22-28.  — and —. 2013. “Jugement majoritaire versus vote majoritaire.” Revue Française d’Économie.

 — and — 2013 How Best to Rank Wines : Majority Judgement. Chapter in the book : Wine Economics : Quantitative Studies and empirical Observations, Palgrave-MacMillan.  — and —. 2014. Judge : Don’t Vote.. Operations Research.  — and —. 2014. What Should “Majority Decision” Mean ?. Chapter in the book : Majority Decisions, Cambridge University Press.  Terra Nova [2011]. Rendre les éctions aux électeurs : le jugement majoritaire. April 21. http ://www.tnova.fr/note/rendre-les-lections-aux-lecteurs-le-jugement-majoritaire

Rida Laraki Majority Judgement