Why Condorcet Consistency Is Essential
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Critical Strategies Under Approval Voting: Who Gets Ruled in and Ruled Out
Critical Strategies Under Approval Voting: Who Gets Ruled In And Ruled Out Steven J. Brams Department of Politics New York University New York, NY 10003 USA [email protected] M. Remzi Sanver Department of Economics Istanbul Bilgi University 80310, Kustepe, Istanbul TURKEY [email protected] January 2005 2 Abstract We introduce the notion of a “critical strategy profile” under approval voting (AV), which facilitates the identification of all possible outcomes that can occur under AV. Included among AV outcomes are those given by scoring rules, single transferable vote, the majoritarian compromise, Condorcet systems, and others as well. Under each of these systems, a Condorcet winner may be upset through manipulation by individual voters or coalitions of voters, whereas AV ensures the election of a Condorcet winner as a strong Nash equilibrium wherein voters use sincere strategies. To be sure, AV may also elect Condorcet losers and other lesser candidates, sometimes in equilibrium. This multiplicity of (equilibrium) outcomes is the product of a social-choice framework that is more general than the standard preference-based one. From a normative perspective, we argue that voter judgments about candidate acceptability should take precedence over the usual social-choice criteria, such as electing a Condorcet or Borda winner. Keywords: approval voting; elections; Condorcet winner/loser; voting games; Nash equilibrium. Acknowledgments. We thank Eyal Baharad, Dan S. Felsenthal, Peter C. Fishburn, Shmuel Nitzan, Richard F. Potthoff, and Ismail Saglam for valuable suggestions. 3 1. Introduction Our thesis in this paper is that several outcomes of single-winner elections may be socially acceptable, depending on voters’ individual views on the acceptability of the candidates. -
Brake & Branscomb
Colorado Secretary of State 8/3/2021 Election Rulemaking These proposed edits to the SOS draft are contributed by Emily Brake (R) and Harvie Branscomb (D), and approved by Frank Atwood, Chair of the Approval Voting Party This document may be found on http://electionquality.com version 1.3 8/10/2021 15:50 Only portions of the recent draft rule text are included here with inline edits and comments highlighted as follows: Comments are highlighted in yellow. INSERTS ARE IN GREEN AND LARGE FONT deletions are in red and include strikeout Other indications of strikeout are from the original tabulation process 2.13.2 In accordance with section 1-2-605(7), C.R.S., no later than 90 days following a General Election, the county clerk in each county must SECRETARY OF STATE WILL PROPOSE cancelLATION OF the registrations of electors TO EACH COUNTY CLERK: [Comment: SOS taking responsibility from counties will lead to less verification and less resilience. The SOS office has not been subject to watcher access but will be as various steps of the conduct of election are taken over.] (a) Whose records have been marked “Inactive – returned mail”, “Inactive – undeliverable ballot”, or “Inactive – NCOA”; AND (b) Who have been mailed a confirmation card; and (c) Who have since THEREAFTER failed to vote in two consecutive general elections. New Rule 2.13.3, amendments to current Rule 2.13.3, repeal of 2.13.5, and necessary renumbering:VOTERS WHO REQUEST AN EMERGENCY BALLOT BE SENT TO THEM ELECTRONICALLY MUST BE DIRECTED BY THE COUNTY CLERK TO THE ONLINE BALLOT DELIVERY SYSTEM MAINTAINED BY THE SECRETARY OF STATE TO RECEIVE THEIR BALLOT ELECTRONICALLY. -
THE SINGLE-MEMBER PLURALITY and MIXED-MEMBER PROPORTIONAL ELECTORAL SYSTEMS : Different Concepts of an Election
THE SINGLE-MEMBER PLURALITY AND MIXED-MEMBER PROPORTIONAL ELECTORAL SYSTEMS : Different Concepts of an Election by James C. Anderson A thesis presented to the University of Waterloo in fulfillment of the thesis requirement for the degree of Master of Arts in Political Science Waterloo, Ontario, Canada, 2006 © James C. Anderson 2006 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Library and Bibliotheque et Archives Canada Archives Canada Published Heritage Direction du Branch Patrimoine de I'edition 395 Wellington Street 395, rue Wellington Ottawa ON K1A 0N4 Ottawa ON K1A 0N4 Canada Canada Your file Votre reference ISBN: 978-0-494-23700-7 Our file Notre reference ISBN: 978-0-494-23700-7 NOTICE: AVIS: The author has granted a non L'auteur a accorde une licence non exclusive exclusive license allowing Library permettant a la Bibliotheque et Archives and Archives Canada to reproduce,Canada de reproduire, publier, archiver, publish, archive, preserve, conserve,sauvegarder, conserver, transmettre au public communicate to the public by par telecommunication ou par I'lnternet, preter, telecommunication or on the Internet,distribuer et vendre des theses partout dans loan, distribute and sell theses le monde, a des fins commerciales ou autres, worldwide, for commercial or non sur support microforme, papier, electronique commercial purposes, in microform,et/ou autres formats. paper, electronic and/or any other formats. The author retains copyright L'auteur conserve la propriete du droit d'auteur ownership and moral rights in et des droits moraux qui protege cette these. this thesis. Neither the thesis Ni la these ni des extraits substantiels de nor substantial extracts from it celle-ci ne doivent etre imprimes ou autrement may be printed or otherwise reproduits sans son autorisation. -
Are Condorcet and Minimax Voting Systems the Best?1
1 Are Condorcet and Minimax Voting Systems the Best?1 Richard B. Darlington Cornell University Abstract For decades, the minimax voting system was well known to experts on voting systems, but was not widely considered to be one of the best systems. But in recent years, two important experts, Nicolaus Tideman and Andrew Myers, have both recognized minimax as one of the best systems. I agree with that. This paper presents my own reasons for preferring minimax. The paper explicitly discusses about 20 systems. Comments invited. [email protected] Copyright Richard B. Darlington May be distributed free for non-commercial purposes Keywords Voting system Condorcet Minimax 1. Many thanks to Nicolaus Tideman, Andrew Myers, Sharon Weinberg, Eduardo Marchena, my wife Betsy Darlington, and my daughter Lois Darlington, all of whom contributed many valuable suggestions. 2 Table of Contents 1. Introduction and summary 3 2. The variety of voting systems 4 3. Some electoral criteria violated by minimax’s competitors 6 Monotonicity 7 Strategic voting 7 Completeness 7 Simplicity 8 Ease of voting 8 Resistance to vote-splitting and spoiling 8 Straddling 8 Condorcet consistency (CC) 8 4. Dismissing eight criteria violated by minimax 9 4.1 The absolute loser, Condorcet loser, and preference inversion criteria 9 4.2 Three anti-manipulation criteria 10 4.3 SCC/IIA 11 4.4 Multiple districts 12 5. Simulation studies on voting systems 13 5.1. Why our computer simulations use spatial models of voter behavior 13 5.2 Four computer simulations 15 5.2.1 Features and purposes of the studies 15 5.2.2 Further description of the studies 16 5.2.3 Results and discussion 18 6. -
MGF 1107 FINAL EXAM REVIEW CHAPTER 9 1. Amy (A), Betsy
MGF 1107 FINAL EXAM REVIEW CHAPTER 9 1. Amy (A), Betsy (B), Carla (C), Doris (D), and Emilia (E) are candidates for an open Student Government seat. There are 110 voters with the preference lists below. 36 24 20 18 8 4 A E D B C C B C E D E D C B C C B B D D B E D E E A A A A A Who wins the election if the method used is: a) plurality? b) plurality with runoff? c) sequential pairwise voting with agenda ABEDC? d) Hare system? e) Borda count? 2. What is the minimum number of votes needed for a majority if the number of votes cast is: a) 120? b) 141? 3. Consider the following preference lists: 1 1 1 A C B B A D D B C C D A If sequential pairwise voting and the agenda BACD is used, then D wins the election. Suppose the middle voter changes his mind and reverses his ranking of A and B. If the other two voters have unchanged preferences, B now wins using the same agenda BACD. This example shows that sequential pairwise voting fails to satisfy what desirable property of a voting system? 4. Consider the following preference lists held by 5 voters: 2 2 1 A B C C C B B A A First, note that if the plurality with runoff method is used, B wins. Next, note that C defeats both A and B in head-to-head matchups. This example shows that the plurality with runoff method fails to satisfy which desirable property of a voting system? 5. -
Absolute Voting Rules Adrian Vermeule
University of Chicago Law School Chicago Unbound Coase-Sandor Working Paper Series in Law and Coase-Sandor Institute for Law and Economics Economics 2005 Absolute Voting Rules Adrian Vermeule Follow this and additional works at: https://chicagounbound.uchicago.edu/law_and_economics Part of the Law Commons Recommended Citation Adrian Vermeule, "Absolute Voting Rules" (John M. Olin Program in Law and Economics Working Paper No. 257, 2005). This Working Paper is brought to you for free and open access by the Coase-Sandor Institute for Law and Economics at Chicago Unbound. It has been accepted for inclusion in Coase-Sandor Working Paper Series in Law and Economics by an authorized administrator of Chicago Unbound. For more information, please contact [email protected]. CHICAGO JOHN M. OLIN LAW & ECONOMICS WORKING PAPER NO. 257 (2D SERIES) Absolute Voting Rules Adrian Vermeule THE LAW SCHOOL THE UNIVERSITY OF CHICAGO August 2005 This paper can be downloaded without charge at: The Chicago Working Paper Series Index: http://www.law.uchicago.edu/Lawecon/index.html and at the Social Science Research Network Electronic Paper Collection: http://ssrn.com/abstract_id=791724 Absolute Voting Rules Adrian Vermeule* The theory of voting rules developed in law, political science, and economics typically compares simple majority rule with alternatives, such as various types of supermajority rules1 and submajority rules.2 There is another critical dimension to these questions, however. Consider the following puzzles: $ In the United States Congress, the votes of a majority of those present and voting are necessary to approve a law.3 In the legislatures of California and Minnesota,4 however, the votes of a majority of all elected members are required. -
On the Distortion of Voting with Multiple Representative Candidates∗
The Thirty-Second AAAI Conference on Artificial Intelligence (AAAI-18) On the Distortion of Voting with Multiple Representative Candidates∗ Yu Cheng Shaddin Dughmi David Kempe Duke University University of Southern California University of Southern California Abstract voters and the chosen candidate in a suitable metric space (Anshelevich 2016; Anshelevich, Bhardwaj, and Postl 2015; We study positional voting rules when candidates and voters Anshelevich and Postl 2016; Goel, Krishnaswamy, and Mu- are embedded in a common metric space, and cardinal pref- erences are naturally given by distances in the metric space. nagala 2017). The underlying assumption is that the closer In a positional voting rule, each candidate receives a score a candidate is to a voter, the more similar their positions on from each ballot based on the ballot’s rank order; the candi- key questions are. Because proximity implies that the voter date with the highest total score wins the election. The cost would benefit from the candidate’s election, voters will rank of a candidate is his sum of distances to all voters, and the candidates by increasing distance, a model known as single- distortion of an election is the ratio between the cost of the peaked preferences (Black 1948; Downs 1957; Black 1958; elected candidate and the cost of the optimum candidate. We Moulin 1980; Merrill and Grofman 1999; Barbera,` Gul, consider the case when candidates are representative of the and Stacchetti 1993; Richards, Richards, and McKay 1998; population, in the sense that they are drawn i.i.d. from the Barbera` 2001). population of the voters, and analyze the expected distortion Even in the absence of strategic voting, voting systems of positional voting rules. -
A Canadian Model of Proportional Representation by Robert S. Ring A
Proportional-first-past-the-post: A Canadian model of Proportional Representation by Robert S. Ring A thesis submitted to the School of Graduate Studies in partial fulfilment of the requirements for the degree of Master of Arts Department of Political Science Memorial University St. John’s, Newfoundland and Labrador May 2014 ii Abstract For more than a decade a majority of Canadians have consistently supported the idea of proportional representation when asked, yet all attempts at electoral reform thus far have failed. Even though a majority of Canadians support proportional representation, a majority also report they are satisfied with the current electoral system (even indicating support for both in the same survey). The author seeks to reconcile these potentially conflicting desires by designing a uniquely Canadian electoral system that keeps the positive and familiar features of first-past-the- post while creating a proportional election result. The author touches on the theory of representative democracy and its relationship with proportional representation before delving into the mechanics of electoral systems. He surveys some of the major electoral system proposals and options for Canada before finally presenting his made-in-Canada solution that he believes stands a better chance at gaining approval from Canadians than past proposals. iii Acknowledgements First of foremost, I would like to express my sincerest gratitude to my brilliant supervisor, Dr. Amanda Bittner, whose continuous guidance, support, and advice over the past few years has been invaluable. I am especially grateful to you for encouraging me to pursue my Master’s and write about my electoral system idea. -
Approval Voting Under Dichotomous Preferences: a Catalogue of Characterizations
Draft – June 25, 2021 Approval Voting under Dichotomous Preferences: A Catalogue of Characterizations Florian Brandl Dominik Peters University of Bonn Harvard University [email protected] [email protected] Approval voting allows every voter to cast a ballot of approved alternatives and chooses the alternatives with the largest number of approvals. Due to its simplicity and superior theoretical properties it is a serious contender for use in real-world elections. We support this claim by giving eight characterizations of approval voting. All our results involve the reinforcement axiom, which requires choices to be consistent across different electorates. In addition, we consider strategyproofness, consistency with majority opinions, consistency under cloning alternatives, and invariance under removing inferior alternatives. We prove our results by reducing them to a single base theorem, for which we give a simple and intuitive proof. 1 Introduction Around the world, when electing a leader or a representative, plurality is by far the most common voting system: each voter casts a vote for a single candidate, and the candidate with the most votes is elected. In pioneering work, Brams and Fishburn (1983) proposed an alternative system: approval voting. Here, each voter may cast votes for an arbitrary number of candidates, and can thus choose whether to approve or disapprove of each candidate. The election is won by the candidate who is approved by the highest number of voters. Approval voting allows voters to be more expressive of their preferences, and it can avoid problems such as vote splitting, which are endemic to plurality voting. Together with its elegance and simplicity, this has made approval voting a favorite among voting theorists (Laslier, 2011), and has led to extensive research literature (Laslier and Sanver, 2010). -
Majority Judgment: a New Voting Method
Paradoxes Impossbilities Majority Judgment Theory Applications of MJ Logiciels JM Experimental Evidences Conclusion Majority Judgment: A New Voting Method Rida Laraki CNRS (Lamsade, Dauphine) and University of Liverpool Colloquium J. Morgenstern, INRIA, Sophia-Antipolis December 11, 2018 (Joint work with Michel Balinski) R. Laraki Majority Judgment: A New Voting Method Paradoxes Impossbilities Majority Judgment Theory ApplicationsMethods of MJ Logiciels of Voting JM Paradoxes Experimental in Theory Evidences Paradoxes Conclusion in Practice 1 Paradoxes Methods of Voting Paradoxes in Theory Paradoxes in Practice 2 Impossbilities May’s Axioms for Two Candidates Arrow’s Impossibility Theorem 3 Majority Judgment From Practice Small Jury Large Electorate 4 Theory Domination Paradox Possibility Manipulation 5 Applications of MJ Trump 2016 Gillets Jaunes Délé´gué CM1 6 Logiciels JM 7 Experimental Evidences 8 Conclusion R. Laraki Majority Judgment: A New Voting Method First-past-the-post: also called plurality voting, used in UK, US and Canada to elect members of house of representatives. A voter designate one candidate. The most designated wins. Two-past-the-post: used in France and several countries (Finland, Austria, Russia, Portugal, Ukraine, etc) to elect the president. A voter designates one candidate. If a candidate is designated by a majority, he is elected. Otherwise, there is a run-off between the two first candidates. Paradoxes Impossbilities Majority Judgment Theory ApplicationsMethods of MJ Logiciels of Voting JM Paradoxes Experimental in Theory Evidences Paradoxes Conclusion in Practice Voting methods most used in elections R. Laraki Majority Judgment: A New Voting Method A voter designate one candidate. The most designated wins. Two-past-the-post: used in France and several countries (Finland, Austria, Russia, Portugal, Ukraine, etc) to elect the president. -
Majority Judgment Vs. Majority Rule ∗
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by University of Liverpool Repository Majority Judgment vs. Majority Rule ∗ Michel Balinski CNRS, CREST, Ecole´ Polytechnique, France, [email protected] and Rida Laraki* CNRS, University of Paris Dauphine-PSL, France, [email protected] and University of Liverpool, United Kingdom June 6, 2019 Abstract The validity of majority rule in an election with but two candidates|and so also of Condorcet consistency| is challenged. Axioms based on evaluating candidates|paralleling those of K. O. May characterizing ma- jority rule for two candidates based on comparing candidates|lead to another method, majority judgment, that is unique in agreeing with the majority rule on pairs of \polarized" candidates. It is a practical method that accommodates any number of candidates, avoids both the Condorcet and Arrow paradoxes, and best resists strategic manipulation. Key words: majority, measuring, ranking, electing, Condorcet consistency, domination paradox, tyranny of majority, intensity problem, majority-gauge, strategy-proofness, polarization. 1 Introduction Elections measure. Voters express themselves, a rule amalgamates them, the candidates' scores|measures of support|determine their order of finish, and the winner. Traditional methods ask voters to express themselves by comparing them: • ticking one candidate at most (majority rule, first-past-the-post) or several candidates (approval voting), candidates' total ticks ranking them; • rank-ordering the candidates (Borda rule, alternative vote or preferential voting, Llull's rule, Dasgupta- Maskin method, . ), differently derived numerical scores ranking them. However, no traditional method measures the support of one candidate.1 Instead, the theory of voting (or of social choice) elevates to a basic distinguishing axiom the faith that in an election between two candidates majority rule is the only proper rule. -
Democracy Without Elections Mainz
Democracy without Elections: Is electoral accountability essential for democracy? Felix Gerlsbeck [email protected] Paper prepared for the workshop “Democratic Anxiety. Democratic Resilience.” Mainz, 15-17 June 2017 DRAFT VERSION, PLEASE DO NOT CITE WITHOUT AUTHOR’S PERMISSION 1. Introduction The idea of choosing political decision-makers by sortition, that is, choosing them randomly from a pool of the entire population or from some qualified subset, through some form of lottery or other randomizing procedure, is familiar to democrats at least since ancient Athens. Apart from the selection of trial juries, however, sortition has all but disappeared from official decision-making procedures within contemporary democratic systems, and free, equal, and regular election through voting by the entire qualified population of candidates who put themselves forward for political office, has taken its place. Nevertheless, there has been renewed interest in the idea of reviving sortition-based elements within modern democratic systems over the last years: a number of democratic theorists see great promise in complementing elected decision-making institutions with those selected randomly. These proposals variously go under the names mini-publics, citizen juries, citizen assemblies, lottocracy, enfranchisement lottery, and even Machiavellian Democracy.1 The roots of this practice go back to ancient Athens. During the 5th century Athenian democracy, the equivalent of the parliamentary body tasked with deliberating 1 See for instance, Guerrero 2014; Fishkin 2009; Warren & Gastil 2015; Ryan & Smith 2014; Saunders 2012; López-Guerra 2014; López-Guerra 2011; McCormick 2011. 1 and drafting policy proposals, the boule, was chosen by lot from the citizens of Athens through a complex system of randomization.