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A Note on Embedding Voting Rules Into Judgment Aggregation
A Note on Embedding Voting Rules into Judgment Aggregation Ulle Endriss Institute for Logic, Language and Computation University of Amsterdam Working Paper, 28 October 2015 (this version: 12 December 2015) Abstract I propose a model of judgment aggregation in which we can distinguish rationality con- straints (to be respected by the individual agents when supplying their judgments) from feasibility constraints (to be respected by the outcome returned by the judgment aggre- gation rule). This allows for a particularly natural way of embedding a wide variety of different voting rules into judgment aggregation. 1 Introduction The field of judgment aggregation is concerned with the design and analysis of procedures for combining the judgments of several agents regarding the truth of a number of logically related statements into a collective judgment (List and Puppe, 2009; Grossi and Pigozzi, 2014; Endriss, 2016). Inspired by questions arising in legal theory (Kornhauser and Sager, 1993), it has received significant attention in both philosophy and economics, starting with the seminal contribution of List and Pettit (2002). More recently, due both to its potential for applications in areas such as multiagent systems and crowdsourcing, and due to the interesting algorithmic questions it raises, judgment aggregation is also receiving increasing attention in computer science and artificial intelligence (Endriss, 2016). While early work on judgment aggregation has focused on applications of the axiomatic method, inspired by closely related work in other areas of social choice theory, to derive a host of impossibility and characterisation results (List and Puppe, 2009), more recently attention has shifted towards designing practically useful aggregation rules (Dietrich and List, 2007a; Miller and Osherson, 2009; Lang et al., 2011; Lang and Slavkovik, 2013; Dietrich, 2014; Nehring et al., 2014; Porello and Endriss, 2014; Endriss and Grandi, 2014; Costantini et al., 2016). -
Tie-Breaking the Highest Median : Alternatives to the Majority Judgment
Noname manuscript No. (will be inserted by the editor) Tie-breaking the Highest Median : Alternatives to the Majority Judgment Adrien Fabre the date of receipt and acceptance should be inserted later Keywords : Voting system; Election; Ranking; Majority Judgment; Acknowledgements I am grateful to Jean-François Laslier, Rida Median; Grades; Evaluative voting; Evaluation; Typical judgment; Laraki as well as three anonymous reviewers for their comments Central Judgment. and suggestions. I am thankful to François Durand for the proofrea- ding. I thank Maria Sarmiento for the grammar check. JEL classification : D71; D72. Replication files All the code, figures and data are Résumé The paper deals with voting rules that require available on github.com/bixiou/highest_median. voters to rate the candidates on a finite evaluation scale and then elect a candidate whose median grade is maxi- mum. These rules differ by the way they choose among candidates with the same median grade. Call proponents (resp. opponents) of a candidate the voters who rate this candidate strictly above (resp. strictly below) her median grade. A simple rule, called the typical judgment, orders tied candidates by the difference between their share of proponents and opponents. An appealing rule, called the usual judgment, divides this difference by the share of median votes. An alternative rule, called the central judg- ment, compares the relative shares of proponents and opponents. The usual judgment is continuous with res- pect to these shares. The majority judgment of Balinski & Laraki(2007) considers the largest of these shares and loses continuity. A result in Balinski & Laraki(2014) aims to characterize the majority judgment and states that only a certain class of functions share some valuable cha- racteristics, like monotonicity. -
Belief Merging Versus Judgment Aggregation
Belief Merging versus Judgment Aggregation Patricia Everaere Sébastien Konieczny Pierre Marquis CRIStAL-CNRS CRIL-CNRS CRIL-CNRS Université Lille 1, France Université d’Artois, France Université d’Artois, France [email protected] [email protected] [email protected] ABSTRACT logically related) issues, from the judgments given on each issue The problem of aggregating pieces of propositional information by the members of a group of n agents. Again, several operators coming from several agents has given rise to an intense research ac- (referred to as rules or correspondences) have been put forward and tivity. Two distinct theories have emerged. On the one hand, belief the rationality issue has been investigated as well. merging has been considered in AI as an extension of belief revi- Belief merging and judgment aggregation have similar, yet dis- sion. On the other hand, judgment aggregation has been developed tinct goals. Especially, a belief merging process and a judgment ag- in political philosophy and social choice theory. Judgment aggre- gregation process do not consider the same inputs and outputs. In gation focusses on some specific issues (represented as formulas a belief merging process, the input is a profile E = (K1;:::;Kn) and gathered into an agenda) on which each agent has a judgment, of propositional belief bases (finite sets of propositional formulas), and aims at defining a collective judgment set (or a set of collective and a formula µ representing some integrity constraints the result of judgment sets). Belief merging considers each source of informa- the process must comply with; it outputs an (aggregated/collective) tion (the belief base of each agent) as a whole, and aims at defining base which satisfies the integrity constraints. -
Causal Comparisons
Fordham Law Review Volume 60 Issue 5 Article 4 1992 Causal Comparisons Robert N. Strassfeld Follow this and additional works at: https://ir.lawnet.fordham.edu/flr Part of the Law Commons Recommended Citation Robert N. Strassfeld, Causal Comparisons, 60 Fordham L. Rev. 913 (1992). Available at: https://ir.lawnet.fordham.edu/flr/vol60/iss5/4 This Article is brought to you for free and open access by FLASH: The Fordham Law Archive of Scholarship and History. It has been accepted for inclusion in Fordham Law Review by an authorized editor of FLASH: The Fordham Law Archive of Scholarship and History. For more information, please contact [email protected]. Causal Comparisons Cover Page Footnote I am grateful to Susan Helper, Peter Junger, and William Marshall for their helpful comments and to Sally Walters for her research assistance. I also thank Heidi Emick for extraordinary secretarial support. This article is available in Fordham Law Review: https://ir.lawnet.fordham.edu/flr/vol60/iss5/4 CAUSAL COMPARISONS ROBERT N. STRASSFELD * Focusing on the multiple meanings of the statement "A was a more important cause of C than was B, " Professor Strassfeld considers the feasibility of compara- tive causation as a means of apportioninglegal responsibilityfor harms He con- cludes that by combining two different interpretations of "more important cause"--judgments of comparative counterfactual similarity and the Uniform ComparativeFault Act approachof comparative responsibility-we can effectively make causal comparisons and avoid the effort to compare such incommen- surables as the defendant'sfault under a strict liability standard and the plain- tiff's fault for failure to exercise reasonable care I. -
The Strange ''Majority Judgment''
The strange ”Majority Judgment” Jean-François Laslier To cite this version: Jean-François Laslier. The strange ”Majority Judgment”. 2018. hal-01965227 HAL Id: hal-01965227 https://hal.archives-ouvertes.fr/hal-01965227 Preprint submitted on 25 Dec 2018 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. The strange “Majority Judgment” Jean-François Laslier* “Majority Judgment” is an evaluative voting rule that picks a candidate with the best median evaluation. This paper deals with the following question: what does one do when choosing according to the best median? This principle amounts to finding which half-population should be neglected in order to satisfy, in the sense of a Rawlsian compromise, the other half. This principle clashes with the definition of democracy as the participation of everyone, not half of the population plus one. Moreover, providing the highest possible level of satisfaction to that half-population that is the easiest to satisfy is not what is achieved by the rules of choice called “majoritarian,” which respect the Condorcet principle. On the contrary, these rules favor consensual solutions, in particular in standard political environments. This explains why the “Majority Judgment” often yields surprising outcomes. -
Discussion Paper Discussion Paper
INSTITUTT FOR FORETAKSØKONOMI INSTITUTT FOR FORETAKSØKONOMI DEPARTMENT OF BUSINESS AND MANAGEMENT SCIENCE DEPARTMENT OF BUSINESS AND MANAGEMENT SCIENCE Norges Handelshøyskole NHH Tlf/Tel: +47 55 95 90 00 FOR 13 2018 Helleveien 30 Faks/Fax: +47 55 95 91 00 ISSN: 1500-4066 Norwegian School of Economics NO-5045 Bergen [email protected] October 2018 Norway www.nhh.no Discussion paper Discussion paper What is wrong with IRV? BY Eivind Stensholt 20.09.18 What is wrong with IRV? BY Eivind Stensholt Norwegian School of Economics Abstract Struggles over the single-seat preferential election method IRV, Instant Runoff Voting, (a.k.a. AV, Alternative Vote or RCV, Ranked-Choice Voting) go on in many arenas: legislatures, courts, websites, and scholarly journals. Monotonicity failures, i.e. elections (preference distributions) that may allow the startling tactical voting of Pushover or its reverse, has come to the forefront. An analysis of 3-candidate elections concludes that monotonicity failures, while not rare, are hard to predict and risky to exploit; it also explains the scarcity of evidence for effects on election results. A more unfortunate possibility is the No-Show accident; the number of ballots with preference order XYZ grows beyond a critical size and cause Z to win instead of Y. An analysis concludes that this must happen often enough to justify a modification of the rules. Pictograms and constellation diagrams are visualization tools that organize the set of possible elections efficiently for the analysis, which obtains explicit classification of elections where Pushover or a No-Show accident may occur or may already have occurred, and of bounds for the number of voters that must be involved. -
Split Cycle: a New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers
Split Cycle: A New Condorcet Consistent Voting Method Independent of Clones and Immune to Spoilers Wesley H. Hollidayy and Eric Pacuitz y University of California, Berkeley ([email protected]) z University of Maryland ([email protected]) March 23, 2021 Abstract We propose a Condorcet consistent voting method that we call Split Cycle. Split Cycle belongs to the small family of known voting methods that significantly narrow the choice of winners in the presence of majority cycles while also satisfying independence of clones. In this family, only Split Cycle satisfies a new criterion we call immunity to spoilers, which concerns adding candidates to elections, as well as the known criteria of positive involvement and negative involvement, which concern adding voters to elections. Thus, in contrast to other clone-independent methods, Split Cycle mitigates both “spoiler effects” and “strong no show paradoxes.” Contents 1 Introduction 2 1.1 The Problem of Spoilers . .4 1.2 The Strong No Show Paradox . .7 1.3 Organization . 10 2 Preliminaries 11 2.1 Profiles, Margin Graphs, and Voting Methods . 11 arXiv:2004.02350v8 [cs.GT] 23 Mar 2021 2.2 Operations on Profiles . 13 3 Split Cycle 14 3.1 Three Main Ideas . 14 3.2 Defining Split Cycle . 16 3.3 Comparison with Beat Path and Ranked Pairs . 20 4 Core Criteria 22 4.1 Condorcet Criteria . 23 4.2 Monotonicity . 23 1 4.3 Independence of Clones . 24 4.4 Narrowing . 25 5 New Criteria 26 5.1 Immunity to Spoilers and Stability for Winners . 27 5.2 Amalgamation . 29 5.3 Rejectability . -
LAW and LEGISLATIVE DIGITAL LIBRARY at the Maine State Law and Legislative Reference Library
MAINE STATE LEGISLATURE The following document is provided by the LAW AND LEGISLATIVE DIGITAL LIBRARY at the Maine State Law and Legislative Reference Library http://legislature.maine.gov/lawlib Reproduced from scanned originals with text recognition applied (searchable text may contain some errors and/or omissions) ACTS AND RESOLVES PASSED BY TilE THIRTY-SIXTH LEGISLATUR,E OF THE STATE OF l\1:AINE, 1857. Published hy the Secretary of State, agreeably to Resolves of June 28, 1820, February 26, 1840, and March 10, 1842. AUGUSTA: STEVENS & BLAINE, PRINTERS TO T11M STATE. 1857. OPINIONS OF THE JUSTICES OF THE S, J. COURT, ON QUESTION PROPOUNDED BY THE SENATE, :MAROH 26, 1857. - STATElYIENT OF QUESTION. Sl'ATE OF MAINE. IN SENATE, March 26, 1857. ORDERED, That the justices or the supreme judicial COUl't be, and they hereby are, required to give their opinions upon the following' question: Are free colored persons, oj African drscent, having a 'residence establ·ished in some town in this state, for I.he I.enll of three months ne.vt preceding any election, allthor'ized under the pl'Ov'isions of the constitu.tion of this state to be elect01's f01' governor, scnators and representaliVis 1 AND IT IS FURTHER ORDERED, That a copy hereof, signed by the president pro icm. and attested by thc secretary of the senate, be com· municated forthwith, by the most expeditions modc, to each one of the justices of the supreme judicial court, and an answer to the forcgoing qur,stion be requested at the earliest possible moment. But if the legislature shall have adJourned before the answer can be prepared, the same shall be returned to the secretary of state, to be by him pll b· lished in the state paper.