scholarly journals Equitable Voting Rules

Econometrica ◽  
2021 ◽  
Vol 89 (2) ◽  
pp. 563-589
Author(s):  
Laurent Bartholdi ◽  
Wade Hann-Caruthers ◽  
Maya Josyula ◽  
Omer Tamuz ◽  
Leeat Yariv
Keyword(s):  
Group Theory ◽  
Social Choice ◽  
Population Size ◽  
Majority Rule ◽  
Square Root ◽  
Voting Rules ◽  
Choice Procedures ◽  
Symmetry Assumption ◽  
Minimal Winning Coalitions ◽  
Crucial Assumption

May's theorem (1952), a celebrated result in social choice, provides the foundation for majority rule. May's crucial assumption of symmetry, often thought of as a procedural equity requirement, is violated by many choice procedures that grant voters identical roles. We show that a weakening of May's symmetry assumption allows for a far richer set of rules that still treat voters equally. We show that such rules can have minimal winning coalitions comprising a vanishing fraction of the population, but not less than the square root of the population size. Methodologically, we introduce techniques from group theory and illustrate their usefulness for the analysis of social choice questions.

A Note on A. D. Taylor’s Property of Independence of Irrelevant Alternatives for Voting Rules

2017 ◽  
Vol 5 (2) ◽  
pp. 99-104 ◽  
Author(s):  
Somdeb Lahiri ◽  
Prasanta K. Pattanaik
Keyword(s):  
Social Choice ◽  
Interesting Property ◽  
Voting Rules ◽  
Independence Of Irrelevant Alternatives ◽  
Choice Procedures ◽  
Voting Procedures

In a widely used textbook on mathematics and politics, Taylor introduced an interesting property of social choice procedures, which we call ‘Taylor’s Independence of Irrelevant Alternatives (TIIA)’. Taylor proved a result showing that every voting procedure belonging to a certain class of voting procedures violates TIIA. The purpose of this note is to supplement Taylor’s result by showing that a large number of voting rules, which do not belong to the class of voting procedures figuring in Taylor’s result, also violate TIIA.

Deliberation, Preference Uncertainty, and Voting Rules

2006 ◽  
Vol 100 (2) ◽  
pp. 209-217 ◽  
Author(s):  
DAVID AUSTEN-SMITH ◽  
TIMOTHY J. FEDDERSEN
Keyword(s):  
Information Sharing ◽  
Majority Rule ◽  
Common Knowledge ◽  
General Setting ◽  
Full Information ◽  
Information Revelation ◽  
Voting Rules ◽  
Unanimity Rule ◽  
Preference Uncertainty ◽  
Voting Rule

A deliberative committee is a group of at least two individuals who first debate about what alternative to choose prior to these same individuals voting to determine the choice. We argue, first, that uncertainty about individuals' private preferences is necessary for full information sharing and, second, demonstrate in a very general setting that the condition under which unanimity can support full information revelation in debate amounts to it being common knowledge that all committee members invariably share identical preferences over the alternatives. It follows that if ever there exists an equilibrium with fully revealing debate under unanimity rule, there exists an equilibrium with fully revealing debate under any voting rule. Moreover, the converse is not true of majority rule if there is uncertainty about individuals' preferences.

The Unexpected Empirical Consensus Among Consensus Methods

2007 ◽  
Vol 18 (7) ◽  
pp. 629-635 ◽  
Author(s):  
Michel Regenwetter ◽  
Aeri Kim ◽  
Arthur Kantor ◽  
Moon-Ho R. Ho
Keyword(s):  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
American Psychological Association ◽  
Decision Makers ◽  
Consensus Methods ◽  
Worst Case ◽  
Large Numbers ◽  
Choice Procedures ◽  
Multimethod Approach

In economics and political science, the theoretical literature on social choice routinely highlights worst-case scenarios and emphasizes the nonexistence of a universally best voting method. Behavioral social choice is grounded in psychology and tackles consensus methods descriptively and empirically. We analyzed four elections of the American Psychological Association using a state-of-the-art multimodel, multimethod approach. These elections provide rare access to (likely sincere) preferences of large numbers of decision makers over five choice alternatives. We determined the outcomes according to three classical social choice procedures: Condorcet, Borda, and plurality. Although the literature routinely depicts these procedures as irreconcilable, we found strong statistical support for an unexpected degree of empirical consensus among them in these elections. Our empirical findings stand in contrast to two centuries of pessimistic thought experiments and computer simulations in social choice theory and demonstrate the need for more systematic descriptive and empirical research on social choice than exists to date.

A leximin characterization of strategy-proof and non-resolute social choice procedures

2002 ◽  
Vol 20 (4) ◽  
pp. 809-829 ◽  
Author(s):  
Donald E. Campbell ◽  
Jerry S. Kelly
Keyword(s):  
Social Choice ◽  
Choice Procedures ◽  
Strategy Proof

scholarly journals Aggregation over Metric Spaces: Proposing and Voting in Elections, Budgeting, and Legislation

2021 ◽  
Vol 70 ◽  
pp. 1413-1439
Author(s):  
Laurent Bulteau ◽  
Gal Shahaf ◽  
Ehud Shapiro ◽  
Nimrod Talmon
Keyword(s):  
Decision Making ◽  
Social Choice ◽  
Metric Space ◽  
Metric Spaces ◽  
Solution Concept ◽  
Abstract Model ◽  
Participatory Budgeting ◽  
Voting Rules ◽  
Ideal Element ◽  
Proxy Voting

We present a unifying framework encompassing a plethora of social choice settings. Viewing each social choice setting as voting in a suitable metric space, we offer a general model of social choice over metric spaces, in which—similarly to the spatial model of elections—each voter specifies an ideal element of the metric space. The ideal element acts as a vote, where each voter prefers elements that are closer to her ideal element. But it also acts as a proposal, thus making all participants equal not only as voters but also as proposers. We consider Condorcet aggregation and a continuum of solution concepts, ranging from minimizing the sum of distances to minimizing the maximum distance. We study applications of our abstract model to various social choice settings, including single-winner elections, committee elections, participatory budgeting, and participatory legislation. For each setting, we compare each solution concept to known voting rules and study various properties of the resulting voting rules. Our framework provides expressive aggregation for a broad range of social choice settings while remaining simple for voters; and may enable a unified and integrated implementation for all these settings, as well as unified extensions such as sybil-resiliency, proxy voting, and deliberative decision making. We study applications of our abstract model to various social choice settings, including single-winner elections, committee elections, participatory budgeting, and participatory legislation. For each setting, we compare each solution concept to known voting rules and study various properties of the resulting voting rules. Our framework provides expressive aggregation for a broad range of social choice settings while remaining simple for voters; and may enable a unified and integrated implementation for all these settings, as well as unified extensions such as sybil-resiliency, proxy voting, and deliberative decision making.

scholarly journals Computational Social Choice Meets Databases

2018 ◽  
Author(s):  
Benny Kimelfeld ◽  
Phokion G. Kolaitis ◽  
Julia Stoyanovich
Keyword(s):  
Computational Complexity ◽  
Social Choice ◽  
Relational Database ◽  
Database Management ◽  
Plurality Rule ◽  
Technical Level ◽  
Computational Social Choice ◽  
Conceptual Level ◽  
Voting Rules ◽  
Conjunctive Queries

We develop a novel framework that aims to create bridges between the computational social choice and the database management communities. This framework enriches the tasks currently supported in computational social choice with relational database context, thus making it possible to formulate sophisticated queries about voting rules, candidates, voters, issues, and positions. At the conceptual level, we give rigorous semantics to queries in this framework by introducing the notions of necessary answers and possible answers to queries. At the technical level, we embark on an investigation of the computational complexity of the necessary answers. In particular, we establish a number of results about the complexity of the necessary answers of conjunctive queries involving the plurality rule that contrast sharply with earlier results about the complexity of the necessary winners under the plurality rule.

scholarly journals Communication, Distortion, and Randomness in Metric Voting

2020 ◽  
Vol 34 (02) ◽  
pp. 2087-2094
Author(s):  
David Kempe
Keyword(s):  
Lower Bound ◽  
Social Choice ◽  
Metric Spaces ◽  
Social Choice Rule ◽  
Voting Rules ◽  
Ordinal Comparison ◽  
First Choice ◽  
Voting Mechanisms ◽  
Sum Of Distances ◽  
Social Choice Rules

In distortion-based analysis of social choice rules over metric spaces, voters and candidates are jointly embedded in a metric space. Voters rank candidates by non-decreasing distance. The mechanism, receiving only this ordinal (comparison) information, must select a candidate approximately minimizing the sum of distances from all voters to the chosen candidate. It is known that while the Copeland rule and related rules guarantee distortion at most 5, the distortion of many other standard voting rules, such as Plurality, Veto, or k-approval, grows unboundedly in the number n of candidates.An advantage of Plurality, Veto, or k-approval with small k is that they require less communication from the voters; all deterministic social choice rules known to achieve constant distortion require voters to transmit their complete rankings of all candidates. This motivates our study of the tradeoff between the distortion and the amount of communication in deterministic social choice rules.We show that any one-round deterministic voting mechanism in which each voter communicates only the candidates she ranks in a given set of k positions must have distortion at least 2n-k/k; we give a mechanism achieving an upper bound of O(n/k), which matches the lower bound up to a constant. For more general communication-bounded voting mechanisms, in which each voter communicates b bits of information about her ranking, we show a slightly weaker lower bound of Ω(n/b) on the distortion.For randomized mechanisms, Random Dictatorship achieves expected distortion strictly smaller than 3, almost matching a lower bound of 3 − 2/n for any randomized mechanism that only receives each voter's top choice. We close this gap, by giving a simple randomized social choice rule which only uses each voter's first choice, and achieves expected distortion 3 − 2/n.

THE CORE IN FUZZY SPATIAL MODELS

2010 ◽  
Vol 06 (01) ◽  
pp. 17-29 ◽  
Author(s):  
JOHN N. MORDESON ◽  
TERRY D. CLARK
Keyword(s):  
Majority Rule ◽  
Spatial Models ◽  
Partial Solution ◽  
Major Conclusion ◽  
Voting Rules ◽  
The Core ◽  
Fuzzy Core

Predictions concerning voting outcomes in crisp spatial models rely heavily on the existence of a core, in the absence of which political players choosing among a set of alternatives by majority rule will not be able to arrive at a stable choice. No matter which option they might initially choose, most voting rules will permit another option to defeat the previously chosen one. Such problems particularly plague majority rule spatial models at dimensionalities greater than one. In a series of recent papers, we have argued that fuzzy spatial models offer a partial solution to this problem. In this paper, we explore the existence of a fuzzy core. Our major conclusion is that a fuzzy core is more likely in two or more dimensions as the number of players increases.

Aggregation of Consumer Ratings of Online Products: Applying Social Choice Theory to Investigate the Cordorcet Efficiency of Mean Rule

2007 ◽  
Vol 51 (13) ◽  
pp. 837-840
Author(s):  
Xianjun Sam Zheng
Keyword(s):  
Sample Size ◽  
Social Choice ◽  
Majority Rule ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Sample Mean ◽  
Condorcet Efficiency ◽  
Size Number ◽  
Consumer Ratings ◽  
The Mean

Mean rule has been popularly used to aggregate consumer ratings of online products. This study applied social choice theory to evaluate the Condorcet efficiency of the mean rule, and to investigate the effect of sample size (number of voters) on the agreement or disagreement between the mean and majority rules. The American National Election Survey data (1968) were used, where three candidates competed for the presidency, and the numerical thermometer scores were provided for each candidate. Random sampling data with varied sample sizes were drew from the survey, and then were aggregated according to the majority rule, the mean rule, and other social choice rules. The results show that the sample winner of the mean rule agrees with the sample majority winner very well; as sample size increases, the sample mean rule even converges faster to the correct population majority winner and ordering than does the sample majority rule. The implications for using aggregation rules for online product rating were also discussed.

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