Social Choice and Voting Rules

2006 ◽  
pp. 383-405
Keyword(s):  
Social Choice ◽  
Voting Rules

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.

scholarly journals Optimal Voting Rules

1995 ◽  
Vol 9 (1) ◽  
pp. 51-64 ◽  
Author(s):  
Peyton Young
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimation ◽  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Likelihood Estimation ◽  
Voting Rules ◽  
Voting Rule ◽  
Marquis De Condorcet ◽  
Kenneth Arrow

Modern social choice theory, following Kenneth Arrow, treats voting as a method for aggregating diverse preferences and values. An earlier view, initiated by Marquis de Condorcet, is that voting is a method for aggregating information. Voters’ opinions differ because they make errors of judgment; absent these errors they would all agree on the best choice. The goal is to design a voting rule that identifies the best choice with highest probability. This paper examines maximum likelihood estimation. Surprisingly, the optimal rule can also be axiomatized by variations of Arrow's axioms.

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.

scholarly journals The superdominance relation, the positional winner, and more missing links between Borda and Condorcet

2018 ◽  
Vol 31 (1) ◽  
pp. 46-65 ◽  
Author(s):  
Raúl Pérez-Fernández ◽  
Bernard De Baets
Keyword(s):  
Eighteenth Century ◽  
Social Choice ◽  
Positional Information ◽  
Voting Rules ◽  
Meeting Point ◽  
Axiomatic Characterizations ◽  
Points Of View ◽  
Choice Set

The field of social choice dates back to the eighteenth century, when Borda and Condorcet started a never-ending discussion about the use of either positional or pairwise information. Three centuries later, after countless axiomatic characterizations of voting rules, impossibility theorems and many other study subjects, researchers still debate whether positional information is really sensitive to manipulation or pairwise information disregards the transitivity of voters’ preferences. In a previous paper, we introduced the notions of supercovering relation and pairwise winner, which resulted in a meeting point for both points of view of the theory of social choice. In this paper, we continue this direction and propose the notions of superdominance relation and positional winner that will prove to be the alter egos of the supercovering relation and the pairwise winner when positional information (rather than pairwise information) is considered. Moreover, we analyse a new interesting choice set: the unsuperdominated set.

scholarly journals Subset Selection Via Implicit Utilitarian Voting

2017 ◽  
Vol 58 ◽  
pp. 123-152 ◽  
Author(s):  
Ioannis Caragiannis ◽  
Swaprava Nath ◽  
Ariel D. Procaccia ◽  
Nisarg Shah
Keyword(s):  
Social Choice ◽  
Subset Selection ◽  
Voting Rules ◽  
For Profit ◽  
Design And Implementation ◽  
Ordinal Preferences ◽  
Not For Profit ◽  
Two Measures ◽  
Voting Methods ◽  
Latent Utility

How should one aggregate ordinal preferences expressed by voters into a measurably superior social choice? A well-established approach -- which we refer to as implicit utilitarian voting -- assumes that voters have latent utility functions that induce the reported rankings, and seeks voting rules that approximately maximize utilitarian social welfare. We extend this approach to the design of rules that select a subset of alternatives. We derive analytical bounds on the performance of optimal (deterministic as well as randomized) rules in terms of two measures, distortion and regret. Empirical results show that regret-based rules are more compelling than distortion-based rules, leading us to focus on developing a scalable implementation for the optimal (deterministic) regret-based rule. Our methods underlie the design and implementation of RoboVote.org, a not-for-profit website that helps users make group decisions via AI-driven voting methods.

scholarly journals Representation of the citizens in a federal union

2018 ◽  
pp. 129-137
Author(s):  
Vincent Merlin
Keyword(s):  
Social Choice ◽  
Voting Rules

The article presents several contributions proposed by game theorist and economists, especially social choice experts, on the design of „good” voting rules in federal unions.

scholarly journals Evaluating Approval-Based Multiwinner Voting in Terms of Robustness to Noise

2020 ◽  
Author(s):  
Ioannis Caragiannis ◽  
Christos Kaklamanis ◽  
Nikos Karanikolas ◽  
George A. Krimpas
Keyword(s):  
Social Choice ◽  
Ground Truth ◽  
Computational Social Choice ◽  
Voting Rules ◽  
Voting Rule ◽  
Robustness To Noise ◽  
Noise Models ◽  
Robust To Noise ◽  
Choice Literature

Approval-based multiwinner voting rules have recently received much attention in the Computational Social Choice literature. Such rules aggregate approval ballots and determine a winning committee of alternatives. To assess effectiveness, we propose to employ new noise models that are specifically tailored for approval votes and committees. These models take as input a ground truth committee and return random approval votes to be thought of as noisy estimates of the ground truth. A minimum robustness requirement for an approval-based multiwinner voting rule is to return the ground truth when applied to profiles with sufficiently many noisy votes. Our results indicate that approval-based multiwinner voting can indeed be robust to reasonable noise. We further refine this finding by presenting a hierarchy of rules in terms of how robust to noise they are.

SOCIAL CHOICE FOR DATA FUSION

2004 ◽  
Vol 03 (04) ◽  
pp. 619-631
Author(s):  
SHANFENG ZHU ◽  
QIZHI FANG ◽  
WEIMIN ZHENG
Keyword(s):  
Decision Theory ◽  
Social Choice ◽  
Choice Theory ◽  
Social Choice Theory ◽  
Information Age ◽  
Theoretic Approach ◽  
Voting Rules ◽  
Graph Theoretic ◽  
Graph Theoretic Approach ◽  
New Algorithms

Social choice theory is the study of decision theory on how to aggregate separate preferences into group's rational preference. It has wide applications, especially on the design of voting rules, and brings far-reaching influence on the development of modern political science and welfare economics. With the advent of the information age, social choice theory finds its up-to-date application on designing effective Metasearch engines. Metasearch engines provide effective searching by combining the results of multiple source search engines that make use of diverse models and techniques. In this work, we analyze social choice algorithms in a graph-theoretic approach. In addition to classical social choice algorithms, such as Borda and Condorcet, we study one special type of social choice algorithms, elimination voting, to tackle Metasearch problem. Some new algorithms are proposed and examined in the fusion experiment on TREC data. It shows that these elimination voting algorithms achieve satisfied performance when compared with Borda algorithm.

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