scholarly journals An Analytical and Experimental Comparison of Maximal Lottery Schemes

2018 ◽  
Author(s):  
Florian Brandl ◽  
Felix Brandt ◽  
Christian Stricker
Keyword(s):  
Social Choice ◽  
Computer Simulations ◽  
Shannon Entropy ◽  
Experimental Comparison ◽  
Computational Social Choice ◽  
Voting Rules ◽  
Weighted Majority ◽  
Support Size ◽  
Interesting Class ◽  
Pareto Efficient

Randomized voting rules are gaining increasing attention in computational and non-computational social choice. A particularly interesting class of such rules are maximal lottery (ML) schemes, which were proposed by Peter Fishburn in 1984 and have been repeatedly recommended for practical use. However, the subtle differences between different ML schemes are often ignored. Two canonical subsets of ML schemes are C1-ML schemes (which only depend on unweighted majority comparisons) and C2-ML schemes (which only depend on weighted majority comparisons). We prove that C2-ML schemes are the only Pareto efficient---but also among the most manipulable---ML schemes. Furthermore, we evaluate the frequency of manipulable preference profiles and the degree of randomization of ML schemes via extensive computer simulations. In general, ML schemes are rarely manipulable and often do not randomize at all, especially when there are only few alternatives. For up to 21 alternatives, the average support size of ML schemes lies below 4 under reasonable assumptions. The average degree of randomization (in terms of Shannon entropy) of C2-ML schemes is significantly lower than that of C1-ML schemes.

scholarly journals An analytical and experimental comparison of maximal lottery schemes

2021 ◽  
Author(s):  
Florian Brandl ◽  
Felix Brandt ◽  
Christian Stricker
Keyword(s):  
Computer Simulations ◽  
Condorcet Winner ◽  
Average Degree ◽  
Experimental Comparison ◽  
Voting Rules ◽  
Weighted Majority ◽  
Interesting Class ◽  
Relative Notion

AbstractMaximal lottery ($$ ML $$ ML ) schemes constitute an interesting class of randomized voting rules that were proposed by Peter Fishburn in 1984 and have been repeatedly recommended for practical use. However, the subtle differences between different $$ ML $$ ML schemes are often overlooked. Two canonical subsets of $$ ML $$ ML schemes are "Image missing" schemes (which only depend on unweighted majority comparisons) and "Image missing" schemes (which only depend on weighted majority comparisons). We prove that "Image missing" schemes are the only homogeneous $$ ML $$ ML schemes that satisfy $$ SD $$ SD -efficiency and $$ SD $$ SD -participation, but are also among the most manipulable $$ ML $$ ML schemes. While all $$ ML $$ ML schemes are manipulable and even violate monotonicity, they are never manipulable when a Condorcet winner exists and satisfy a relative notion of monotonicity. We also evaluate the frequency of manipulable preference profiles and the degree of randomization of $$ ML $$ ML schemes via extensive computer simulations. In summary, $$ ML $$ ML schemes are rarely manipulable and often do not randomize at all, especially for few alternatives. The average degree of randomization of "Image missing" schemes is consistently lower than that of "Image missing" schemes.

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 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.

Full Implementation under Ambiguity

2021 ◽  
Vol 13 (1) ◽  
pp. 148-178
Author(s):  
Huiyi Guo ◽  
Nicholas C. Yannelis
Keyword(s):  
Social Choice ◽  
Expected Utility ◽  
Sufficient Conditions ◽  
Choice Functions ◽  
Maxmin Expected Utility ◽  
Special Cases ◽  
Social Choice Functions ◽  
Bayesian Implementation ◽  
Pareto Efficient ◽  
Choice Set

This paper introduces the maxmin expected utility framework into the problem of fully implementing a social choice set as ambiguous equilibria. Our model incorporates the Bayesian framework and the Wald-type maxmin preferences as special cases and provides insights beyond the Bayesian implementation literature. We establish necessary and almost sufficient conditions for a social choice set to be fully implementable. Under the Wald-type maxmin preferences, we provide easy-to-check sufficient conditions for implementation. As applications, we implement the set of ambiguous Pareto-efficient and individually rational social choice functions, the maxmin core, the maxmin weak core, and the maxmin value. (JEL D71, D81, D82)

Computer simulations of voting systems

2000 ◽  
Vol 03 (01n04) ◽  
pp. 181-194 ◽  
Author(s):  
Dominique Lepelley ◽  
Ahmed Louichi ◽  
Fabrice Valognes
Keyword(s):  
Monte Carlo ◽  
Computer Simulations ◽  
Monte Carlo Methods ◽  
Scoring Rules ◽  
Voting Systems ◽  
Voting Rules ◽  
Asymptotic Case ◽  
Majority Principle ◽  
Voting Procedures ◽  
Democratic Principles

All voting procedures are susceptible to give rise, if not to paradoxes, at least to violations of some democratic principles. In this paper, we evaluate and compare the propensity of various voting rules -belonging to the class of scoring rules- to satisfy two versions of the majority principle. We consider the asymptotic case where the numbers of voters tends to infinity and, for each rule, we study with the help of Monte Carlo methods how this propensity varies as a function of the number of candidates.

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.

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