Analyzing the practical relevance of voting paradoxes via ehrhart theory, computer simulations, and empirical data

Felix Brandt, Christian Geist, Martin Strobel

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

16 Scopus citations

Abstract

Results from social choice theory are increasingly used to argue about collective decision making in computational multiagent systems. A large part of the social choice literature studies voting paradoxes in which seemingly mild properties are violated by common voting rules. In this paper, we investigate the likelihood of the Condorcet Loser Paradox (CLP) and the Agenda Contraction Paradox (ACP) using Ehrhart theory, computer simulations, and empirical data. We present the first analytical results for the CLP on four alternatives and show that our experimental results, which go well beyond four alternatives, are in almost perfect congruence with the analytical results. It turns out that the CLP-which is often cited as a major flaw of some Condorcet extensions such as Dodgson's rule, Young's rule, and MaxiMin-is of no practical relevance. The ACP, on the other hand, frequently occurs under various distributional assumptions about the voters' preferences. The extent to which it is real threat, however, strongly depends on the voting rule, the underlying distribution of preferences, and, somewhat surprisingly, the parity of the number of voters.

Original languageEnglish
Title of host publicationAAMAS 2016 - Proceedings of the 2016 International Conference on Autonomous Agents and Multiagent Systems
PublisherInternational Foundation for Autonomous Agents and Multiagent Systems (IFAAMAS)
Pages385-393
Number of pages9
ISBN (Electronic)9781450342391
StatePublished - 2016
Event15th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2016 - Singapore, Singapore
Duration: 9 May 201613 May 2016

Publication series

NameProceedings of the International Joint Conference on Autonomous Agents and Multiagent Systems, AAMAS
ISSN (Print)1548-8403
ISSN (Electronic)1558-2914

Conference

Conference15th International Conference on Autonomous Agents and Multiagent Systems, AAMAS 2016
Country/TerritorySingapore
CitySingapore
Period9/05/1613/05/16

Keywords

  • Ehrhart theory
  • Social choice theory
  • Voting

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