Condorcet Relaxation In Spatial Voting

Arnold Filtser, Omrit Filtser

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

Abstract

Consider a set of voters V, represented by a multiset in a metric space (X,d). The voters have to reach a decision - a point in X. A choice p ? X is called a ß-plurality point for V, if for any other choice q ? X it holds that |{v ? V | ß · d(p,v) = d(q,v)}| = |V2|. In other words, at least half of the voters “prefer” p over q, when an extra factor of ß is taken in favor of p. For ß = 1, this is equivalent to Condorcet winner, which rarely exists. The concept of ß-plurality was suggested by Aronov, de Berg, Gudmundsson, and Horton [SoCG 2020] as a relaxation of the Condorcet criterion. Denote by ß(*X,d) the value sup{ß | every finite multiset V in X admits a ß-plurality point}. The parameter ß* determines the amount of relaxation required in order to reach a stable decision. Aronov et al. showed that for the Euclidean plane ß(*R2,k·k2) = v23, and more generally, for ddimensional Euclidean space, v1d = ß(*Rd,k·k2) = v23. In this paper, we show that 0.557 = ß(*Rd,k·k2) for any dimension d (notice that v1d < 0.557 for any d = 4).

Original languageEnglish
Title of host publication35th AAAI Conference on Artificial Intelligence, AAAI 2021
PublisherAssociation for the Advancement of Artificial Intelligence
Pages5407-5414
Number of pages8
ISBN (Electronic)9781713835974
StatePublished - 1 Jan 2021
Externally publishedYes
Event35th AAAI Conference on Artificial Intelligence, AAAI 2021 - Virtual, Online
Duration: 2 Feb 20219 Feb 2021

Publication series

Name35th AAAI Conference on Artificial Intelligence, AAAI 2021
Volume6B

Conference

Conference35th AAAI Conference on Artificial Intelligence, AAAI 2021
CityVirtual, Online
Period2/02/219/02/21

ASJC Scopus subject areas

  • Artificial Intelligence

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