On the manipulability of approval voting and related scoring rules

H.J.M. Peters, S. Roy, A.J.A. Storcken

Research output: Contribution to journalArticleAcademicpeer-review

Abstract

We characterize all preference profiles at which the approval (voting) rule is manipulable, under three extensions of preferences to sets of candidates: by comparison of worst candidates, best candidates, or by comparison based on stochastic dominance. We perform a similar exercise for k-approval rules, where voters approve of a fixed number k of candidates. These results can be used to compare (k-)approval rules with respect to their manipulability. Analytical results are obtained for the case of two voters, specifically, the values of k for which the k-approval rule is minimally manipulable-has the smallest number of manipulable preference profiles-under the various preference extensions are determined. For the number of voters going to infinity, an asymptotic result is that the k-approval rule with k around half the number of candidates is minimally manipulable among all scoring rules. Further results are obtained by simulation and indicate that k-approval rules may improve on the approval rule as far as manipulability is concerned.

Original languageEnglish
Pages (from-to)399-429
Number of pages31
JournalSocial Choice and Welfare
Volume39
Issue number2-3
DOIs
Publication statusPublished - Jul 2012

Keywords

  • SOCIAL CHOICE FUNCTIONS
  • MINIMAL MANIPULATABILITY
  • MANIPULATION
  • INTERJACENCY

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