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Gibbard–Satterthwaite games for k-approval voting rules

Author

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  • Grandi, Umberto
  • Hughes, Daniel
  • Rossi, Francesca
  • Slinko, Arkadii

Abstract

The Gibbard–Satterthwaite theorem states that for any non-dictatorial voting system there will exist an election where a voter, called a manipulator, can change the election outcome in their favour by voting strategically. When a given preference profile admits several manipulators, voting becomes a game played by these voters, who have to reason strategically about each other’s actions. To complicate the game even further, some voters, called countermanipulators, may try to counteract potential actions of manipulators. Previously, voting manipulation games have been studied mostly for the Plurality rule. We extend this to k-Approval voting rules. However, unlike previous studies, we assume that voters are boundedly rational and do not think beyond manipulating or countermanipulating. We classify all 2-by-2 games that can be encountered by these strategic voters, and investigate the complexity of arbitrary voting manipulation games, identifying conditions on strategy sets that guarantee the existence of a Nash equilibrium in pure strategies.

Suggested Citation

  • Grandi, Umberto & Hughes, Daniel & Rossi, Francesca & Slinko, Arkadii, 2019. "Gibbard–Satterthwaite games for k-approval voting rules," Mathematical Social Sciences, Elsevier, vol. 99(C), pages 24-35.
    • Handle: RePEc:eee:matsoc:v:99:y:2019:i:c:p:24-35
    DOI: 10.1016/j.mathsocsci.2019.03.001
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    Cited by:

    1. Elkind, Edith & Grandi, Umberto & Rossi, Francesca & Slinko, Arkadii, 2020. "Cognitive hierarchy and voting manipulation in k-approval voting," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 193-205.
    2. Bolle, Friedel, 2019. "When will party whips succeed? Evidence from almost symmetric voting games," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 24-34.
    3. Jindapon, Paan & Van Essen, Matt, 2019. "Political business cycles in a dynamic bipartisan voting model," Mathematical Social Sciences, Elsevier, vol. 102(C), pages 15-23.

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