Gibbard–Satterthwaite games for k-approval voting rules

Umberto Grandi, Daniel Hughes, Francesca Rossi and Arkadii Slinko

Mathematical Social Sciences, 2019, vol. 99, issue C, 24-35

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.

Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:eee:matsoc:v:99:y:2019:i:c:p:24-35

DOI: 10.1016/j.mathsocsci.2019.03.001

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