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Cognitive hierarchy and voting manipulation in k-approval voting

Abstract : By the Gibbard-Satterthwaite theorem, every reasonable voting rule for three or more alternatives is susceptible to manipulation: there exist elections where one or more voters can change the election outcome in their favour by unilaterally modifying their vote. When a given election admits several such voters, strategic voting becomes a game among potential manipulators: a manipulative vote that leads to a better outcome when other voters are truthful may lead to disastrous results when other voters choose to manipulate as well. We consider this situation from the perspective of a boundedly rational voter, using an appropriately adapted cognitive hierarchy framework to model voters' limitations. We investigate the complexity of algorithmic questions that such a voter faces when deciding on whether to manipulate. We focus on k-approval voting rules, with k ≥ 1. We provide polynomial-time algorithms for k = 1, 2 and hardness results for k ≥ 4 (NP and co-NP), supporting the claim that strategic voting, albeit ubiquitous in collective decision making, is computationally hard if the manipulators try to reason about each others' actions.
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https://hal.archives-ouvertes.fr/hal-03066890
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Submitted on : Tuesday, December 15, 2020 - 2:44:06 PM
Last modification on : Tuesday, October 19, 2021 - 2:23:33 PM
Long-term archiving on: : Tuesday, March 16, 2021 - 7:44:45 PM

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Edith Elkind, Umberto Grandi, Francesca Rossi, Arkadii Slinko. Cognitive hierarchy and voting manipulation in k-approval voting. Mathematical Social Sciences, Elsevier, 2020, 108, pp.193-205. ⟨10.1016/j.mathsocsci.2020.07.001⟩. ⟨hal-03066890⟩

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