Cognitive Hierarchy and Voting Manipulation
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, and use the cognitive hierarchy framework to identify good strategies. We then investigate the associated algorithmic questions under the k-approval voting rule. We obtain positive algorithmic results for k=1 and 2, and NP- and coNP-hardness results for k>3.
Cite
@article{arxiv.1707.08598,
title = {Cognitive Hierarchy and Voting Manipulation},
author = {Edith Elkind and Umberto Grandi and Francesca Rossi and Arkadii Slinko},
journal= {arXiv preprint arXiv:1707.08598},
year = {2017}
}