Cognitive Hierarchy and Voting Manipulation

TL;DR

This paper explores strategic voting manipulation in elections with three or more options, using cognitive hierarchy theory to identify effective strategies and analyzing the computational complexity under k-approval rules.

Contribution

It applies the cognitive hierarchy framework to voting manipulation, providing algorithmic solutions for k=1,2 and complexity results for k>3.

Findings

Positive algorithms for k=1 and 2

NP- and coNP-hardness for k>3

Insights into strategic voting behavior

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.