Gibbard-Satterthwaite Games for k-Approval Voting Rules

TL;DR

This paper models strategic voting under k-approval rules as Gibbard-Satterthwaite games, analyzing conditions for the existence of Nash equilibria among boundedly rational voters who manipulate or counter-manipulate.

Contribution

It introduces Gibbard-Satterthwaite games for k-approval voting and investigates conditions ensuring pure strategy Nash equilibria.

Findings

Conditions guaranteeing Nash equilibria are identified.

Analysis of strategic interactions among manipulators and counter-manipulators.

Extension of voting game theory to k-approval rules.

Abstract

The Gibbard-Satterthwaite theorem implies the existence of voters, called manipulators, who can change the election outcome in their favour by voting strategically. When a given preference profile admits several such manipulators, voting becomes a game played by these voters, who have to reason strategically about each others' actions. To complicate the game even further, counter-manipulators may then try to counteract the actions of manipulators. Our voters are boundedly rational and do not think beyond manipulating or countermanipulating. We call these games Gibbard--Satterthwaite Games. In this paper we look for conditions that guarantee the existence of a Nash equilibria in pure strategies.