Sequential Elimination Voting Games

TL;DR

This paper models sequential elimination voting as a game, analyzing strategic behavior's impact on fairness and efficiency, and providing bounds on social welfare loss with experimental insights.

Contribution

It introduces a game-theoretic analysis of sequential elimination voting, proving outcome invariance in subgame-perfect equilibria and quantifying social welfare loss due to strategic manipulation.

Findings

Outcome is consistent across all subgame-perfect Nash equilibria.

Strategic behavior can significantly reduce social welfare in worst cases.

Experimental results show average manipulation impact is often lower than worst-case bounds.

Abstract

Voting by sequential elimination is a low-communication voting protocol: voters play in sequence and eliminate one or more of the remaining candidates, until only one remains. While the fairness and efficiency of such protocols have been explored, the impact of strategic behaviour has not been addressed. We model voting by sequential elimination as a game. Given a fixed elimination sequence, we show that the outcome is the same in all subgame-perfect Nash equilibria of the corresponding game, and is polynomial-time computable. We measure the loss of social welfare due to strategic behaviour, with respect to the outcome under sincere behaviour, and with respect to the outcome maximizing social welfare. We give tight bounds for worst-case ratios, and show using experiments that the average impact of manipulation can be much lower than in the worst case.