Subgame-Perfect Nash Equilibria of Plurality Voting with Abstention: a PSPACE-Completeness Result for Restricted Ballots

2026-09-21

AI Summary

研究通过限制选民投票范围，证明了在子博弈完美均衡下决定指定候选人是否获胜的问题是PSPACE-完全的，解决了一个关于多数投票制中弃权选项的开放问题。

Abstract

We consider sequential Plurality elections in which each voter may abstain or vote for a single candidate. Each voter assigns utilities to all candidates; for each voter, this induces a (weak) order over the candidates. Ties are resolved uniformly at random, and voting has a small positive cost, so that a voter prefers to abstain when their vote cannot change the election outcome. We consider a variant of this model where, for each voter, we additionally specify a prefix of her ranking, so that she is only allowed to vote for a candidate from that prefix (or abstain). We prove that for this variant of the model, deciding whether a designated candidate is among the election winners in a subgame-perfect equilibrium of the associated extensive-form game is PSPACE-complete. This partially resolves an open problem from the work of Desmedt and Elkind [2010].

Problem

• Plurality Voting
• Subgame-Perfect Nash Equilibria
• PSPACE-Completeness
• Restricted Ballots

Innovation

• Plurality Voting
• Subgame-Perfect Equilibrium
• PSPACE-Completeness
• Restricted Ballots