AI 中文总结
本研究证明在带弃权（不执行）的序贯多数投票中，若选民仅能投票给其偏好前缀内的候选人，判定指定候选人是否为子博弈完美均衡下的获胜者具有PSPACE完备性，部分解决了Desmedt和Elkind的开放问题。
AI 中文摘要
我们考虑序贯多数选举，其中每位选民可以弃权（不执行）或投票给单个候选人。每位选民对所有候选人赋予效用；这为每位选民在候选人上诱导出一个（弱）序。平局以均匀随机方式解决，且投票具有较小的正成本，因此当选民的投票无法改变选举结果时，其更倾向于弃权（不执行）。我们考虑该模型的一个变体，其中对于每位选民，我们额外指定其排序的一个前缀，使得其只能投票给该前缀中的候选人（或弃权（不执行））。我们证明，对于该模型变体，在相关扩展式博弈的子博弈完美均衡中，判定指定候选人是否为选举获胜者之一是PSPACE完全的。这部分解决了Desmedt和Elkind [2010]工作中提出的一个开放问题。
英文摘要
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].
