We study strategic candidate nomination by parties in elections decided by Plurality voting. Each party selects a nominee before the election, and the winner is chosen from the nominated candidates based on the voters' preferences. We introduce a new restriction on these preferences, which we call party-aligned single-peakedness: all voters agree on a common ordering of the parties along an ideological axis, but may differ in their perceptions of the positions of individual candidates within each party. The preferences of each voter are single-peaked with respect to their own axis over the candidates, which is consistent with the global ordering of the parties. We present a polynomial-time algorithm for recognizing whether a preference profile satisfies party-aligned single-peakedness. In this domain, we give polynomial-time algorithms for deciding whether a given party can become the winner under some (or all) nominations, and whether this can occur in some pure Nash equilibrium. We also prove a tight result about the guaranteed existence of pure strategy Nash equilibria for elections with up to three parties for single-peaked and party-aligned single-peaked preference profiles.

翻译：我们研究在多数制投票决定的选举中，各政党对候选人的策略性提名问题。每个政党在选举前选定一名提名人，获胜者将根据选民偏好从被提名的候选人中产生。我们引入了一种新的偏好限制条件，称为政党对齐的单峰偏好：所有选民在意识形态轴线上对政党的排序达成共识，但可能对每个政党内部候选人的具体位置持有不同看法。每位选民的偏好相对于其自身的候选人轴线呈单峰分布，且该轴线与政党的全局排序保持一致。我们提出了一种多项式时间算法，用于判断偏好分布是否满足政党对齐的单峰性。在此领域内，我们给出了多项式时间算法，用于判定特定政党是否能在某些（或所有）提名情况下获胜，以及这种情况是否可能出现在某些纯策略纳什均衡中。我们还证明了对于单峰偏好及政党对齐单峰偏好分布，当政党数量不超过三个时，纯策略纳什均衡必然存在的严格结论。