Extreme idealism and equilibrium in the Hotelling–Downs model of political competition
在经典霍特林-唐斯模型中，当选民偏好分布为单峰时，三个及以上策略候选人无纯策略均衡。本文引入两个非策略的理想主义候选人，证明在非退化单峰分布下均衡得以恢复，且均衡中极端候选人为理想主义者，策略候选人平台不重叠，若多于一个策略候选人则选民分布必须不对称。
In the classic Hotelling–Downs model of political competition, no pure strategy equilibrium with three or more strategic candidates exists when the distribution of voters’ preferred policies is unimodal. I study the effect of introducing two idealist candidates to the model who are non-strategic (i.e., fixed to their policy platforms), while allowing for an unlimited number of strategic candidates. Doing so, I show that equilibrium is restored for a non-degenerate set of unimodal distributions. In addition, the equilibria have the following features: (1) the left-most and right-most candidates (i.e., extremists) are idealists; (2) strategic candidates never share their policy platforms, which instead are spread out across the policy space; and (3) if more than one strategic candidate enters, the distribution of voter preferences must be asymmetric. I also show that equilibria can accommodate idealist fringes of candidates toward the extremes of the political spectrum.