Extreme idealism and equilibrium in the Hotelling\u2013Downs model of political competition

Abstract

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.