Extreme idealism and equilibrium in the Hotelling–Downs 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.

Hotelling competition and the gamma distribution

“…In political party competition (Xefteris, 2016;Ronayne, 2016), the unit interval represents the political spectrum (from left to right) and C represents the distribution of voters over that space. People vote for the party whose platform is closest to their position on the political spectrum and each political party chooses a platform (a location on the unit interval) to maximise its expected number of votes.…”

“…This pure location game is a simplified version of Hotelling's (1929) seminal location model that ignores the firms' pricing decision. The game has been hugely influential in the social sciences and it has been applied in a number of different contexts including general spatial competition (Boppana et al, 2016;Núñez and Scarsini, 2017), competition between firms through product differentiation (Gabszewicz and Thisse, 1992), political party competition (Xefteris, 2016;Ronayne, 2016), and contests between professional forecasters (Laster et al, 1999;Ottaviani and Sørensen, 2006;Ewerhart, 2015).…”