Two candidate competition on differentiated policy sets

Abstract

In the classical spatial model of two candidate competition, an equilibrium exists only if the distribution of voter ideal points is such that every median hyperplane passes through a single policy. The necessity of this condition crucially depends upon both candidates being able to propose any policy in a Euclidean space. We assume that each candidate is affiliated with a party which restricts the policies that its candidate can propose and that voters have Euclidean spatial preferences. We show that if the candidates can only make proposals from disjoint sets of policies, then an equilibrium exists if each median hyperplane passes through a region with a nonempty interior that contains the equilibrium policy. An equilibrium, if it exists, is generically robust to perturbations of the voters' ideal points.