Global and local equilibrium in majority voting

A great deal of discussion in the area of majjity voting centers around the question of the existence of equilibrium and in particular global and local equilibria (see, for example,[1],[2]). The purpose of this note is to clarify the relations between global and local equilibrium. We show that under relatively mild conditions a local equilibrium will also be a global equilibrium. Let X be the issue space. We assume that X is a convex subset of R n. Let V be a finite set of voters with cardinality IV.