Dominance in spatial voting with imprecise ideals

Abstract

We introduce a dominance relationship in spatial voting with Euclidean preferences, by treating voter ideal points as balls of radius $$\delta$$ . Values $$\delta >0$$ model imprecision or ambiguity as to voter preferences from the perspective of a social planner. The winning coalitions may be any consistent monotonic collection of voter subsets. We characterize the minimum value of $$\delta$$ for which the $$\delta$$ -core, the set of undominated points, is nonempty. In the case of simple majority voting, the core is the yolk center and $$\delta$$ is the yolk radius.