Probabilistic Fixed Ballot Rules and Hybrid Domains

Abstract

We characterize a class of preference domains called hybrid * domains. These are specific collections of preferences that are single-peaked at the "extremes" and unrestricted in the "middle". They are characterized by the familiar properties of minimal richness, diversity and no-restoration. We also study the structure of strategy-proof and unanimous Random Social Choice Functions on these domains. We show them to be special cases of probabilistic fixed ballot rules (or PFBR). These PFBRs are not necessarily decomposable, i.e., cannot be written as a convex combination of their deterministic counterparts. We identify a necessary and sufficient condition under which decomposability holds for anonymous PFBRs.