Resolute refinements of social choice correspondences

TL;DR

This paper investigates conditions under which social choice correspondences can be refined to be resolute while preserving properties like anonymity and neutrality, especially when individuals and alternatives are partitioned into subgroups.

Contribution

It identifies necessary and sufficient arithmetical conditions for resolute refinements that maintain efficiency, anonymity, neutrality, and immunity to reversal bias.

Findings

Derived conditions for resolute refinements with desired properties

Applicable to social choice correspondences with subgroup partitions

Ensures refinements preserve key social choice properties

Abstract

Many classical social choice correspondences are resolute only in the case of two alternatives and an odd number of individuals. Thus, in most cases, they admit several resolute refinements, each of them naturally interpreted as a tie-breaking rule, satisfying different properties. In this paper we look for classes of social choice correspondences which admit resolute refinements fulfilling suitable versions of anonymity and neutrality. In particular, supposing that individuals and alternatives have been exogenously partitioned into subcommittees and subclasses, we find out arithmetical conditions on the sizes of subcommittees and subclasses that are necessary and sufficient for making any social choice correspondence which is efficient, anonymous with respect to subcommittees, neutral with respect to subclasses and possibly immune to the reversal bias admit a resolute refinement sharing the same properties.