Characterization of tie-breaking plurality rules

Abstract

We introduce a new condition for social choice functions, called “equal treatment of congruent distributions.” It requires some invariance between two preference profiles that share a type of congruity property with respect to the associated distributions of votes. It also implies two equal treatment conditions: one is a natural weakening of anonymity, which is the most standard equal treatment condition for individuals, and the other is a natural weakening of neutrality, which is the most standard equal treatment one for alternatives. Thus, equal treatment of congruent distributions plays the role of weak equal treatment conditions both for individuals and for alternatives. As our main results, we characterize a class of social choice functions that satisfy equal treatment of congruent distributions and some mild positive responsiveness conditions, and it is shown to coincide with the class of tie-breaking plurality rules, which are selections of the well-known plurality rule.