Simple Collective Identity Functions

Abstract

A Collective Identity Function (CIF) is a rule which aggregates personal opinions on whether an individual belongs to a certain identity into a social decision. A simple CIF is one which can be expressed in terms of winning coalitions. We characterize simple CIFs and explore various CIFs of the literature by exploiting their ability of being expressed in terms of winning coalitions. We also use our setting to introduce conditions that ensure the equal treatment of individuals as voters or as outcomes.