Separation of Decisions in Group Identification

We study a model of group identification in which individuals' opinions as to the membership of a group are aggregated to form a list of the group's members. Potential aggregation rules are studied through the axiomatic approach. We introduce two axioms, meet separability and join separability, each of which requires the list of members generated by the aggregation rule to be independent of whether the question of membership in a group is separated into questions of membership in two other groups. We use these axioms to characterize a class of "one vote" rules, in which one opinion determines whether an individual is considered to be a member of a group. We then use this characterization to provide new axiomatizations of the liberal rule, in which each individual determines for himself whether he is a member of the group, as the only non-degenerate anonymous rule satisfying the meet separability and join separability axioms.