Asking infinite voters ‘Who is a J?’: Group Identification Problems in N

Abstract

We analyze the problem of classifing individuals in a group N taking into account their opinions about which of them should belong to a specific subgroup N0 ⊆ N, in the case that |N| > ∞. We show that this problem is relevant in cases in which the group changes in time and/or is subject to uncertainty. The approach followed here to find the ensuing classification is by means of a Collective Identity Function (CIF) that maps the set of opinions into a subset of N. Kasher and Rubinstein (1997) characterized different CIFs axiomatically when |N| < ∞, in particular the Liberal and Oligarchic aggregators. We show that in the infinite setting the liberal result is still valid but the result no longer holds for the oligarchic case and give a characterization of all the aggregators satisfying the same axioms as the Oligarchic CIF. In our motivating examples, the solution obtained according to the alternative CIF is most cogent.