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

FEDERICO FIORAVANTI; FERNANDO TOHMÉ

Jornada; Jornadas Latinoamericanas de Teoría Económica; 2019

We analyze the problem of classifying individuals in a group N taking into account theiropinions about which of them should belong to a specific subgroup N ⊆ N, in the case that|N| > ∞.We show that this problem is relevant in cases in which the group changes in timeand/or is subject to uncertainty. The approach followed here to find the ensuing classificationis by means of a Collective Identity Function (CIF) that maps the set of opinions intoa subset of N. Kasher and Rubinstein (Logique & Analyse, 160, 385?395 1997) characterizeddifferent CIFs axiomatically when |N| < ∞, in particular, the Liberal and Oligarchicaggregators. We show that in the infinite setting, the liberal result is still valid but the resultno longer holds for the oligarchic case and give a characterization of all the aggregatorssatisfying the same axioms as the Oligarchic CIF. In our motivating examples, the solutionobtained according to the alternative CIF is most cogent.