Asking infinite voters "Who is a J?", and other Group Identification Problem topics

FEDERICO FIORAVANTI

Bahía Blanca

Congreso; Reunión Anual de la UMA 2016; 2016

Group Identication Problem arises when the membership of an individ-ual in a group depends on the judgement of other members. Kasher (JewishCollective Identity - 1993) presents the problem in terms of an aggregatorfunction, such that the decision on wheter an individual belongs to the Jgroup depends on the view of all the members of the society. The collectiveidentity of J is thus determined by the individual views on "who is a J".Kasher and Rubinstein (On the Question "Who is a J?" - 1997) presents anaxiomatic approach to this problem. They consider the aggregator functionJ : (J1; :::; JN) NN ! J((J1; :::; JN) N where N is the group of votersand i 2 Jk indicates that individual k thinks that i is a J. They characterize,using dierent axioms, the Liberal aggregator, the Dictatorship aggregatorand the Oligarchic aggregator.We deal with this problem in two dierent ways: the consideration of a slightly dierent family of axioms. This opensthe question of the existence and uniqueness of aggregators satisfyingthem. the analysis of the case with an innite number of voters. The idea isto determine, at the very least, if the results of the nite setting arestill valid.In both cases some existence results are going to be shown.