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Journal of Classification
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29-03-2019

Asking Infinite Voters ‘Who is a J?’: Group Identification Problems in \(\mathbb {N}\)

Authors: Federico Fioravanti, Fernando Tohmé

Published in: Journal of Classification | Issue 1/2020

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Abstract

We analyze the problem of classifying individuals in a group N taking into account their opinions 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 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 (Logique & Analyse, 160, 385–395 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.
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Metadata
Title
Asking Infinite Voters ‘Who is a J?’: Group Identification Problems in
Authors
Federico Fioravanti
Fernando Tohmé
Publication date
29-03-2019
Publisher
Springer US
Published in
Journal of Classification / Issue 1/2020
Print ISSN: 0176-4268
Electronic ISSN: 1432-1343
DOI
https://doi.org/10.1007/s00357-018-9295-5

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