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

  • Federico FioravantiEmail author
  • Fernando Tohmé
Article
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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 NN, 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.

Keywords

Social choice Aggregation group identification problem Infinite voters 

Notes

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Copyright information

© The Classification Society 2019

Authors and Affiliations

  1. 1.INMABBUniversidad Nacional del Sur, CONICETBahía BlancaArgentina

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