Alternative Axioms in Group Identification Problems
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Alternative Axioms in Group Identification Problems Federico Fioravanti1
· Fernando Tohme´ 1
© The Classification Society 2020
Abstract Group identification problems are introduced as the issue of classifying the members of a group in terms of the opinions of their potential members. This involves a finite set of agents N = {1, 2, . . . , n}, each one having an opinion about which agents should be classified as belonging to a specific subgroup J . A Collective Identity Function (CIF) aggregates those opinions yielding the class of members deemed J . A social planner postulate axioms, intended to ensure fair and socially desirable outcomes, characterizing different CIFs. We postulate axioms (classical and different to the ones found in the literature) constraining the spheres of influence of the agents. We show that some of them lead to different characterizations of the CIFs while in another instance we find an impossibility result. Keywords Group identification · Social choice · Decisiveness · Classification · Liberalism
1 Introduction People, countries, and inanimate objects, among other entities, are customarily classified in groups. Sometimes these classifications are simple and obvious, as for instance organizing countries by the continent to which they belong. However, if we want to identify the members of a particular community or, say, regroup countries in terms of their degree of “eco-friendliness,” the classification is far from evident, and the assessment of the individuals or nations involved matters for the final result. Kasher and Rubinstein (K-R) analyzed this problem (“Who is a J?”, 1997), presenting it as a question of defining appropriate aggregation functions over profiles of opinions. Each person in a society is assumed to have an opinion about which individuals, including theirself, may or not belong to the group. The opinion of an individual is thus identified with a subset of the class of all agents. Then, to determine the identities of the individuals who will finally be deemed to belong to the group, the opinions of all the individuals are aggregated. There exist many ways in which this aggregation can be carried out, each embodied in an aggregator function, which they Federico Fioravanti
[email protected] Fernando Tohm´e [email protected] 1
INMABB, Universidad Nacional del Sur, CONICET, Av. Alem 1253, 8000 Bah´ıa Blanca, Argentina
Journal of Classification
call a Collective Identity Function (CIF). K-R characterize three different CIFs, each of which reflects a particular notion of “fairness.” The “Liberal” CIF classifies as a J any individual that sees theirself as being a member of J ; the “Dictatorial” CIF is such that a single individual decides who is in J , and the “Oligarchic” one, in which this decision is made by a specific group of individuals. K-R’s original contribution started a line of work extending and modifying it. So, for instance, Saporiti (2012), modified K-R’s axioms; Sung and Dimitrov (2003), who provided new characterizations; Cho and Ju (2017) t
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