Alternative Axioms in Group Identification Problems

TL;DR

This paper explores alternative axioms in group identification, analyzing how different fairness constraints influence collective identity functions and revealing new possibilities and impossibility results.

Contribution

It introduces new axioms constraining agents' influence in group identification, leading to novel CIFs and demonstrating limitations of certain axiomatic frameworks.

Findings

Different axioms lead to new CIFs.

Some axioms produce impossibility results.

Constraints on influence affect group classification outcomes.

Abstract

Kasher and Rubinstein (1997) introduced the problem of classifying the members of a group in terms of the opinions of their potential members. This involves a finite set of agents $N = \{1,2,\ldots,n\}$, 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 $J$. Kasher and Rubinstein postulate axioms, intended to ensure fair and socially desirable outcomes, characterizing different CIFs. We follow their lead by replacing their liberal axiom by other axioms, constraining the spheres of influence of the agents. We show that some of them lead to different CIFs while in another instance we find an impossibility result.