Fuzzy Group Identification Problems

TL;DR

This paper extends the classic group identification problem to a fuzzy setting, allowing agents to express degrees of membership, and explores aggregation methods that can bypass previous impossibility results.

Contribution

It introduces a fuzzy model for group identification and characterizes aggregation methods that overcome key limitations of the original crisp model.

Findings

Fuzzy model generalizes the classic group identification problem.

Certain aggregation rules can bypass previous impossibility results.

The fuzzy approach offers more flexible solutions for group membership consensus.

Abstract

We present a fuzzy version of the Group Identification Problem ("Who is a J?") introduced by Kasher and Rubinstein (1997). We consider a class $N = \{1,2,\ldots,n\}$ of agents, each one with an opinion about the membership to a group J of the members of the society, consisting in a function $\pi : N \to [0; 1]$, indicating for each agent, including herself, the degree of membership to J. We consider the problem of aggregating those functions, satisfying different sets of axioms and characterizing different aggregators. While some results are analogous to those of the originally crisp model, the fuzzy version is able to overcome some of the main impossibility results of Kasher and Rubinstein.