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.

中文翻译：

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群识别问题中的替代公理

Kasher 和 Rubinstein (1997) 介绍了根据潜在成员的意见对群体成员进行分类的问题。这涉及到一组有限的代理 $N = \{1,2,\ldots,n\}$，每个代理都对哪些代理应该被归类为属于特定的子组 J.A 集体身份函数 (CIF) 有意见聚合这些意见，产生被视为 $J$ 的成员类别。Kasher 和 Rubinstein 假设公理，旨在确保公平和社会期望的结果，表征不同的 CIF。我们效仿他们，用其他公理代替他们的自由公理，限制代理人的影响范围。我们表明，其中一些会导致不同的 CIF，而在另一种情况下，我们发现了不可能的结果。