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 N′⊆ N, 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.

中文翻译：

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询问无限投票者“谁是 J？”：ℕ $\mathbb {N}$ 中的组识别问题

我们分析了对组 N 中的个体进行分类的问题，考虑到他们对哪些人应该属于特定子组 N′⊆ N 的意见，在 |N| 的情况下。> ∞。我们表明，这个问题与组随时间变化和/或受到不确定性影响的情况相关。此处采用的方法是通过集体身份函数 (CIF) 将意见集映射到 N. Kasher 和 Rubinstein (Logique & Analyse, 160, 385–395 1997) 的子集，以不同的 CIF 为特征当 |N| 时不言自明 < ∞，特别是自由和寡头聚合器。我们证明，在无限设置中，自由主义的结果​​仍然有效，但该结果不再适用于寡头情况，并给出了满足与寡头 CIF 相同公理的所有聚合器的特征。在我们的激励示例中，根据替代 CIF 获得的解决方案是最有说服力的。