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On the Fractional Extension of Group Identification

초록/요약

We extend a group identification model in which each individual is classified into groups based on opinions. We ask what if individuals belong to more than one group with different degrees. Then we allow membership to be fractional, to quantify the extent of belonging. With our primary axiom, independence of irrelevant opinions, we propose and characterize three nested families of rules. Our first proposal is the weighted-average rules, in which one’s membership is determined by taking a weighted average of all entries of a problem. Yet some of those rules neither discern which opinion is about whom nor do they explain why some opinions can be treated differently. To remedy the former drawback, we focus on the agentwise weighted-average rules, in which one’s membership is only influenced by the opinions that directly concern her. As for the latter drawback, we further narrow down to the symmetrized agentwise weighted-average rules, each of which shows varying degrees of respect for liberalism and social approval and seeks a compromise between them.

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