Collective rationality and decisiveness coherence
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Arrow’s impossibility theorem states that if an aggregation rule satisfies unrestricted domain, weak Pareto, independence of irrelevant alternatives, and collective rationality, then there exists a dictator. Among others, Arrow’s postulate of collective rationality is controversial. We propose a new axiom for an aggregation rule, decisiveness coherence, which is weaker than collective rationality. It is shown that given the Arrovian axioms other than collective rationality, a dictatorship arises if and only if decisiveness coherence is satisfied. Moreover, we introduce weak versions of decisive coherence and examine these implications.
I thank Maggie Penn, a managing editor of this journal, and three anonymous referees for their helpful comments. I thank Marc Fleurbaey, Kohei Kamaga, Koichi Tadenuma, Maurice Salles, Yohei Sekiguchi, and Kotaro Suzumura for discussions and comments. This work was supported by JSPS KAKENHI Grant number 26870477 and Postdoctoral Fellowship for Research Abroad of JSPS. I also thank the hospitality of Princeton University.
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