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Preference aggregation and atoms in measures

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  • Cato, Susumu

Abstract

This paper examines the aggregation of preferences with a finitely additive measure space of agents. We consider three types of non-dictatorship axioms: non-dictatorship, coalitional non-dictatorship, and atomic non-dictatorship. First, we show that the existence of an atom is a necessary and sufficient condition for the existence of a social welfare function that satisfies weak Pareto, independence of irrelevant alternatives, and coalitional non-dictatorship. Second, we simultaneously impose non-dictatorship and coalitional non-dictatorship, and specify a necessary and sufficient condition for the finitely additive measure that guarantees the compatibility among the axioms. Third, we impose all non-dictatorship axioms and show that the corresponding measure is extremely restricted.

Suggested Citation

  • Cato, Susumu, 2021. "Preference aggregation and atoms in measures," Journal of Mathematical Economics, Elsevier, vol. 94(C).
  • Handle: RePEc:eee:mateco:v:94:y:2021:i:c:s0304406820301233
    DOI: 10.1016/j.jmateco.2020.11.002
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    References listed on IDEAS

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