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Incompleteness, regularity, and collective preference

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  • Susumu Cato

Abstract

This paper examines the incompleteness of collective preference. We provide a series of Arrovian impossibility theorems without completeness. First, we consider the notion of regularity introduced by Eliaz and Ok (2006, Games and Economic Behavior 56, 61–86); it is an appropriate richness property for strict preference when preference is allowed to be incomplete. We examine the implication of imposing regularity on collective preference. Second, we propose responsiveness, a variation of positive responsiveness. This axiom requires that some changes in individual preferences make an alternative weakly better than another. Third, we consider coherency conditions for collective preferences; this conditionally requires the existence of comparable pairs in a certain manner. We prove an impossibility result for each condition using Arrovian axioms.

Suggested Citation

  • Susumu Cato, 2020. "Incompleteness, regularity, and collective preference," Metroeconomica, Wiley Blackwell, vol. 71(2), pages 333-344, May.
    • Handle: RePEc:bla:metroe:v:71:y:2020:i:2:p:333-344
    DOI: 10.1111/meca.12276
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    Cited by:

    1. Wesley H. Holliday & Mikayla Kelley, 2020. "A note on Murakami’s theorems and incomplete social choice without the Pareto principle," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(2), pages 243-253, August.

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