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A short proof of Deb’s Theorem on Schwartz’s rule

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  • Athanasios Andrikopoulos

    (University of Ioannina)

Abstract

Schwartz in (Nous,7, 1972, Definition, 3) introduces a generalization of the Condorcet criterion, which is the classical approach to rational choice in the context of cycles, and he defines the Schwartz set. Deb (J Econ Theory 16:103–110, 1977) shows that the Schwartz set consists of the maximal elements according to the transitive closure of the asymmetric part of a binary relation corresponding to a choice process or representing the decision maker’s preferences. This note provides a short and simple proof of Deb’s theorem on the characterization of the Schwartz set.

Suggested Citation

  • Athanasios Andrikopoulos, 2016. "A short proof of Deb’s Theorem on Schwartz’s rule," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 39(2), pages 333-336, November.
    • Handle: RePEc:spr:decfin:v:39:y:2016:i:2:d:10.1007_s10203-016-0180-6
    DOI: 10.1007/s10203-016-0180-6
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    References listed on IDEAS

    as
    1. Deb, Rajat, 1977. "On Schwartz's rule," Journal of Economic Theory, Elsevier, vol. 16(1), pages 103-110, October.
    2. Kalai, Ehud & Schmeidler, David, 1977. "An admissible set occurring in various bargaining situations," Journal of Economic Theory, Elsevier, vol. 14(2), pages 402-411, April.
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    More about this item

    Keywords

    Condorcet winner; Schwartz set;

    JEL classification:

    • D7 - Microeconomics - - Analysis of Collective Decision-Making

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