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Recoverability of choice functions and binary relations: some duality results

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  • Kotaro Suzumura
  • Yongsheng Xu

Abstract

Banerjee and Pattanaik (1996) proved a theorem that the maximal set with respect to a quasi-ordering can be fully recovered by defining the greatest sets with respect to each and every ordering extension thereof and taking their union. Donaldson and Weymark (1998) proved a theorem that a quasi-ordering can be fully recovered by taking the intersection of all the ordering extensions thereof. These recoverability theorems are obviously related, but their exact relationship has never been clarified in the literature. This paper examines the issue of choice-functional recoverability and relational recoverability in a general framework, and establishes several remarkable duality relationships. Copyright Springer-Verlag 2003

Suggested Citation

  • Kotaro Suzumura & Yongsheng Xu, 2003. "Recoverability of choice functions and binary relations: some duality results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(1), pages 21-37, August.
    • Handle: RePEc:spr:sochwe:v:21:y:2003:i:1:p:21-37
    DOI: 10.1007/s00355-003-0199-9
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    Cited by:

    1. Athanasios Andrikopoulos, 2011. "Characterization of the existence of semicontinuous weak utilities for binary relations," Theory and Decision, Springer, vol. 70(1), pages 13-26, January.
    2. Bossert, Walter & Sprumont, Yves & Suzumura, Kotaro, 2002. "Upper semicontinuous extensions of binary relations," Journal of Mathematical Economics, Elsevier, vol. 37(3), pages 231-246, May.
    3. Clemens Puppe & Yongsheng Xu, 2010. "Essential alternatives and freedom rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 35(4), pages 669-685, October.
    4. Suzumura, Kotaro & Xu, Yongsheng, 2003. "On constrained dual recoverability theorems," Mathematical Social Sciences, Elsevier, vol. 45(2), pages 143-154, April.
    5. T. Demuynck, 2009. "Common ordering extensions," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 09/593, Ghent University, Faculty of Economics and Business Administration.

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