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A note on the extension of a binary relation on a set to the power set

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  • Cato, Susumu

Abstract

This paper is concerned with the problem of extending an antisymmetric binary relation on a set to a linear order on the power set. A necessary and sufficient condition is offered.

Suggested Citation

  • Cato, Susumu, 2012. "A note on the extension of a binary relation on a set to the power set," Economics Letters, Elsevier, vol. 116(1), pages 46-48.
    • Handle: RePEc:eee:ecolet:v:116:y:2012:i:1:p:46-48
    DOI: 10.1016/j.econlet.2011.12.074
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    References listed on IDEAS

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    1. Bossert, Walter & Suzumura, Kotaro, 2010. "Consistency, Choice, and Rationality," Economics Books, Harvard University Press, number 9780674052994, Spring.
    2. Fishburn, Peter C., 1984. "Comment on the Kannai-Peleg impossibility theorem for extending orders," Journal of Economic Theory, Elsevier, vol. 32(1), pages 176-179, February.
    3. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    4. Barbera, Salvador & Pattanaik, Prasanta K., 1984. "Extending an order on a Set to the power set: Some remarks on Kannai and Peleg's approach," Journal of Economic Theory, Elsevier, vol. 32(1), pages 185-191, February.
    5. Eric S. Maskin, 2008. "Mechanism Design: How to Implement Social Goals," American Economic Review, American Economic Association, vol. 98(3), pages 567-576, June.
    6. Kannai, Yakar & Peleg, Bezalel, 1984. "A note on the extension of an order on a set to the power set," Journal of Economic Theory, Elsevier, vol. 32(1), pages 172-175, February.
    7. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288, Elsevier.
    8. Holzman, Ron, 1984. "An extension of Fishburn's theorem on extending orders," Journal of Economic Theory, Elsevier, vol. 32(1), pages 192-196, February.
    9. Gardenfors, Peter, 1976. "Manipulation of social choice functions," Journal of Economic Theory, Elsevier, vol. 13(2), pages 217-228, October.
    10. repec:bla:econom:v:43:y:1976:i:172:p:381-90 is not listed on IDEAS
    11. Bossert, Walter, 1989. "On the extension of preferences over a set to the power set: An axiomatic characterization of a quasi-ordering," Journal of Economic Theory, Elsevier, vol. 49(1), pages 84-92, October.
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    Cited by:

    1. Cato, Susumu, 2013. "Remarks on Suzumura consistent collective choice rules," Mathematical Social Sciences, Elsevier, vol. 65(1), pages 40-47.

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    More about this item

    Keywords

    Extension theorem; Power set; Suzumura consistency; Strategy-proofness;
    All these keywords.

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • D60 - Microeconomics - - Welfare Economics - - - General
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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