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The Duality Between the Anti-Exchange Closure Operators and the Path Independent Choice Operators on a Finite Set

Author

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  • Monjardet, B.
  • Raderanirina, V.

Abstract

In this paper, we show that the correspondence discovered by Koshevoy ([18]) and Johnson and Dean ([15],[16]) between anti-exchange closure operators and path independent choice operators is a duality between two semilattices of such operators. Then we use this duality to obtain results concerning the "ordinal" representations of path independent choice functions from the theory of anti-exchange closure operators.

Suggested Citation

  • Monjardet, B. & Raderanirina, V., 2000. "The Duality Between the Anti-Exchange Closure Operators and the Path Independent Choice Operators on a Finite Set," Papiers d'Economie Mathématique et Applications 2000.121, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:fth:pariem:2000.121
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    Cited by:

    1. is not listed on IDEAS
    2. Gabriela Bordalo & Nathalie Caspard & Bernard Monjardet, 2009. "Going down in (semi)lattices of finite Moore families and convex geometries," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00308785, HAL.
    3. Bernard Monjardet, 2007. "Some Order Dualities In Logic, Games And Choices," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 1-12.
    4. Danilov, V. & Koshevoy, G., 2005. "Mathematics of Plott choice functions," Mathematical Social Sciences, Elsevier, vol. 49(3), pages 245-272, May.
    5. Matthew Ryan, 2010. "Mixture sets on finite domains," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(2), pages 139-147, November.
    6. repec:ebl:ecbull:v:4:y:2004:i:3:p:1-3 is not listed on IDEAS
    7. Bernard Monjardet & Vololonirina Raderanirina, 2004. "Lattices of choice functions and consensus problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 23(3), pages 349-382, December.
    8. Monjardet, Bernard, 2003. "The presence of lattice theory in discrete problems of mathematical social sciences. Why," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 103-144, October.
    9. Danilov, V. & Koshevoy, G., 2006. "A new characterization of the path independent choice functions," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 238-245, March.

    More about this item

    Keywords

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    JEL classification:

    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies

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