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Some order dualities in logic, games and choices

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  • Bernard Monjardet

    (CERMSEM)

Abstract

We first present the concept of duality appearing in order theory, i.e. the notions of dual isomorphism and of Galois connection. Then we describe two fundamental dualities, the duality extension/intention associated with a binary relation between two sets, and the duality between implicational systems and closure systems. Finally we present two «concrete» dualities occurring in social choice and in choice functions theories

Suggested Citation

  • Bernard Monjardet, 2004. "Some order dualities in logic, games and choices," Cahiers de la Maison des Sciences Economiques b04018, Université Panthéon-Sorbonne (Paris 1).
    • Handle: RePEc:mse:wpsorb:b04018
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    File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04018.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Stefano Vannucci, 2002. "Effectivity Functions and Stable Governance Structures," Annals of Operations Research, Springer, vol. 109(1), pages 99-127, January.
    3. Monjardet, Bernard & Raderanirina, Vololonirina, 2001. "The duality between the anti-exchange closure operators and the path independent choice operators on a finite set," Mathematical Social Sciences, Elsevier, vol. 41(2), pages 131-150, March.
    4. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
    5. Bernard Monjardet, 2005. "Social choice theory and the “Centre de Mathématique Sociale”: some historical notes," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 25(2), pages 433-456, December.
    6. B. Monjardet, 1978. "An Axiomatic Theory of Tournament Aggregation," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 334-351, November.
    7. Johnson, Mark R. & Dean, Richard A., 2001. "Locally complete path independent choice functions and their lattices," Mathematical Social Sciences, Elsevier, vol. 42(1), pages 53-87, July.
    8. Caspard, N. & Monjardet, B., 2000. "The Lattice of Closure Systems, Closure Operators and Implicational Systems on a Finite Set : A Survey," Papiers d'Economie Mathématique et Applications 2000.120, Université Panthéon-Sorbonne (Paris 1).
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Michele Crescenzi, 2023. "Group knowledge and individual introspection," Papers 2305.08729, arXiv.org, revised Sep 2024.

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    More about this item

    Keywords

    Antiexchange closure operator; closure system; Galois connection; implicational system; Galois lattice; path-independent choice function; preference aggregation rule; simple game;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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