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Some Order Dualities In Logic, Games And Choices

Author

Listed:
  • BERNARD MONJARDET

    (CERMSEM, Université Paris I, Maison des Sciences Economiques, 106-112 bd de l'Hopital, 75647 Paris Cedex 13, France;
    CAMS, EHESS, France)

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 occuring in social choice and in choice functions theories.

Suggested Citation

  • 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.
  • Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:01:n:s0219198907001242
    DOI: 10.1142/S0219198907001242
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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. B. Monjardet, 1978. "An Axiomatic Theory of Tournament Aggregation," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 334-351, November.
    3. Stefano Vannucci, 2002. "Effectivity Functions and Stable Governance Structures," Annals of Operations Research, Springer, vol. 109(1), pages 99-127, January.
    4. 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.
    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. 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.
    7. 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).
    8. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
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    Cited by:

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

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    More about this item

    Keywords

    03; 06; 91; JEL Classification: C00; JEL Classification: D71;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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