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Some Order Dualities In Logic, Games And Choices

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  • 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.

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Bibliographic Info

Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

Volume (Year): 09 (2007)
Issue (Month): 01 ()
Pages: 1-12

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Handle: RePEc:wsi:igtrxx:v:09:y:2007:i:01:p:1-12

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Related research

Keywords: 03; 06; 91; JEL Classification: C00; JEL Classification: D71;

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  1. 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).
  2. 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).
  3. 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.
  4. Bernard Monjardet, 2005. "Social choice theory and the “Centre de Mathématique Sociale”: some historical notes," Social Choice and Welfare, Springer, vol. 25(2), pages 433-456, December.
  5. repec:hal:journl:halshs-00214289 is not listed on IDEAS
  6. 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.
  7. 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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