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Some Order Dualities In Logic, Games And Choices

  • BERNARD MONJARDET

    ()

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

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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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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  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. Bernard Monjardet, 2005. "Social choice theory and the "Centre de Mathématique Sociale". Some historical notes," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00198573, HAL.
  3. 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).
  4. Monjardet, B. & Raderanirina, V., 1999. "The Duality Between the Anti-Exchange Closure Operators and the Path Independent Choice Operators on a Finite Set," Papiers d'Economie Mathématique et Applications 1999-68, Université Panthéon-Sorbonne (Paris 1).
  5. 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.
  6. Bernard Monjardet & Raderanirina Vololonirina, 2001. "The duality between the anti-exchange closure operators and the path independent choice operators on a finite set," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00214289, HAL.
  7. repec:hal:journl:halshs-00214289 is not listed on IDEAS
  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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