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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.

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File URL: ftp://mse.univ-paris1.fr/pub/mse/cahiers2004/B04018.pdf
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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b04018.

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Length: 15 pages
Date of creation: Feb 2004
Date of revision:
Handle: RePEc:mse:wpsorb:b04018

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

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References

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  1. 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).
  2. repec:hal:journl:halshs-00214289 is not listed on IDEAS
  3. repec:hal:cesptp:halshs-00198573 is not listed on IDEAS
  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. 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).
  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.
  8. 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.
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