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Some order dualities in logic, games and choices

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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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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  1. 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.
  2. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
  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, 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. repec:hal:journl:halshs-00214289 is not listed on IDEAS
  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. 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.
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