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Some order dualities in logic, games and choices

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Author Info
Bernard Monjardet () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)

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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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Publisher Info
Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00202326_v1.

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Date of creation: Mar 2007
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Publication status: Published, International Game Theory Review, 2007, 9, 1, 1-12
Handle: RePEc:hal:cesptp:halshs-00202326_v1

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Related research
Keywords: antiexchange closure operator; Galois connection; implicational system; path-independent choice function; simple game.;

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  1. 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).
  2. 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. [Downloadable!] (restricted)
  3. Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July. [Downloadable!] (restricted)
  4. 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_v1, HAL. [Downloadable!]
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  5. 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. [Downloadable!] (restricted)
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  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. [Downloadable!] (restricted)
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This page was last updated on 2009-11-27.

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