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Some order dualities in logic, games and choices

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Author Info
Bernard Monjardet () (CERMSEM)

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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 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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Publisher 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
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Handle: RePEc:mse:wpsorb:b04018

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Related research
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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Find related papers by JEL classification:
C00 - Mathematical and Quantitative Methods - - General - - - General
D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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References listed on IDEAS
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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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