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Some Order Dualities In Logic, Games And Choices

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

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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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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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Related research
Keywords: 03; 06; 91; JEL Classification: C00; JEL Classification: D71;

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Find related papers by JEL classification:
B4 - Schools of Economic Thought and Methodology - - Economic Methodology
C0 - Mathematical and Quantitative Methods - - General
C6 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming
C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
D5 - Microeconomics - - General Equilibrium and Disequilibrium
D7 - Microeconomics - - Analysis of Collective Decision-Making
M2 - Business Administration and Business Economics; Marketing; Accounting - - Business Economics

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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)
    Other versions:
  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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