Some order dualities in logic, games and choices
AbstractWe 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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Bibliographic InfoPaper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number b04018.
Length: 15 pages
Date of creation: Feb 2004
Date of revision:
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Antiexchange closure operator; closure system; Galois connection; implicational system; Galois lattice; path-independent choice function; preference aggregation rule; simple game.;
Other versions of this item:
- C00 - Mathematical and Quantitative Methods - - General - - - General
- D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
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- 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 MathÃÂ©matique et Applications
1999-68, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- 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.
- Monjardet, B. & Raderanirina, V., 2000. "The Duality Between the Anti-Exchange Closure Operators and the Path Independent Choice Operators on a Finite Set," Papiers d'Economie MathÃÂ©matique et Applications 2000.121, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- repec:hal:journl:halshs-00214289 is not listed on IDEAS
- repec:hal:cesptp:halshs-00198573 is not listed on IDEAS
- 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.
- Caspard, N. & Monjardet, B., 2000. "The Lattice of Closure Systems, Closure Operators and Implicational Systems on a Finite Set : A Survey," Papiers d'Economie MathÃÂ©matique et Applications 2000.120, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
- 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.
- Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
- 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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