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 occuring in social choice and in choice functions theories.
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Bibliographic InfoArticle provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.
Volume (Year): 09 (2007)
Issue (Month): 01 ()
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Web page: http://www.worldscinet.com/igtr/igtr.shtml
Other versions of this item:
- B4 - Schools of Economic Thought and Methodology - - Economic Methodology
- C0 - Mathematical and Quantitative Methods - - General
- C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
- 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
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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
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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).
- 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).
- 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.
- 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.
- repec:hal:journl:halshs-00214289 is not listed on IDEAS
- 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.
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