The duality between the anti-exchange closure operators and the path independent choice operators on a finite set
AbstractIn this paper, we show that the correspondence discovered by Koshevoy () and Johnson and Dean (,) between anti-exchange closure operators and path independent choice operators is a duality between two semilattices of such operators. Then we use this duality to obtain results concerning the "ordinal" representations of path independent choice functions from the theory of anti-exchange closure operators.
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Bibliographic InfoArticle provided by Elsevier in its journal Mathematical Social Sciences.
Volume (Year): 41 (2001)
Issue (Month): 2 (March)
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Web page: http://www.elsevier.com/locate/inca/505565
Other versions of this item:
- 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).
- Bernard Monjardet & Raderanirina Vololonirina, 2001. "The duality between the anti-exchange closure operators and the path independent choice operators on a finite set," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00214289, HAL.
- 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).
- D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
- D51 - Microeconomics - - General Equilibrium and Disequilibrium - - - Exchange and Production Economies
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.:
- Richard A. Dean & Mark R. Johnson, 2000. "Locally Complete Path Independent Choice Functions and Their Lattices," Econometric Society World Congress 2000 Contributed Papers 0622, Econometric Society.
- Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-91, November.
- 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).
- Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
- Edelman, Paul H., 1997. "A note on voting," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 37-50, August.
- Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
- 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.
- Bernard Monjardet, 2007.
"Some Order Dualities In Logic, Games And Choices,"
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- Bernard Monjardet, 2004. "Some order dualities in logic, games and choices," Cahiers de la Maison des Sciences Economiques b04018, Université Panthéon-Sorbonne (Paris 1).
- Bernard Monjardet, 2007. "Some order dualities in logic, games and choices," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00202326, HAL.
- Gabriela Bordalo & Nathalie Caspard & Bernard Monjardet, 2009. "Going down in (semi)lattices of finite Moore families and convex geometries," UniversitÃ© Paris1 PanthÃ©on-Sorbonne (Post-Print and Working Papers) halshs-00308785, HAL.
- Danilov, V. & Koshevoy, G., 2006. "A new characterization of the path independent choice functions," Mathematical Social Sciences, Elsevier, vol. 51(2), pages 238-245, March.
- Matthew Ryan, 2010. "Mixture sets on finite domains," Decisions in Economics and Finance, Springer, vol. 33(2), pages 139-147, November.
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