The Duality Between the Anti-Exchange Closure Operators and the Path Independent Choice Operators on a Finite Set
In this paper, we show that the correspondence discovered by Koshevoy (1999) and, Johnson and Dean (1998) 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 old and new results concerning the "ordinal" representations of choice functions from the theory of anti-exchange closure operators.
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|Date of creation:||1999|
|Date of revision:|
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- Plott, Charles R, 1973. "Path Independence, Rationality, and Social Choice," Econometrica, Econometric Society, vol. 41(6), pages 1075-91, November.
- Sen, Amartya K, 1971. "Choice Functions and Revealed Preference," Review of Economic Studies, Wiley Blackwell, vol. 38(115), pages 307-17, July.
- Edelman, Paul H., 1997. "A note on voting," Mathematical Social Sciences, Elsevier, vol. 34(1), pages 37-50, August.
- Koshevoy, Gleb A., 1999. "Choice functions and abstract convex geometries," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 35-44, July.
- 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.
- Caspard, N. & Monjardet, B., 2000. "The Lattice of Closure Systems, Closure Operators and Implicational Systems on a Finite Set : A Survey," Papiers d'Economie MathÃ©matique et Applications 2000.120, UniversitÃ© PanthÃ©on-Sorbonne (Paris 1).
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