The duality between the anti-exchange closure operators and the path independent choice operators on a finite set

Bernard Monjardet and Raderanirina Vololonirina
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Raderanirina Vololonirina: CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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Abstract: In this paper, we show that the correspondence discovered by Koshevoy ([18]) and Johnson and Dean ([15],[16]) 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.

Keywords: semilattice; Anti-exchange closure operator; choice function; convex geometry; path independence; partial order; semilattice.; demi-treillis; fermeture; fonction de choix; géométrie convexe; indépendance du chemin; ordre (search for similar items in EconPapers)
Date: 2001
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00214289
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Citations: View citations in EconPapers (7)

Published in Mathematical Social Sciences, 2001, 41 (2), pp.131-150

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Related works:
Journal Article: The duality between the anti-exchange closure operators and the path independent choice operators on a finite set (2001)
Working Paper: The duality between the anti-exchange closure operators and the path independent choice operators on a finite set (2001)
Working Paper: The Duality Between the Anti-Exchange Closure Operators and the Path Independent Choice Operators on a Finite Set (2000)
Working Paper: The Duality Between the Anti-Exchange Closure Operators and the Path Independent Choice Operators on a Finite Set (1999)
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