Lattices of choice functions and consensus problems

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 consider the three classes of choice functionssatisfying the three significant axioms called heredity (H), concordance (C) and outcast (O). We show that the set of choice functions satisfying any one of these axioms is a lattice, and we study the properties of these lattices. The lattice of choice functions satisfying (H) is distributive, whereas the lattice of choice functions verifying (C) is atomistic and lower bounded, and so has many properties. On the contrary, the lattice of choice functions satisfying(O) is not even ranked. Then using results of the axiomatic and metric latticial theories of consensus as well as the properties of our three lattices of choice functions, we get results to aggregate profiles of such choice functions into one (or several) collective choice function(s).

Keywords: lattice; outcast; Aggregation; choice function; distributive; heredity; Agregation; concordance; consensus; distance; distributif; fonction de choix; hérédité; treillis (search for similar items in EconPapers)
Date: 2004
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00203346
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Citations: View citations in EconPapers (7)

Published in Social Choice and Welfare, 2004, 23, pp.349-382

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Journal Article: Lattices of choice functions and consensus problems (2004)
Working Paper: Lattices of choice functions and consensus problems (2004)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00203346

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