Bernard Monjardet () (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS : UMR8095 - Université Panthéon-Sorbonne - Paris I) Raderanirina Vololonirina (CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique - CNRS : UMR8095 - Université Panthéon-Sorbonne - Paris I)
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. 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).
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Length: Date of creation: 2004 Date of revision: Publication status: Published, Social Choice and Welfare, 2004, 23, 349-382 Handle: RePEc:hal:cesptp:halshs-00203346_v1
Note: View the original document on HAL open archive server: http://halshs.archives-ouvertes.fr/halshs-00203346/en/ Contact details of provider: Web page: http://hal.archives-ouvertes.fr/
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