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 ([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.Anti-exchange closure operator, choice function, convex geometry, path independence,partial order, semilattice.

Lattices of choice functions and consensus problems

. 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).Aggregation, choice function, concordance, consensus, distance, distributive, heredity, lattice, outcast

Lattices of choice functions and consensus problems

. 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).Dans ce texte nous étudions les trois classes de fonctions de choix vérifiant les trois importantes propriétés d'hérédité (H), concordance (C) et «outcast» (O). Nous montrons que chacune de ces classes est un treillis dont nous étudions les propriétés. Le treillis des fonctions de choix vérifiant (H) est distributif, tandis que celui des fonctions de choix vérifiant (C) est atomistique et borné inférieurement ce qui lui confére de nombreuses autre propriétés. Par contre, le treillis des fonctions de choix vérifiant (O) n'est pas même rangé. Utilisant ensuite des résultats des théories axiomatiques et métriques du consensus ainsi que les propriétés de nos trois treillis, nous obtenons des résultats sur l'agrégation de fonctions de choix individuelles appartenant à ces classes en une (ou plusieurs) fonctions de choix collective(s

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 ([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.Dans cet article, nous montrons que la correspondance découverte par Koshevoy ([18]) et Johnson et Dean ([15],[16]) entre les fermetures « anti-échanges » et les fonctions de choix « chemin-indépendantes » est une dualité entre les deux demi-treillis de ces applications. Nous utilisons cette dualité pour obtenir des résultats sur la représentation des fonctions de choix « chemin-indépendantes » au moyen de la théorie des fermetures « anti-échanges »

Lattices of choice functions and consensus problems

In this paper we consider the three classes of choice functions satisfying 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). Copyright Springer-Verlag 2004

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

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : RP 15483 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc

Lattices of choice functions and consensus problems

SIGLEAvailable from INIST (FR), Document Supply Service, under shelf-number : RP 16424 / INIST-CNRS - Institut de l'Information Scientifique et TechniqueFRFranc