Lattices of choice functions and consensus problems
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).
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Bibliographic InfoPaper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00203346.
Date of creation: 2004
Date of revision:
Publication status: Published, Social Choice and Welfare, 2004, 23, 349-382
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Aggregation; choice function; concordance; consensus; distance; distributive; heredity; lattice; outcast;
Other versions of this item:
- Bernard Monjardet & Vololonirina Raderanirina, 2004. "Lattices of choice functions and consensus problems," Social Choice and Welfare, Springer, vol. 23(3), pages 349-382, December.
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