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Lattices of choice functions and consensus problems.
- Source :
- Social Choice & Welfare; Dec2004, Vol. 23 Issue 3, p349-382, 34p, 5 Diagrams
- Publication Year :
- 2004
-
Abstract
- 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). [ABSTRACT FROM AUTHOR]
- Subjects :
- LATTICE theory
SET theory
GROUP theory
AXIOMS
FOUNDATIONS of geometry
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 01761714
- Volume :
- 23
- Issue :
- 3
- Database :
- Complementary Index
- Journal :
- Social Choice & Welfare
- Publication Type :
- Academic Journal
- Accession number :
- 14854079
- Full Text :
- https://doi.org/10.1007/s00355-003-0251-9