GEOMETRIC AND COMBINATORIAL PROPERTIES OF THE POLYTOPE OF BINARY CHOICE-PROBABILITIES

Autor(en): SUCK, R
Stichwörter: BINARY CHOICE PROBABILITIES; Business & Economics; CONVEX POLYHEDRA; DOUBLY STOCHASTIC MATRICES; Economics; LINEAR ORDERING PROBLEM; Mathematical Methods In Social Sciences; Mathematics; Mathematics, Interdisciplinary Applications; OMEGA-N; PERMUTATION POLYTOPE; Social Sciences, Mathematical Methods
Erscheinungsdatum: 1992
Herausgeber: ELSEVIER SCIENCE BV
Journal: MATHEMATICAL SOCIAL SCIENCES
Volumen: 23
Ausgabe: 1
Startseite: 81
Seitenende: 102
Zusammenfassung: 
A system of binary choice probabilities on a finite set is representable if the probabilities are compatible with a probability distribution over the family of linear orders of the set. In geometric terms representable binary choice probabilities form a polytope the vertices of which correspond to the permutations in a matrix indicating the dominant element in each pair (Definition 1.1). In this paper we develop the geometrical aspect reconciling two branches of research-choice theory and optimization connected with the linear ordering problem which until recently developed independently. We show that most results of the choice literature are already known and have a geometric meaning, i.e. they describe facets of the polytope. In particular a few combinatorial results concerning these kinds of permutation matrices are proved, the geometric aspect is introduced and a few well-known results of the polytope under consideration are established. Then the known necessary conditions are analysed concerning their facet-defining properties. Moreover, we show that the diagonal inequality recently proved by Gilboa (1990) contains facet-defining cases.
ISSN: 01654896
DOI: 10.1016/0165-4896(92)90039-8

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