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Journal Articles Journal of Mathematical Psychology Year : 1990

A necessary but insufficient condition for the stochastic binary choice problem

Itzhak Gilboa
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Abstract

The "stochastic binary choice problem" is the following: Let there be given n alternatives, to be denoted by N = {1, ..., n}. For each of the n! possible linear orderings {m}m = 1n of the alternatives, define a matrix Yn × n(m)(1 ≤ m ≤ n!) as follows: Given a real matrix Qn × n, when is Q in the convex hull of {Y(m)}m? In this paper some necessary conditions on Q--the "diagonal inequality"--are formulated and they are proved to generalize the Cohen-Falmagne conditions. A counterexample shows that the diagonal inequality is insufficient (as are hence, perforce, the Cohen-Falmagne conditions). The same example is used to show that Fishburn's conditions are also insufficient.

Dates and versions

hal-00481658 , version 1 (07-05-2010)

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Cite

Itzhak Gilboa. A necessary but insufficient condition for the stochastic binary choice problem. Journal of Mathematical Psychology, 1990, vol.34, n°4, pp.371-392. ⟨10.1016/0022-2496(90)90019-6⟩. ⟨hal-00481658⟩

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