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A necessary but insufficient condition for the stochastic binary choice problem

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.
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Submitted on : Friday, May 7, 2010 - 10:13:43 AM
Last modification on : Sunday, November 18, 2012 - 7:39:03 PM

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

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