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.

Keywords: Probability; Stochastic model; Choice; Human (search for similar items in EconPapers)
Date: 1990-12
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Citations: View citations in EconPapers (5)

Published in Journal of Mathematical Psychology, 1990, vol.34, n°4, pp.371-392. ⟨10.1016/0022-2496(90)90019-6⟩

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Working Paper: A Necessary but Insufficient Condition for the Stochastic Binary Choice Problem (1989)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00481658

DOI: 10.1016/0022-2496(90)90019-6

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