TY - JOUR

T1 - A necessary but insufficient condition for the stochastic binary choice problem

AU - Gilboa, Itzhak

PY - 1990/12

Y1 - 1990/12

N2 - 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: Yab(m) = 1 0 a≻mb otherwise. 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.

AB - 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: Yab(m) = 1 0 a≻mb otherwise. 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.

UR - http://www.scopus.com/inward/record.url?scp=38249018161&partnerID=8YFLogxK

U2 - 10.1016/0022-2496(90)90019-6

DO - 10.1016/0022-2496(90)90019-6

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AN - SCOPUS:38249018161

SN - 0022-2496

VL - 34

SP - 371

EP - 392

JO - Journal of Mathematical Psychology

JF - Journal of Mathematical Psychology

IS - 4

ER -