A short proof of a theorem of Falmagne.
A central question in probabilistic preference theory is to find testable necessary and sufficient conditions on experimental choice data, i.e. the complete system of choice probabilities, such that these data satisfy the random utility model. Under the non-coincidence assumption, a complete system of choice probabilities arises from the random utility model if and only if it is induced by rankings. This fundamental result was proved by \textit{J. C. Falmagne} [J. Math. Psychol. 18, 52--72 (1978; Zbl 0408.62093)], involving Block-Marschak inequalities and the normalization equalities for a complete system of choice probabilities. The purpose of the present note is to provide a short proof for the Falmagne basin result using an approach that combines Möbius inversion and network flows. Interesting remarks on the proof evolution of the Falmagne's theorem are also given.
scientific article; zbMATH DE number 2073687