A short proof of a theorem of Falmagne.
type: Item
instance of: scholarly article
title: A short proof of a theorem of Falmagne.
zbMATH Open document ID: 1053.60009
author: D. Massart
published in: Journal of Mathematical Psychology
publication date: 2004-06-11T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 60E10
Mathematics Subject Classification ID: 60E15
Mathematics Subject Classification ID: 62P15
Mathematics Subject Classification ID: 91E99
zbMATH DE Number: 2073687
zbMATH Keywords: Falmagne theorem
zbMATH Keywords: probabilistic preference theory
zbMATH Keywords: complete system of choice probabilities
zbMATH Keywords: random utility model
zbMATH Keywords: Block-Marschak inequalities
zbMATH Keywords: normalization equalities
zbMATH Keywords: Möbius inversion
zbMATH Keywords: network flows
reviewed by: Neculai Curteanu
MaRDI profile type: Publication
full work available at URL: j.jmp.2003.11.003
OpenAlex ID: W1972194169
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DOI: 10.1016/J.JMP.2003.11.003
description: scientific article; zbMATH DE number 2073687