A Representation Theorem for Finite Best-Worst Random Utility Models

2020/08/22 by Hans Colonius, Colonius, Hans
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #math.OC #math.PR

paper · pdf · doi:10.48550/arxiv.2008.09782

arxiv created 2020/09/07 · arxiv updated 2020/09/08

Abstract

This paper investigates best-worst choice probabilities (picking the best and the worst alternative from an offered set). It is shown that non-negativity of best-worst Block-Marschak polynomials is necessary and sufficient for the existence of a random utility representation. The representation theorem is obtained by extending proof techniques employed by Falmagne (1978) for a corresponding result on best choices (picking the best alternative from an offered set).

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