2024/08/15 by Hans Colonius, Colonius, Hans
Decision Sciences · #FOS: Mathematics #Optimization and Control (math.OC) #Risk and Portfolio Optimization
paper · pdf · doi:10.48550/arxiv.2408.08165
openalex publication_date 2024/08/15 · openalex created_date 2024/09/18 · openalex updated_date 2026/07/28
This paper investigates the random utility representation of best-worst choice probabilities (picking the best and the worst alternative from an offered set). Doignon (2023) presented a complete characterization of the best-worst-choice polytope on four alternatives. Moreover, using polytope methods he showed that the Block-Marschak inequalities for best-worst choices are not sufficient for a random utility representation of best-worst choices for sets of four or more alternatives. Following the approach of Falmagne (1978), we construct a probability measure on the set of rankings for a set of four alternatives implying a random utility representation.