A representation theorem for finite best–worst random utility models

Abstract This paper investigates the representation of 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 for a corresponding result on best choices (picking the best alternative from an offered set) developed by Falmagne (1978).