4.1 Article

A representation theorem for finite best-worst random utility models

Journal

JOURNAL OF MATHEMATICAL PSYCHOLOGY
Volume 104, Issue -, Pages -

Publisher

ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jmp.2021.102596

Keywords

Best-worst choices; Random utility theory; Block-Marschak polynomials

Funding

  1. DFG, Germany [CO 94/6-1]

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This paper examines the representation of best-worst choice probabilities and establishes that the non-negativity of best-worst Block-Marschak polynomials is necessary and sufficient for the existence of a random utility representation. The representation theorem is derived by extending proof techniques from a previous study on best choices by Falmagne (1978).
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). (C) 2021 Elsevier Inc. All rights reserved.

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