Axioms for unique subjective probability on finite sets
type: Item
instance of: scholarly article
title: Axioms for unique subjective probability on finite sets
zbMATH Open document ID: 0693.92022
DOI: 10.1016/0022-2496(89)90026-6
author: Peter Fishburn
author: Fred Roberts
published in: Journal of Mathematical Psychology
publication date: 1989-01-01T00:00:00Z
review text: The authors discuss axioms for a comparative probability relation on a finite set which imply the existence of a unique probability measure that agrees with the comparative relation. Special attention is paid to three axiomatizations that extend a sufficient condition for finite uniqueness developed by \textit{R. D. Luce} [Ann. Math. Stat. 38, 780-786 (1967; Zbl 0158.165)] to cases of uniqueness not covered by his condition. Two of the axiomatizations, due to \textit{L. Van Lier} [J. Math. Psychol. 33, No.1, 91-98 (1989; Zbl 0665.60003)] and the present authors, use only simple and intuitively straightforward conditions for uniqueness. Their conditions are sufficient but not necessary. The third axiomatization, proposed by the authors, presents conditions that are necessary and sufficient for uniqueness but which are much more complex than the merely sufficient conditions. The structure of the family of unique representations is also investigated for each axiomatization.
Mathematics Subject Classification ID: 91E99
Mathematics Subject Classification ID: 60A99
Mathematics Subject Classification ID: 60A05
zbMATH DE Number: 4135773
zbMATH Keywords: comparative probability relation
zbMATH Keywords: axiomatizations
zbMATH Keywords: conditions for uniqueness
Wikidata QID: Q114685156
reviewed by: Ivan Křivý
MaRDI profile type: Publication
full work available at URL: 0022-2496(89)90026-6
OpenAlex ID: W1985233768
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description: scientific article; zbMATH DE number 4135773