Axioms for unique subjective probability on finite sets
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.
scientific article; zbMATH DE number 4135773