Indeterminate Probabilities and Utilities on Finite Sets

by Robert F. Nau (The Annals of Statistics 20:4 1737-1767, December 1992)

Abstract: This paper presents a quasi-Bayesian model of subjective uncertainty in which beliefs which are represented by sets of probabilities with indeterminate boundaries. The model is derived from a system of axioms of binary preferences which differs from standard axiom systems insofar as completeness is not assumed and transitivity is weakened. Under this system, beliefs are represented by lower and upper probabilities qualified by numerical confidence weights which can be operationally elicited through the acceptance of bets with limited stakes, a generalization of the operational method of de Finetti

Key words: Subjective probability, lower and upper probabilities, confidence-weighted probabilities, second-order probabilities, coherence, ambiguity, incompleteness, fuzzy sets, combination of probability judgments

(See also the description of this paper in my research summary.)