This paper presents a quasi-Bayesian model of subjective uncertainty in which beliefs which are represented by lower and upper probabilities qualified by numerical confidence weights. The representation 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. Confidence-weighted probabilities may be elicited through the acceptance of bets with limited stakes, a generalization of the operational method of de Finetti. The model is applicable to the reconciliation of inconsistent probability judgments and to the sensitivity analysis of Bayesian decision models.
"Indeterminate Probabilities on Finite Sets." Ann. Statist. 20 (4) 1737 - 1767, December, 1992. https://doi.org/10.1214/aos/1176348888