This paper uses “revealed probability trade-offs” to provide a natural foundation for probability weighting in the famous von Neumann and Morgenstern axiomatic set-up for expected utility. In particular, it shows that a rank-dependent preference functional is obtained in this set-up when the independence axiom is weakened to stochastic dominance and a probability trade-off consistency condition. In contrast with the existing axiomatizations of rank-dependent utility, the resulting axioms allow for complete flexibility regarding the outcome space. Consequently, a parameter-free test/elicitation of rank-dependent utility becomes possible. The probability-oriented approach of this paper also provides theoretical foundations for probabilistic attitudes towards risk. It is shown that the preference conditions that characterize the shape of the probability weighting function can be derived from simple probability trade-off conditions.

Despite the increasing importance of multiple priors in various domains of economics, choice-based incentive-compatible multiple-prior elicitation remains an open problem. This paper develops a solution, comprising a preference-based identification of a subject’s probability interval for an event, and a method for eliciting it. The method applies under weak decision-theoretic assumptions, with no need for probabilistic sophistication. To demonstrate its feasibility, we implement it in three incentivized experiments on artificial and natural sources of uncertainty. Intervals elicited by our method are sensitive to the direction and amount of information and are typically consistent with “objective” probabilities where available. We find a predominance of non-degenerate probability intervals, with intervals being wider when there is less information or predictability. The probability intervals elicited with our method are similar to those stated by subjects on aggregate, suggesting that the method can provide behavioural foundations for the use of stated probability-interval techniques in the field.

We often deal with uncertain events for which no probabilities are known. Several normative models have been proposed. Descriptive studies have usually been qualitative, or they estimated ambiguity aversion through one single number. This paper introduces the source method, a tractable method for quantitatively analyzing uncertainty empirically. The theoretical key is the distinction between different sources of uncertainty, within which subjective (choice-based) probabilities can still be defined. Source functions convert those subjective probabilities into willingness to bet. We apply our method in an experiment, where we do not commit to particular ambiguity attitudes but let the data speak.