Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown

TLDR

This paper proposes a new gamble‑tradeoff method for eliciting utilities in decision under risk or uncertainty. The tradeoff method is tested on monetary outcomes and life‑duration outcomes, demonstrating its applicability across different outcome domains. The method allows utility elicitation even when probabilities are ambiguous or unknown, remains robust against probability distortions and misconceptions, retains validity under prospect theory and cumulative prospect theory, but requires slightly more questions and more complex lotteries, and reveals higher risk aversion for life duration while eliciting similar utility curvature.

Abstract

This paper proposes a new method, the (gamble-)tradeoff method, for eliciting utilities in decision under risk or uncertainty. The elicitation of utilities, to be used in the expected utility criterion, turns out to be possible even if probabilities are ambiguous or unknown. A disadvantage of the tradeoff method is that a few more questions usually must be asked to clients. Also, the lotteries that are needed are somewhat more complex than in the certainty-equivalent method or in the probability-equivalent method. The major advantage of the tradeoff method is its robustness against probability distortions and misconceptions, which constitute a major cause of violations of expected utility and generate inconsistencies in utility elicitation. Thus the tradeoff method retains full validity under prospect theory, rank-dependent utility, and the combination of the two, i.e., cumulative prospect theory. The tradeoff method is tested for monetary outcomes and for outcomes describing life-duration. We find higher risk aversion for life duration, but the tradeoff method elicits similar curvature of utility. Apparently the higher risk aversion for life duration is due to more pronounced deviations from expected utility.