Error Propagation in the Elicitation of Utility and Probability Weighting Functions

Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities and probability weights is the following three-stage procedure. First, a probability is elicited whose subjective weight is one half. Second, the utility function is elicited through the midpoint chaining certainty equivalent method using the probability elicited at the first stage. Finally, the probability weighting function is elicited through the probability equivalent method. Efficient elicitation of utility and probability weighting functions Pavlo Blavatskyy Institute for Empirical Research in Economics University of Zurich Winterthurerstrasse 30 CH-8006 Zurich Switzerland Phone: +41(1)6343586 Fax: +41(1)6344978 e-mail: [email protected] November 2004 Abstract: Elicitation methods in decision making under risk allow a researcher to infer the subjective utilities of outcomes as well as the subjective weights of probabilities from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes into account the inevitable distortion of preferences by random errors and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities (weights) of many outcomes (probabilities) is the following three-stage procedure. First, a probability is elicited whose subjective weight is one half. Second, an individual’s utility function is elicited through the midpoint chaining certainty equivalent method employing the probability elicited at the first stage as an input. Finally, an individual’s probability weighting function is elicited through the probability equivalent method.