Error Propagation in the Elicitation of Utility and Probability Weighting Functions

Abstract

Blavatskyy, P Blavatskyy, P (2006) AbstractElicitation 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 functionsPavlo Blavatskyy 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.

Measuring the time stability of Prospect Theory preferences

“…5 In general, one has to decide between the theoretical elegance of an elicitation procedure on the one hand and its practical applicability on the other. Blavatskyy (2006) comes to the conclusion that the theoretically optimal elicitation procedure uses a non-parametric three-stage design. While theoretically appealing, such sophisticated elicitation methods show limitations in practice (see e.g.…”

A parametric analysis of prospect theory’s functionals for the general population

“…This approach, however, requires data that have a chained nature which may introduce error propagation leading to less precise inference (Wakker and Deneffe 1996;Blavatskyy 2006) and, in theory, an incentive compatibility problem .…”

“…This method is robust against subjective probability distortion (Wakker and Deneffe 1996) such that the measurement of utility does not depend on the estimates of the probability weights. Our stochastic specification allows for decision errors, and it naturally accommodates the propagation of errors that is introduced by the chaining of the questions that is at the heart the trade-off method (Blavatskyy 2006). Furthermore, the data contains background variables that can be linked to the obtained preference parameters to shed light on how the various components of risk attitudes vary in the population.…”

The influence of probabilities on the response mode bias in utility elicitation

“…Finally, probability weighting was considered a major impact factor on biases in utility assessment (e.g., Kahneman and Tversky 1979;Lattimore et al 1992;Tversky and Kahneman 1992;Wu and Gonzalez 1996;Gonzalez and Wu 1999;Abdellaoui 2000;Bleichrodt and Pinto 2000;Bleichrodt et al 2001Bleichrodt et al , 2007Blavatskyy 2006). Probability weighting is rooted in subjects' nonlinear understanding of probabilities, which causes high probabilities to be underweighted and low probabilities to be overweighted relative to their actual values.…”

“…Knowing the strength of the potential bias in various settings can form the basis for new elicitation methods softening its impact (McCord and de Neufville 1986;Delquié 1993;Wakker and Deneffe 1996;Abdellaoui 2000;Bleichrodt and Pinto 2000;Bleichrodt et al 2001;Blavatskyy 2006).…”