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Does probability weighting matter in probability elicitation?

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Abstract

One of the most widely used methods for probability encoding in decision analysis uses binary comparisons (choices) between two lotteries: one that depends on the values of the random variable of interest and another that is contingent on an external reference chance device (typically a probability wheel). This note investigates the degree to which differences in probability weighting functions between the two types of events could affect the practice of subjective probability encoding. We develop a general methodology to investigate this question and illustrate it with two popular probability weighting functions over the range of parameters reported in the literature. We use this methodology to (a) alert decision analysts and researchers to the possibility of reversals, (b) identify the circumstances under which overt preferences for one lottery over the other are not affected by the weighting function, (c) document the magnitude of the differences between choices based on probabilities and their corresponding weighting functions, and (d) offer practical recommendations for probability elicitation.

Highlights

► We analyze the effects of differential weighting transformations in probability elicitation. ► Most elicited probabilities are insensitive to the shape and parameters of the weighting functions. ► Inconsistencies are observed with similar probabilities and extreme weighting functions.

Section snippets

Acknowledgments

This work was supported by the National Science Foundation under Award Number SES 06-20008.

We wish to thank Aurelien Baillon for identifying this problem, and Craig Fox, Richard Gonzalez, Peter Wakker, Thomas Wallsten, the Associate Editor and the anonymous referees for useful comments on an earlier version.

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