Abstract
This paper provides an efficient method to measure utility under prospect theory. Our method minimizes both the number of elicitations required to measure utility and the cognitive burden for subjects, being based on the elicitation of certainty equivalents for two-outcome prospects. We applied our method in an experiment and were able to replicate the main findings on prospect theory, suggesting that our method measures what it is intended to. Our data confirmed empirically that risk seeking and concave utility can coincide under prospect theory. Utility did not depend on the probability used in the elicitation, which offers support for the validity of prospect theory.
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Notes
The idea of simultaneously estimating decision weights and utility was also recently used by Viscusi and Evans (2006).
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Acknowledgments
Peter Wakker and two anonymous referees provided helpful comments. Mohammed Abdellaoui and Olivier L’Haridon’s research was supported by the French National Research Agency (ANR, Risk Attitude). Han Bleichrodt’s research was supported by a grant from the Netherlands Organization for Scientific Research.
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Appendices
Appendix 1
1.1 Illustration of questions
Illustration of a task in the gain domain
Illustration of a task in the mixed domain
Appendix 2
2.1 Explanation of the bisection method
The bisection method used to generate the iterations is illustrated in Table 10 for L 1 for \(p_\ell = {1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}\) and the elicitation of \(L_6^ * \) for \(p_g = p_\ell = {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\). The prospect that is chosen is printed in bold. Starting values in the iterations were always chosen so that prospects had equal expected value. Depending on the choice made, the certain outcome was increased or decreased. The size of the change was always half the size of the change in the previous question with the restriction that numbers should always be a multiple of 10. When a number was not a multiple of 10 it was rounded downwards. The method resulted in an interval within which the indifference value should lie. The midpoint of this interval was taken as the indifference value. For example, in Table 10 the indifference value for \(L_6^ * \) should lie between −3,960 and −3,680. Then we took as the indifference value −3,820. In the elicitation of utility on the gain and loss domains, the certainty equivalents were elicited in five iterations. In the elicitation of the loss aversion coefficients, we used six iterations. We used one additional iteration in the elicitation of the loss aversion coefficients because the intervals \(G_j^ * - L_j^ * \) were larger than the intervals |x j − y j |.
Appendix 3
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Abdellaoui, M., Bleichrodt, H. & L’Haridon, O. A tractable method to measure utility and loss aversion under prospect theory. J Risk Uncertainty 36, 245–266 (2008). https://doi.org/10.1007/s11166-008-9039-8
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DOI: https://doi.org/10.1007/s11166-008-9039-8