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Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty

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Author Info

  • Mohammed Abdellaoui

    ()
    (GRID-CNRS, Ecole Nationale Supérieure d'Arts et Métiers, Maison de la Recherche de l'ESTP, 30 Avenue du Président Wilson, 94230 Cachan, France)

  • Frank Vossmann

    ()
    (Lehrstuhl für Bankbetriebslehre, Universität Mannheim, 68131 Mannheim, Germany)

  • Martin Weber

    ()
    (Lehrstuhl für Bankbetriebslehre, Universität Mannheim, 68131 Mannheim, Germany)

Abstract

This paper reports the results of an experimental parameter-free elicitation and decomposition of decision weights under uncertainty. Assuming cumulative prospect theory, utility functions were elicited for gains and losses at an individual level using the tradeoff method. Subsequently, decision weights were elicited through certainty equivalents of uncertain two-outcome prospects. Furthermore, decision weights were decomposed using observable choice instead of invoking other empirical primitives, as in previous experimental studies. The choice-based elicitation of decision weights allows for a quantitative study of their characteristics, and also allows, among other things, for the examination of the sign-dependence hypothesis for observed choice under uncertainty. Our results confirm concavity of the utility function in the gain domain and bounded subadditivity of decision weights and choice-based subjective probabilities. We also find evidence for sign dependence of decision weights.

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File URL: http://dx.doi.org/10.1287/mnsc.1050.0388
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Bibliographic Info

Article provided by INFORMS in its journal Management Science.

Volume (Year): 51 (2005)
Issue (Month): 9 (September)
Pages: 1384-1399

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Handle: RePEc:inm:ormnsc:v:51:y:2005:i:9:p:1384-1399

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Keywords: decision under uncertainty; Choquet expected utility; cumulative prospect theory; decision weights; choice-based probabilities; probability weighting;

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  1. Michael Kilka & Martin Weber, 2001. "What Determines the Shape of the Probability Weighting Function Under Uncertainty?," Management Science, INFORMS, vol. 47(12), pages 1712-1726, December.
  2. Wakker, Peter & Tversky, Amos, 1993. " An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-75, October.
  3. Lattimore, Pamela K. & Baker, Joanna R. & Witte, Ann D., 1992. "The influence of probability on risky choice: A parametric examination," Journal of Economic Behavior & Organization, Elsevier, vol. 17(3), pages 377-400, May.
  4. Quiggin, John & Horowitz, John, 1995. "Time and Risk," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 37-55, January.
  5. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-59, July.
  6. Craig R. Fox & Amos Tversky, 1998. "A Belief-Based Account of Decision Under Uncertainty," Management Science, INFORMS, vol. 44(7), pages 879-895, July.
  7. Peter Wakker & Daniel Deneffe, 1996. "Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown," Management Science, INFORMS, vol. 42(8), pages 1131-1150, August.
  8. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
  9. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
  10. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  11. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-87, May.
  12. Tversky, Amos & Kahneman, Daniel, 1992. " Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
  13. Pamela K. Lattimore & Joanna R. Baker & A. Dryden Witte, 1992. "The Influence Of Probability on Risky Choice: A parametric Examination," NBER Technical Working Papers 0081, National Bureau of Economic Research, Inc.
  14. Fox, Craig R & Rogers, Brett A & Tversky, Amos, 1996. "Options Traders Exhibit Subadditive Decision Weights," Journal of Risk and Uncertainty, Springer, vol. 13(1), pages 5-17, July.
  15. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
  16. Heath, Chip & Tversky, Amos, 1991. " Preference and Belief: Ambiguity and Competence in Choice under Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 5-28, January.
  17. Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-80, November.
  18. Camerer, Colin & Weber, Martin, 1992. " Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-70, October.
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