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

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  • Abdellaoui, Mohammed
  • Vossman, Frank
  • Weber, Martin

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 trade-off method. Then decision weights were elicited using certainty equivalents of uncertain two-outcome prospects. Furthermore, decision weights were decomposed using observable choice instead of invoking other empirical primitives as in the previous experimental studies. The choice-based elicitation of decision weights allows for a quantitative study of their characteristics, and also allows, among other things, to confront the sign-dependence hypothesis with observed choice under uncertainty. Our results confirm concavity of the utility function in the gain domain and bounded sub-additivity of decision weights as well as choice-based subjective probabilities. We also find evidence of sign-dependence of decision weights.

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Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 3756.

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Date of creation: Feb 2003
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Handle: RePEc:cpr:ceprdp:3756

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Keywords: choquet expected utility; cumulative prospect theory; decision under uncertainty (ambiguity); decision weights; probability weighting; subjective probabilities;

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References

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  1. Quiggin, John & Horowitz, John, 1995. "Time and Risk," Journal of Risk and Uncertainty, Springer, vol. 10(1), pages 37-55, January.
  2. 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.
  3. Craig R. Fox & Amos Tversky, 1998. "A Belief-Based Account of Decision Under Uncertainty," Management Science, INFORMS, vol. 44(7), pages 879-895, July.
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  7. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
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  13. 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.
  14. 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.
  15. 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.
  16. Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
  17. 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.
  18. 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.
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