Nonlinear Decision Weights in Choice Under Uncertainty
In most real-world decisions, consequences are tied explicitly to the outcome of events. Previous studies of decision making under uncertainty have indicated that the psychological weight attached to an event, called a decision weight, usually differs from the probability of that event. We investigate two sources of nonlinearity of decision weights: subadditivity of probability judgments, and the overweighting of small probabilities and underweighting of medium and large probabilities. These two sources of nonlinearity are combined into a two-stage model of choice under uncertainty. In the first stage, events are taken into subjective probability judgments, and the second stage takes probability judgments into decision weights. We then characterize the curvature of the decision weights by extending a condition employed by Wu and Gonzalez (1996) in the domain of risk to the domain of uncertainty and show that the nonlinearity of decision weights can be decomposed into subadditivity of probability judgments and the curvature of the probability weighting function. Empirical tests support the proposed two-stage model and indicate that decision weights are concave then convex. More specifically, our results lend support for a new property of subjective probability judgments, interior additivity (subadditive at the boundaries, but additive away from the boundaries), and show that the probability weighting function is inverse S-shaped as in Wu and Gonzalez (1996).
Volume (Year): 45 (1999)
Issue (Month): 1 (January)
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- 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.
- Wu, George, 1994. "An Empirical Test of Ordinal Independence," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 39-60, July.
- Wu, George & Gonzalez, Richard, 1998. "Common Consequence Conditions in Decision Making under Risk," Journal of Risk and Uncertainty, Springer, vol. 16(1), pages 115-139, April.
- 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.
- Craig R. Fox & Amos Tversky, 1995. "Ambiguity Aversion and Comparative Ignorance," The Quarterly Journal of Economics, Oxford University Press, vol. 110(3), pages 585-603.
- 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.
- Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
- Segal, Uzi, 1987.
"Some remarks on Quiggin's anticipated utility,"
Journal of Economic Behavior & Organization,
Elsevier, vol. 8(1), pages 145-154, March.
- Uzi Segal, 1986. "Some Remarks on Quiggin's Anticipated Utility," UCLA Economics Working Papers 392, UCLA Department of Economics.
- John C. Hershey & Paul J. H. Schoemaker, 1985. "Probability Versus Certainty Equivalence Methods in Utility Measurement: Are they Equivalent?," Management Science, INFORMS, vol. 31(10), pages 1213-1231, October.
- Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-196, March.
- Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
- Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
- George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
- Gilboa, Itzhak, 1987. "Expected utility with purely subjective non-additive probabilities," Journal of Mathematical Economics, Elsevier, vol. 16(1), pages 65-88, February.
- Itzhak Gilboa, 1987. "Expected Utility with Purely Subjective Non-Additive Probabilities," Post-Print hal-00756291, HAL.
- Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
- David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
- Tversky, Amos & Wakker, Peter, 1995. "Risk Attitudes and Decision Weights," Econometrica, Econometric Society, vol. 63(6), pages 1255-1280, November.
- Craig R. Fox & Amos Tversky, 1998. "A Belief-Based Account of Decision Under Uncertainty," Management Science, INFORMS, vol. 44(7), pages 879-895, July.
- Camerer, Colin & Weber, Martin, 1992. "Recent Developments in Modeling Preferences: Uncertainty and Ambiguity," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 325-370, October.
- 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. Full references (including those not matched with items on IDEAS)
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