Advances in prospect theory: Cumulative representation of uncertainty
Purchase on Springer.com
$39.95 / €34.95 / £29.95*
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.
We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability.
This article has benefited from discussions with Colin Camerer, Chew Soo-Hong, David Freedman, and David H. Krantz. We are especially grateful to Peter P. Wakker for his invaluable input and contribution to the axiomatic analysis. We are indebted to Richard Gonzalez and Amy Hayes for running the experiment and analyzing the data. This work was supported by Grants 89-0064 and 88-0206 from the Air Force Office of Scientific Research, by Grant SES-9109535 from the National Science Foundation, and by the Sloan Foundation.
- Allais, Maurice. (1953). “Le comportement de l'homme rationel devant le risque, critique des postulates et axiomes de l'ecole americaine,” Econometrica 21, 503–546.
- Arrow, Kenneth J. (1982). “Risk Perception in Psychology and Economics,” Economic Inquiry 20, 1–9.
- Camerer, Colin F. (1989). “An Experimental Test of Several Generalized Utility Theories,” Journal of Risk and Uncertainty 2, 61–104.
- Camerer, Colin F. (1992). “Recent Tests of Generalizations of Expected Utility Theory.” In W. Edwards (ed.), Utility: Theories, Measurement and Applications, Boston, MA: Kluwer Academic Publishers.
- Camerer, Colin F. and Teck-Hua Ho. (1991). “Nonlinear Weighting of Probabilities and Violations of the Betweenness Axiom.” Unpublished manuscript, The Wharton School, University of Pennsylvania.
- Chew, Soo-Hong. (1989). “An Axiomatic Generalization of the Quasilinear Mean and the Gini Mean with Application to Decision Theory,” Unpublished manuscript, Department of Economics, University of California at Irvine.
- Choquet, Gustave. (1955). “Theory of Capacities,” Annales de L'Institut Fourier 5, 131–295.
- Cohen, Michele, Jean-Yves Jaffray, and Tanios Said. (1987). “Experimental Comparison of Individual Behavior Under Risk and Under Uncertainty for Gains and for Losses,” Organizational Behavior and Human Decision Processes 39, 1–22.
- Ellsberg, Daniel. (1961). “Risk, Ambiguity, and the Savage Axioms,” Quarterly Journal of Economics 75, 643–669.
- Fishburn, Peter C. (1988). Nonlinear Preference and Utility Theory. Baltimore, MD: The Johns Hopkins University Press.
- Gilboa, Itzhak. (1987). “Expected Utility with Purely Subjective Non-additive Probabilities,” Journal of Mathematical Economics 16, 65–88.
- Heath, Chip and Amos Tversky. (1991). “Preference and Belief: Ambiguity and Competence in Choice Under Uncertainty,” Journal of Risk and Uncertainty 4, 5–28.
- Hershey, John C. and Paul J. H. Schoemaker. (1980). “Prospect Theory's Reflection Hypothesis: A Critical Examination,” Organizational Behavior and Human Performance 25, 395–418.
- Hogarth, Robin and Hillel Einhorn. (1990). “Venture Theory: A Model of Decision Weights,” Management Science 36, 780–803.
- Kachelmeier, Steven J. and Mohamed Shehata. (1991). “Examining Risk Preferences Under High Monetary Incentives: Experimental Evidence from The People's Republic of China,” American Economic Review, forthcoming.
- Kahneman, Daniel, Paul Slovic, and Amos Tversky (eds.). (1982). Judgment Under Uncertainty: Heuristics and Biases. New York: Cambridge University Press.
- Kahneman, Daniel and Amos Tversky. (1979). “Prospect Theory: An Analysis of Decision Under Risk,” Econometrica 47, 263–291.
- Kahneman, Daniel and Amos Tversky. (1984). “Choices, Values and Frames,” American Psychologist 39, 341–350.
- Loomes, Graham and Robert Sugden. (1987). “Regret Theory: An Alternative Theory of Rational Choice Under Uncertainty,” The Economic Journal 92, 805–824.
- Loomes, Graham and Robert Sugden. (1987). “Some Implications of a More General Form of Regret Theory,” Journal of Economic Theory 41, 270–287.
- Luce, R. Duncan and Peter C. Fishburn. (1991). “Rank- and Sign-dependent Linear Utility Models for Finite First-order Gambles,” Journal of Risk and Uncertainty 4, 29–59.
- Machina, Mark J. (1987). “Choice Under Uncertainty: Problems Solved and Unsolved,” Economic Perspectives 1(1), 121–154.
- Marschak, Jacob. (1950). “Rational Behavior, Uncertain Prospects, and Measurable Utility,” Econometrica 18, 111–114.
- Nakamura, Yutaka. (1990). “Subjective Expected Utility with Non-additive Probabilities on Finite State Space,” Journal of Economic Theory 51, 346–366.
- Prelec, Drazen. (1989). “On the Shape of the Decision Weight Function.” Unpublished manuscript, Harvard Graduate School of Business Administration.
- Prelec, Drazen. (1990). “A ‘Pseudo-endowment’ Effect, and its Implications for Some Recent Non-expected Utility Models,” Journal of Risk and Uncertainty 3, 247–259.
- Quiggin, John. (1982). “A Theory of Anticipated Utility,” Journal of Economic Behavior and Organization 3, 323–343.
- Savage, Leonard J. (1954). The Foundations of Statistics. New York: Wiley.
- Schmeidler, David. (1989). “Subjective Probability and Expected Utility without Additivity,” Econometrica 57, 571–587.
- Segal, Uzi. (1989). “Axiomatic Representation of Expected Utility with Rank-dependent Probabilities,” Annals of Operations Research 19, 359–373.
- Smith, Vernon L. and James M. Walker. (1992). “Monetary Rewards and Decision Cost in Experimental Economics.” Unpublished manuscript, Economic Science Lab, University of Arizona.
- Starmer, Chris and Robert Sugden. (1989). “Violations of the Independence Axiom in Common Ratio Problems: An Experimental Test of Some Competing Hypotheses,” Annals of Operations Research, 19, 79–102.
- Tversky, Amos. (1969). “The Intransitivity of Preferences,” Psychology Review 76, 31–48.
- Tversky, Amos and Daniel Kahneman. (1986). “Rational Choice and the Framing of Decisions,” The Journal of Business 59(4), part 2, S251-S278.
- Tversky, Amos and Daniel Kahneman. (1991). “Loss Aversion in Riskless Choice: A Reference Dependent Model,” Quarterly Journal of Economics 107(4), 1039–1061.
- Tversky, Amos, Shmuel Sattath, and Paul Slovic. (1988). “Contingent Weighting in Judgment and Choice,” Psychological Review 95(3), 371–384.
- Tversky, Amos, Paul Slovic, and Daniel Kahneman. (1990). “The Causes of Preference Reversal,” The American Economic Review 80(1), 204–217.
- Viscusi, Kip W. (1989). “Prospective Reference Theory: Toward an Explanation of the Paradoxes,” Journal of Risk and Uncertainty 2, 235–264.
- Wakker, Peter P. (1989a). Additive Representations of Preferences: A New Foundation in Decision Analysis. Dordrecht, The Netherlands: Kluwer Academic Publishers.
- Wakker, Peter P. (1989b). “Continuous Subjective Expected Utility with Nonadditive Probabilities,” Journal of Mathematical Economics 18, 1–27.
- Wakker, Peter P. (1990). “Separating Marginal Utility and Risk Aversion.” Unpublished manuscript, University of Nijmegen, The Netherlands.
- Wakker, Peter P. (1991). “Additive Representations of Preferences, a New Foundation of Decision Analysis; the Algebraic Approach.” In J. D. Doignon and J. C. Falmagne (eds.), Mathematical Psychology: Current Developments. Berlin: Springer, pp. 71–87.
- Wakker, Peter P. (1992). “Additive Representations on Rank-ordered Sets; Part II: The Topological Approach,” Journal of Mathematical Economics, forthcoming.
- Wakker, Peter P. and Amos Tversky. (1991). “An Axiomatization of Cumulative Prospect Theory.” Unpublished manuscript, University of Nijmegan, the Netherlands.
- Wehrung, Donald A. (1989). “Risk Taking over Gains and Losses: A Study of Oil Executives,” Annals of Operations Research 19, 115–139.
- Weymark, J. A. (1981). “Generalized Gini Inequality Indices,” Mathematical Social Sciences 1, 409–430.
- Yaari, Menahem E. (1987). “The Dual Theory of Choice Under Risk,” Econometrica 55, 95–115.
- Advances in prospect theory: Cumulative representation of uncertainty
Journal of Risk and Uncertainty
Volume 5, Issue 4 , pp 297-323
- Cover Date
- Print ISSN
- Online ISSN
- Kluwer Academic Publishers
- Additional Links
- cumulative prospect theory
- Industry Sectors