Abstract
Many different functional forms have been suggested for both the value function and probability weighting function of Cumulative Prospect Theory (Tversky and Kahneman, 1992). There are also many stochastic choice functions available. Since these three components only make predictions when considered in combination, this paper examines the complete pattern of 256 model variants that can be constructed from twenty functions. All these variants are fit to experimental data and their explanatory power assessed. Significant interaction effects are observed. The best model has a power value function, a risky weighting function due to Prelec (1998), and a Logit function.
Similar content being viewed by others
References
Abdellaoui, Mohammed. (2000). “Parameter Free Elicitation of Utilities and Probability Weighting Functions,” Management Science 46, 1497–1512.
Abdellaoui, Mohammed, Frank Vossmann and Martin Weber. (2003). “Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty,” Manuscript obtained from authors.
Akaike, Hirotugu (1973). “Information Theory and an Extension of the Maximum Likelihood Principle,” in: B. N. Petrox and F. Caski (Eds.), Second International Symposium on Information Theory. Budapest, Hungary: Akademiai Kiado pp. 267–281.
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. [In French].
Ballinger, T. Parker and Nathaniel T. Wilcox (1997). “Decisions, Error and Heterogeneity,” Economic Journal 107, 1090–1105.
Barberis, Nicholas and Ming Huang. (2005). “Stocks as Lotteries: The Implications of Probability Weighting for Securities Prices,” Manuscript Obtained from Authors.
Becker, Gordon M, Maurice H. De Groot and Jacob Marschak. (1963a). “An Experimental Study of Some Stochastic Models for Wagers,” Behavioural Science 3, 199–202.
Becker, Gordon M., Maurice H. De Groot and Jacob Marschak (1963b). Stochastic Models of Choice Behaviour. Behavioural Science 8, 41–55.
Bell, David E. (1995a). “Risk, Return and Utility,” Management Science 41(1), 23–30
Bell, David E. (1995b). “A Contextual Uncertainty Condition for Behavior Under Risk,” Management Science 41(7), 1145–1150
Bell, David E. and Peter C. Fishburn. (2000). “Utility Functions for Wealth, Journal of Risk and Uncertainty 20, 5–44.
Bell, David E. and Peter C. Fishburn (2001). “Strong One-Switch Utility,” Management Science 47(4), 601–604
Birnbaum, Michael H. and Alfredo Chavez. (1997). “Tests of Theories of Decision Making: Violations of Branch Independence and Distribution Independence,” Organizational Behavior and Human Decision Processes 71, 161–194.
Birnbaum, Michael H, Jamie N. Patton and Melissa K. Lott. (1999). “Evidence Against Rank Dependent Utility Theories: Tests of Cumulative Independence, Interval Dependence, Stochastic Dominance and Transitivity,” Organizational Behavior and Human Decision Processes 77, 44–83.
Bleichrodt, Hans and Jose, Luis Pinto. (2000). “A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis,” Management Science 46(11), 1485–1496
Blondel, Serge. (2002). “Testing Theories of Choice Under Risk: Estimation of Individual Functionals,” Journal of Risk and Uncertainty 24(3), 251–265
Brandstätter, Eduard, Anton Kühberger and Friedrich Schneider. (2002). “A Cognitive-Emotional Account of the Shape of the Probability Weighting Function,” Journal of Behavioral Decision Making 15 , 79–100.
Burnham, Kenneth P. and David R. Anderson. (2002). Model Selection and Multimodel Inference. New York: Springer-Verlag.
Buschena, David and David Zilberman (2000). “Generalized Expected Utility, Heteroscedastic Error, and Path Dependence in Risky Choice,” Journal of Risk and Uncertainty 20, 67–88.
Camerer, Colin F. (1989). “An Experimental Test of Several Generalized Utility Theories,” Journal of Risk and Uncertainty 2, 61–104.
Camerer, Colin F. and Robin M. Hogarth (1999). “The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework,” Journal of Risk and Uncertainty 19, 7–42.
Camerer, Colin F. and Teck-Hua Ho. (1994). “Violations of the Betweeness Axiom and Nonlineraity in Probability,” Journal of Risk and Uncertainty 8, 167–196.
Carbone, Enrica. (1997). “Investigation of Stochastic Preference Theory Using Experimental Data,” Economic Letters 57(3), 305–311
Carbone, Enrica and John D. Hey. (1994). “Discriminating Between Preference Functionals: A Preliminary Monte Carlo Study,” Journal of Risk and Uncertainty 8, 223–242.
Carbone, Enrica and John D. Hey. (1995). “A Comparison of the Estimates of EU and Non-EU Preference Functionals Using Data from Pairwise Choice and Complete Ranking Experiments,” Geneva Papers on Risk and Insurance Theory 20, 111–133.
Carbone, Enrica and John D. Hey. (2000). “Which Error Story is Best,” Journal of Risk and Uncertainty 20, 161–176.
Chechile, Richard A. and Alan D. J. Cooke. (1997). “An Experimental Test of a General Class of Utility Models: Evidence for Context Dependency,” Journal of Risk and Uncertainty 14, 75–93.
Debreu, Gerard. (1958). “Stochastic Choice and Cardinal Utility,” Econometrica 26(3), 440–444
Doctor, Jason, N. et al. (2004). “A New and More Robust Test of QALYs,” Journal of Health Economics 23, 353–367.
Fennema, Hein and Marcel van Assen. (1998). “Measuring the Utility of Losses by Means of the Trade-Off Method,” Journal of Risk and Uncertainty 17, 277–295.
Fennema, Hein and Peter, Wakker. (1997). “Original and Cumulative Prospect Theory: A Discussion of Empirical Differences,” Journal of Behavioral Decision Making 10, 53–64.
Fishburn, Peter C. and Gary A. Kochenberger. (1979). “Two Piece Von Neumann-Morgernstern Utility Functions,” Decision Sciences 10(4), 503–518
Goldstein, William M. and Hillel J. Einhorn. (1987). “Expression Theory and the Preference Reversal Phenomena,” Psychological Review 94, 236–254.
Gonzalez, Richard and George Wu. (1999). “On the Shape of Probability Weighting Function,” Cognitive Psychology 38, 129–166.
Guthrie, Chris. (2003). “Prospect Theory, Risk Preference, and the Law,” Northwestern University Law Review 97(3), 1115–1163
Grünwald, Peter. (2000). “Model Selection Based on Minimum Description Length.” Journal of Mathematical Psychology 44, 133–152.
Harless, David W. and Colin F. Camerer. (1994). “The Predictive Utility of Generalized Expected Utility Theories,” Econometrica 62(6), 1251–1290
Herrnstein, Richard J. (1997). The Matching Law: Papers in Psychology and Economics. H. Rachlin and D. I. Laibson (Eds.). New York: Russell Sage Foundation.
Hertwig, Raph and Andreas Ortmann. (2001). “Experimental Practices in Economics: A Methodological Challenge to Psychologists?,” Behavioral and Brain Sciences 24, 383–451.
Hey, John D. (1995). “Experimental Investigations of Errors in Decision Making Under Risk,” European Economic Review 39, 633–640.
Hey, John D. and Chris Orme. (1994). “Investigating Generalizations of the Expected Utility Theory Using Experimental Data,” Econometrica 62(6), 1291–1326
Hoeting, Jennifer A. et al. (1999). “Bayesian Model Averaging: A Tutorial,” Statistical Science 14, 382–401.
Ingersoll Jonathan E, Jr. (1987). Theory of Financial Decision Making. Savage, MD: Rowman and Littlefield.
Isaac, R. Mark and Duncan James. (2000). “Just Who Are You Calling Risk Averse?,” Journal of Risk and Uncertainty 20(2), 177–187
Kachelmeier, Steven J. and Mohamed Shehata. (1992). “Examining Risk Preferences Under High Monetary Incentives: Experimental Evidence from the People's Republic of China,” American Economic Review 82(5), 1120–1141
Karmarkar, Uday. (1978). “Subjectively Weighted Utility: A Descriptive Extension of the Expected Utility Model,” Organizational Behavior and Human Performance 21, 61–72.
Karmarkar, Uday. (1979). “Subjectively Weighted Utility and Allais Paradox,” Organizational Behavior and Human Performance 24, 67–72.
Lattimore, Pamela K, Joanna R. Baker and Ann D. Witte. (1992). “The Influence of Probability on Risky Choice,” Journal of Economic Behaviour and Organization 17, 377–400.
Lichtenstein, Sarah and Paul Slovic. (1971). “Reversals of Preferences Between Bids and Choices in Gambling Decisions,” Journal of Experimental Psychology 89, 46–55.
Loomes, Graham and Robert Sugden. (1995). “Incorporating a Stochastic Element into Decision Theories,” European Economic Review 39, 641–648.
Loomes, Graham and Robert Sugden. (1998). “Testing Different Stochastic Specifications of Risky Choice,” Economica 65, 581–598.
Loomes, Graham, Peter Moffat and Robert Sugden. (2002). “A Microeconometric Test of Alternative Stochastic Theories of Risk Choice,” Journal of Risk and Uncertainty 24, 103–130.
Luce, R. Duncan. (1959). Individual Choice Behavior. New York: John Wiley & Sons.
Luce, R. Duncan. (1991). “Rank and Sign Dependent Linear Utility Models for Binary Gambles,” Journal of Economic Theory 53, 75–100.
Luce, R. Duncan. (2000). Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches. Mahwah, NJ: Erlbaum.
Luce, R. Duncan (2001). “Reduction Invariance and Prelec's Weighting Functions,” Journal of Mathematical Psychology 45(1), 167–179
Luce, R. Duncan and Peter C. Fishburn. (1991). “Rank and Sign Dependent Linear Utility Models of Finite First-Order Gambles,” Journal of Risk and Uncertainty 4, 29–59.
Luce, R. Duncan and Peter C. Fishburn. (1995). “A Note on Deriving Rank-Dependent Utility Using Additive Joint Receipts,” Journal of Risk and Uncertainty 11, 5–16.
Luce, R. Duncan, Barbara, A. Mellers and Shi-jie, Chang. (1993). “Is Choice the Correct Primitive? On Using Certainty Equivalents and Reference Levels to Predict Choices Amoung Gambles,” Journal of Risk and Uncertainty 6, 115–143.
Mellers, Barbara A. et al. (1992). “Preferences, Prices, and Ratings in Risky Decision Making,” Journal of Experimental Psychology: Human Perception and Performance 18, 347–361.
Mosteller, Frederick and Philip Nogee. (1951). “An Experimental Measurement of Utility,” Journal of Political Economy 59, 371–404.
Myung, In Jae (2000). “Importance of Complexity in Model Selection.” Journal of Mathematical Psychology 44(1), 190–204
Myung, In Jae and Mark A. Pitt (1997). “Applying Occam's Razor in Modeling Cognition: A Bayesian Approach,” Psychonomic Bulletin and Review 4(1), 79–95
Myung, In Jae, Cheongtag Kim, and Mark A. Pitt (2000). “Towards an Explanation of the Power Law Artifact: Insights From Response Surface Analysis,” Memory and Cognition 28(5), 832–840
Prelec, Drazen. (1998). “The Probability Weighting Function,” Econometrica 66(3), 497–528
Quiggin, John (1982). “A Theory of Anticipated Utility.” Journal of Economic Behaviour and Organization 3, 323–343.
Rich, Elaine and Kevin Knight. (1991). Artificial Intelligence. New York, NY: McGraw-Hill.
Segal, Uzi. (1989). “Anticipated Utility: A Measure Representation Approach,” Annals of Operations Research 19, 359–373.
Slovic, Paul. (1972). “Psychological Study of Human Judgement: Implications for Investment Decision Making,” Journal of Finance 27, 779–799.
Smith, Vernon L. and James M. Walker. (1993). “Monetary Rewards and Decision Cost in Experimental Economics,” Economic Inquiry 31(2), 245–261
Sneddon, Robert and R. Duncan Luce. (2001). “Empirical Comparisons of Bilinear and Nonbilinear Utility Theories,” Organizational Behavior and Human Decision Processes 84(1), 71–94
Starmer, Chris. (2000). “Development in Non-Expected Utility Theory: The Hunt for a Descriptive Theory of Choice Under Risk,” Journal of Economic Literature 38, 332–382.
Starmer, Chris and Robert Sugden. (1989a). “Violations of the Independence Axiom in Common Ratio Problems: An Experimental Test,” Annals of Operations Research 19, 79–102.
Starmer, Chris and Robert Sugden. (1989b). “Probability and Juxtaposition Effects: An Experimental Investigation of the Common Ratio Effect,” Journal of Risk and Uncertainty 2, 159–178.
Stevens, S. Smitty. (1957). “On the Psychophysical Law,” Psychological Review 64, 153–181.
Stewart, Neil et al. (2002). “Prospect Relativity: How Choice Options Influence Decision Under Risk,” Journal of Experimental Psychology: General 132(1), 23–46
Tversky, Amos and Craig R. Fox (1995). “Weighing Risk and Uncertainty.” Psychological Review 102(2), 269–283
Tversky, Amos and Daniel Kahneman. (1992). “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Risk and Uncertainty 5, 297–323.
Von Neumann John and Oskar Morgenstern. (1944). Theory of Games and Economic Behavior. Princeton, NJ: Princeton University Press.
Wakker, Peter and Amos Tversky. (1993). “An Axiomatization of Cumulative Prospect Theory,” Journal of Risk and Uncertainty 7, 147–176.
Wakker, Peter, Ido Erev and Elke Weber. (1994). “Comonotonic Independence: The Critical Test Between Classical and Rank-Dependent Utility Theories,” Journal of Risk and Uncertainty 9, 195–230.
Weber, Elke U. and Britt Kirsner. (1997). “Reasons for Rank-Dependent Utility Evaluation,” Journal of Risk and Uncertainty 14, 41–61.
Wu, George and Richard Gonzalez. (1996). “Curvature of the Probability Weighting Function,” Management Science 42(12), 1676–1690
Yaari, Menahem E. (1987). “The Dual Theory of Choice Under Risk,” Econometrica 55(1), 95–115
Author information
Authors and Affiliations
Corresponding author
Additional information
JEL Classification C52 · D81
Rights and permissions
About this article
Cite this article
Stott, H.P. Cumulative prospect theory's functional menagerie. J Risk Uncertainty 32, 101–130 (2006). https://doi.org/10.1007/s11166-006-8289-6
Issue Date:
DOI: https://doi.org/10.1007/s11166-006-8289-6