IDEAS home Printed from https://ideas.repec.org/a/kap/jrisku/v32y2006i2p101-130.html
   My bibliography  Save this article

Cumulative prospect theory's functional menagerie

Author

Listed:
  • Henry Stott

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. Copyright Springer Science + Business Media, LLC 2006

Suggested Citation

  • Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
    • Handle: RePEc:kap:jrisku:v:32:y:2006:i:2:p:101-130
    DOI: 10.1007/s11166-006-8289-6
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11166-006-8289-6
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s11166-006-8289-6?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Loomes, Graham & Moffatt, Peter G & Sugden, Robert, 2002. "A Microeconometric Test of Alternative Stochastic Theories of Risky Choice," Journal of Risk and Uncertainty, Springer, vol. 24(2), pages 103-130, March.
    2. repec:bla:econom:v:65:y:1998:i:260:p:581-98 is not listed on IDEAS
    3. Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
    4. Camerer, Colin F & Hogarth, Robin M, 1999. "The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework," Journal of Risk and Uncertainty, Springer, vol. 19(1-3), pages 7-42, December.
    5. Luce, R Duncan & Mellers, Barbara A & Chang, Shi-jie, 1993. "Is Choice the Correct Primitive? On Using Certainty Equivalents and Reference Levels to Predict Choices among Gambles," Journal of Risk and Uncertainty, Springer, vol. 6(2), pages 115-143, April.
    6. 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.
    7. 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.
    8. David E. Bell & Peter C. Fishburn, 2001. "Strong One-Switch Utility," Management Science, INFORMS, vol. 47(4), pages 601-604, April.
    9. Birnbaum, Michael H. & Patton, Jamie N. & Lott, Melissa K., 1999. "Evidence against Rank-Dependent Utility Theories: Tests of Cumulative Independence, Interval Independence, Stochastic Dominance, and Transitivity, , , ," Organizational Behavior and Human Decision Processes, Elsevier, vol. 77(1), pages 44-83, January.
    10. Luce, R. Duncan, 1991. "Rank- and sign-dependent linear utility models for binary gambles," Journal of Economic Theory, Elsevier, vol. 53(1), pages 75-100, February.
    11. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    12. Harless, David W & Camerer, Colin F, 1994. "The Predictive Utility of Generalized Expected Utility Theories," Econometrica, Econometric Society, vol. 62(6), pages 1251-1289, November.
    13. John D. Hey, 2018. "Experimental investigations of errors in decision making under risk," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 17, pages 381-388, World Scientific Publishing Co. Pte. Ltd..
    14. Enrica Carbone & John D. Hey, 2018. "Discriminating between Preference Functionals: A Preliminary Monte Carlo Study," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 4, pages 99-118, World Scientific Publishing Co. Pte. Ltd..
    15. Gerard Debreu, 1957. "Stochastic Choice and Cardinal Utility," Cowles Foundation Discussion Papers 39, Cowles Foundation for Research in Economics, Yale University.
    16. 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.
    17. David E. Bell, 1995. "A Contextual Uncertainty Condition for Behavior Under Risk," Management Science, INFORMS, vol. 41(7), pages 1145-1150, July.
    18. Mohammed Abdellaoui & Frank Vossmann & Martin Weber, 2005. "Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty," Management Science, INFORMS, vol. 51(9), pages 1384-1399, September.
    19. Luce, R Duncan & Fishburn, Peter C, 1995. "A Note on Deriving Rank-Dependent Utility Using Additive Joint Receipts," Journal of Risk and Uncertainty, Springer, vol. 11(1), pages 5-16, July.
    20. Isaac, R Mark & James, Duncan, 2000. "Just Who Are You Calling Risk Averse?," Journal of Risk and Uncertainty, Springer, vol. 20(2), pages 177-187, March.
    21. Kachelmeier, Steven J & Shehata, Mohamed, 1992. "Examining Risk Preferences under High Monetary Incentives: Experimental Evidence from the People's Republic of China," American Economic Review, American Economic Association, vol. 82(5), pages 1120-1141, December.
    22. Serge Blondel, 2002. "Testing Theories of Choice Under Risk: Estimation of Individual Functionals," Journal of Risk and Uncertainty, Springer, vol. 24(3), pages 251-265, May.
    23. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
    24. Wakker, Peter & Erev, Ido & Weber, Elke U, 1994. "Comonotonic Independence: The Critical Test between Classical and Rank-Dependent Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 9(3), pages 195-230, December.
    25. Weber, Elke U & Kirsner, Britt, 1997. "Reasons for Rank-Dependent Utility Evaluation," Journal of Risk and Uncertainty, Springer, vol. 14(1), pages 41-61, January.
    26. Birnbaum, Michael H. & Chavez, Alfredo, 1997. "Tests of Theories of Decision Making: Violations of Branch Independence and Distribution Independence," Organizational Behavior and Human Decision Processes, Elsevier, vol. 71(2), pages 161-194, August.
    27. Smith, Vernon L & Walker, James M, 1993. "Monetary Rewards and Decision Cost in Experimental Economics," Economic Inquiry, Western Economic Association International, vol. 31(2), pages 245-261, April.
    28. Enrica Carbone & John D. Hey, 2018. "Which Error Story is Best?," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 16, pages 365-380, World Scientific Publishing Co. Pte. Ltd..
    29. John D. Hey & Chris Orme, 2018. "Investigating Generalizations Of Expected Utility Theory Using Experimental Data," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 3, pages 63-98, World Scientific Publishing Co. Pte. Ltd..
    30. Starmer, Chris & Sugden, Robert, 1989. "Probability and Juxtaposition Effects: An Experimental Investigation of the Common Ratio Effect," Journal of Risk and Uncertainty, Springer, vol. 2(2), pages 159-178, June.
    31. Slovic, Paul, 1972. "Psychological Study of Human Judgment: Implications for Investment Decision-Making," Journal of Finance, American Finance Association, vol. 27(4), pages 779-799, September.
    32. Blondel, Serge, 2002. "Testing Theories of Choice under Risk: Estimation of Individual Functionals," Journal of Risk and Uncertainty, Springer, vol. 24(3), pages 251-265, May.
    33. Carbone, Enrica, 1997. "Investigation of stochastic preference theory using experimental data," Economics Letters, Elsevier, vol. 57(3), pages 305-311, December.
    34. Sneddon, Robert & Luce, R. Duncan, 2001. "Empirical Comparisons of Bilinear and Nonbilinear Utility Theories," Organizational Behavior and Human Decision Processes, Elsevier, vol. 84(1), pages 71-94, January.
    35. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    36. Frederick Mosteller & Philip Nogee, 1951. "An Experimental Measurement of Utility," Journal of Political Economy, University of Chicago Press, vol. 59(5), pages 371-371.
    37. Graham Loomes & Robert Sugden, 1998. "Testing Different Stochastic Specificationsof Risky Choice," Economica, London School of Economics and Political Science, vol. 65(260), pages 581-598, November.
    38. Chechile, Richard A & Cooke, Alan D J, 1997. "An Experimental Test of a General Class of Utility Models: Evidence for Context Dependency," Journal of Risk and Uncertainty, Springer, vol. 14(1), pages 75-93, January.
    39. Doctor, Jason N. & Bleichrodt, Han & Miyamoto, John & Temkin, Nancy R. & Dikmen, Sureyya, 2004. "A new and more robust test of QALYs," Journal of Health Economics, Elsevier, vol. 23(2), pages 353-367, March.
    40. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    41. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    42. Bell, David E & Fishburn, Peter C, 2000. "Utility Functions for Wealth," Journal of Risk and Uncertainty, Springer, vol. 20(1), pages 5-44, January.
    43. Camerer, Colin F, 1989. "An Experimental Test of Several Generalized Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 2(1), pages 61-104, April.
    44. Luce, R Duncan & Fishburn, Peter C, 1991. "Rank- and Sign-Dependent Linear Utility Models for Finite First-Order Gambles," Journal of Risk and Uncertainty, Springer, vol. 4(1), pages 29-59, January.
    45. Ballinger, T Parker & Wilcox, Nathaniel T, 1997. "Decisions, Error and Heterogeneity," Economic Journal, Royal Economic Society, vol. 107(443), pages 1090-1105, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Jakusch, Sven Thorsten & Meyer, Steffen & Hackethal, Andreas, 2019. "Taming models of prospect theory in the wild? Estimation of Vlcek and Hens (2011)," SAFE Working Paper Series 146, Leibniz Institute for Financial Research SAFE, revised 2019.
    2. Michael H. Birnbaum & Ulrich Schmidt & Miriam D. Schneider, 2017. "Testing independence conditions in the presence of errors and splitting effects," Journal of Risk and Uncertainty, Springer, vol. 54(1), pages 61-85, February.
    3. Peter Brooks & Horst Zank, 2005. "Loss Averse Behavior," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 301-325, December.
    4. Jakusch, Sven Thorsten, 2017. "On the applicability of maximum likelihood methods: From experimental to financial data," SAFE Working Paper Series 148, Leibniz Institute for Financial Research SAFE, revised 2017.
    5. Andersen, Steffen & Harrison, Glenn W. & Lau, Morten Igel & Rutström, Elisabet E., 2010. "Behavioral econometrics for psychologists," Journal of Economic Psychology, Elsevier, vol. 31(4), pages 553-576, August.
    6. Pavlo Blavatskyy, 2007. "Stochastic expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 34(3), pages 259-286, June.
    7. Peter Brooks & Simon Peters & Horst Zank, 2014. "Risk behavior for gain, loss, and mixed prospects," Theory and Decision, Springer, vol. 77(2), pages 153-182, August.
    8. Ulrich Schmidt & Chris Starmer & Robert Sugden, 2008. "Third-generation prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 203-223, June.
    9. Diecidue, Enrico & Schmidt, Ulrich & Zank, Horst, 2009. "Parametric weighting functions," Journal of Economic Theory, Elsevier, vol. 144(3), pages 1102-1118, May.
    10. George Wu & Alex B. Markle, 2008. "An Empirical Test of Gain-Loss Separability in Prospect Theory," Management Science, INFORMS, vol. 54(7), pages 1322-1335, July.
    11. David Bruner, 2009. "Changing the probability versus changing the reward," Experimental Economics, Springer;Economic Science Association, vol. 12(4), pages 367-385, December.
    12. John Hey & Andrea Morone & Ulrich Schmidt, 2009. "Noise and bias in eliciting preferences," Journal of Risk and Uncertainty, Springer, vol. 39(3), pages 213-235, December.
    13. Wilcox, Nathaniel T., 2011. "'Stochastically more risk averse:' A contextual theory of stochastic discrete choice under risk," Journal of Econometrics, Elsevier, vol. 162(1), pages 89-104, May.
    14. Horst Zank, 2010. "On probabilities and loss aversion," Theory and Decision, Springer, vol. 68(3), pages 243-261, March.
    15. Liang Zou, 2006. "An Alternative to Prospect Theory," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 1-28, May.
    16. John D. Hey, 2018. "Why We Should Not Be Silent About Noise," World Scientific Book Chapters, in: Experiments in Economics Decision Making and Markets, chapter 13, pages 309-329, World Scientific Publishing Co. Pte. Ltd..
    17. Birnbaum, Michael H., 2004. "Tests of rank-dependent utility and cumulative prospect theory in gambles represented by natural frequencies: Effects of format, event framing, and branch splitting," Organizational Behavior and Human Decision Processes, Elsevier, vol. 95(1), pages 40-65, September.
    18. Adam Booij & Bernard Praag & Gijs Kuilen, 2010. "A parametric analysis of prospect theory’s functionals for the general population," Theory and Decision, Springer, vol. 68(1), pages 115-148, February.
    19. Pavlo R. Blavatskyy & Ganna Pogrebna, 2010. "Models of stochastic choice and decision theories: why both are important for analyzing decisions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(6), pages 963-986.
    20. Schmidt, Ulrich & Birnbaum, Michael, 2014. "The Impact of Experience on Violations of Independence and Coalescing," VfS Annual Conference 2014 (Hamburg): Evidence-based Economic Policy 100463, Verein für Socialpolitik / German Economic Association.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:kap:jrisku:v:32:y:2006:i:2:p:101-130. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.