IDEAS home Printed from https://ideas.repec.org/p/zur/iewwpx/231.html
   My bibliography  Save this paper

A Stochastic Expected Utility Theory

Author

Listed:
  • Pavlo R. Blavatskyy

Abstract

This paper proposes a new model that explains the violations of expected utility theory through the role of random errors. The paper analyzes decision making under risk when individuals make random errors when they compute expected utilities. Errors are drawn from the normal distribution, which is truncated so that the stochastic utility of a lottery cannot be greater (lower) than the utility of the highest (lowest) possible outcome. The standard deviation of random errors is higher for lotteries with a wider range of possible outcomes. It converges to zero for lotteries converging to a degenerate lottery. The model explains all major stylized empirical facts such as the Allais paradox and the fourfold pattern of risk attitudes. The model fits the data from ten well-known experimental studies at least as good as cumulative prospect theory.

Suggested Citation

  • Pavlo R. Blavatskyy, "undated". "A Stochastic Expected Utility Theory," IEW - Working Papers 231, Institute for Empirical Research in Economics - University of Zurich.
    • Handle: RePEc:zur:iewwpx:231
    as

    Download full text from publisher

    File URL: https://www.econ.uzh.ch/apps/workingpapers/wp/iewwp231.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Loomes, Graham & Sugden, Robert, 1998. "Testing Different Stochastic Specifications of Risky Choice," Economica, London School of Economics and Political Science, vol. 65(260), pages 581-598, November.
    2. 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.
    3. Shlomo Benartzi & Richard H. Thaler, 1995. "Myopic Loss Aversion and the Equity Premium Puzzle," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 73-92.
    4. Chew, Soo Hong, 1983. "A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox," Econometrica, Econometric Society, vol. 51(4), pages 1065-1092, July.
    5. Uri Gneezy & John A. List & George Wu, 2006. "The Uncertainty Effect: When a Risky Prospect is Valued Less than its Worst Possible Outcome," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(4), pages 1283-1309.
    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. 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..
    8. Wu, George, 1994. "An Empirical Test of Ordinal Independence," Journal of Risk and Uncertainty, Springer, vol. 9(1), pages 39-60, July.
    9. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60(2), pages 151-151.
    10. Bernasconi, Michele, 1994. "Nonlinear Preferences and Two-Stage Lotteries: Theories and Evidence," Economic Journal, Royal Economic Society, vol. 104(422), pages 54-70, January.
    11. 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.
    12. Conlisk, John, 1989. "Three Variants on the Allais Example," American Economic Review, American Economic Association, vol. 79(3), pages 392-407, June.
    13. 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.
    14. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    15. 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.
    16. Chris Starmer, 1992. "Testing New Theories of Choice under Uncertainty using the Common Consequence Effect," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 813-830.
    17. 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.
    18. Machina, Mark J, 1982. ""Expected Utility" Analysis without the Independence Axiom," Econometrica, Econometric Society, vol. 50(2), pages 277-323, March.
    19. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    20. Neilson, William S & Stowe, Jill, 2002. "A Further Examination of Cumulative Prospect Theory Parameterizations," Journal of Risk and Uncertainty, Springer, vol. 24(1), pages 31-46, January.
    21. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    22. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    23. 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.
    24. Prelec, Drazen, 1990. "A "Pseudo-Endowment" Effect, and Its Implications for Some Recent Nonexpected Utility Models," Journal of Risk and Uncertainty, Springer, vol. 3(3), pages 247-259, September.
    25. Battalio, Raymond C & Kagel, John H & Jiranyakul, Komain, 1990. "Testing between Alternative Models of Choice under Uncertainty: Some Initial Results," Journal of Risk and Uncertainty, Springer, vol. 3(1), pages 25-50, March.
    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. Pavlo Blavatskyy, 2007. "Stochastic expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 34(3), pages 259-286, June.
    2. Bruno S. Frey, "undated". "Knight Fever towards an Economics of Awards," IEW - Working Papers 239, Institute for Empirical Research in Economics - University of Zurich.
    3. Pavlo Blavatskyy, 2018. "A second-generation disappointment aversion theory of decision making under risk," Theory and Decision, Springer, vol. 84(1), pages 29-60, January.
    4. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    5. Pavlo R. Blavatskyy, "undated". "Axiomatization of a Preference for Most Probable Winner," IEW - Working Papers 230, Institute for Empirical Research in Economics - University of Zurich.
    6. Blavatskyy, Pavlo R., 2006. "Violations of betweenness or random errors?," Economics Letters, Elsevier, vol. 91(1), pages 34-38, April.
    7. Peter Brooks & Horst Zank, 2005. "Loss Averse Behavior," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 301-325, December.
    8. Pavlo Blavatskyy, 2004. "Axiomatization of a Preference for Most Probably Winner," CERGE-EI Working Papers wp226, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    9. Pavlo R. Blavatskyy & Francesco Feri, 2018. "Violations of betweenness and choice shifts in groups," Theory and Decision, Springer, vol. 85(3), pages 321-331, October.
    10. D. A. Peel & Jie Zhang & D. Law, 2008. "The Markowitz model of utility supplemented with a small degree of probability distortion as an explanation of outcomes of Allais experiments over large and small payoffs and gambling on unlikely outc," Applied Economics, Taylor & Francis Journals, vol. 40(1), pages 17-26.
    11. 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.
    12. Henry Stott, 2006. "Cumulative prospect theory's functional menagerie," Journal of Risk and Uncertainty, Springer, vol. 32(2), pages 101-130, March.
    13. 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.
    14. 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.
    15. Simone Ferrari-Toniolo & Leo Chi U. Seak & Wolfram Schultz, 2022. "Risky choice: Probability weighting explains independence axiom violations in monkeys," Journal of Risk and Uncertainty, Springer, vol. 65(3), pages 319-351, December.
    16. Helga Fehr-Duda & Thomas Epper, 2012. "Probability and Risk: Foundations and Economic Implications of Probability-Dependent Risk Preferences," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 567-593, July.
    17. Pavlo Blavatskyy & Valentyn Panchenko & Andreas Ortmann, 2023. "How common is the common-ratio effect?," Experimental Economics, Springer;Economic Science Association, vol. 26(2), pages 253-272, April.
    18. Liang Zou, 2006. "An Alternative to Prospect Theory," Annals of Economics and Finance, Society for AEF, vol. 7(1), pages 1-28, May.
    19. 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.
    20. 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..

    More about this item

    Keywords

    decision theory; stochastic utility; expected utility theory; cumulative prospect theory;
    All these keywords.

    JEL classification:

    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:zur:iewwpx:231. 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: Severin Oswald (email available below). General contact details of provider: .

    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.