Experimental Economics

, 12:133 | Cite as

Expected utility theory and prospect theory: one wedding and a decent funeral

  • Glenn W. HarrisonEmail author
  • E. Elisabet Rutström


Choice behavior is typically evaluated by assuming that the data is generated by one latent decision-making process or another. What if there are two (or more) latent decision-making processes generating the observed choices? Some choices might then be better characterized as being generated by one process, and other choices by the other process. A finite mixture model can be used to estimate the parameters of each decision process while simultaneously estimating the probability that each process applies to the sample. We consider the canonical case of lottery choices in a laboratory experiment and assume that the data is generated by expected utility theory and prospect theory decision rules. We jointly estimate the parameters of each theory as well as the fraction of choices characterized by each. The methodology provides the wedding invitation, and the data consummates the ceremony followed by a decent funeral for the representative agent model that assumes only one type of decision process. The evidence suggests support for each theory, and goes further to identify under what demographic domains one can expect to see one theory perform better than the other. We therefore propose a reconciliation of the debate over two of the dominant theories of choice under risk, at least for the tasks and samples we consider. The methodology is broadly applicable to a range of debates over competing theories generated by experimental and non-experimental data.


Expected utility theory Prospect theory Mixture models 

JEL Classification

D81 C91 C51 C12 


  1. Andersen, S., Harrison, G. W., & Rutström, E. E. (2006a). Choice behavior, asset integration, and natural reference points (Working Paper 06-07). Department of Economics, College of Business Administration, University of Central Florida. Google Scholar
  2. Andersen, S., Harrison, G. W., Lau, M. I., & Rutström, E. E. (2006b). Dual criteria decisions (Working Paper 06-11). Department of Economics, College of Business Administration, University of Central Florida. Google Scholar
  3. Andersen, S., Harrison, G. W., Lau, M. I., & Rutström, E. E. (2008). Eliciting risk and time preferences. Econometrica, 76(3), 583–618. CrossRefGoogle Scholar
  4. Araña, J. E., & León, C. J. (2005). Flexible mixture distribution modeling of dichotomous choice contingent valuation with heterogeneity. Journal of Environmental Economics & Management, 50(1), 170–188. CrossRefGoogle Scholar
  5. Atkinson, A. C. (1970). A method for discriminating between models. Journal of the Royal Statistical Society, Series B, 32, 323–344. Google Scholar
  6. Bardsley, N., & Moffatt, P. G. (2007). The experimetrics of public goods: inferring motivations from contributions. Theory and Decision, 62(2), 161–193. CrossRefGoogle Scholar
  7. Benartzi, S., & Thaler, R. H. (1995). Myopic loss aversion and the equity premium puzzle. Quarterly Journal of Economics, 111(1), 75–92. Google Scholar
  8. Benhabib, J., & Bisin, A. (2005). Modeling internal commitment mechanisms and self-control: a neuroeconomics approach to consumption-saving decisions. Games and Economic Behavior, 52, 460–492. CrossRefGoogle Scholar
  9. Brandstätter, E., Gigerenzer, G., & Hertwig, R. (2006). The priority heuristic: making choices without trade-offs. Psychological Review, 113(2), 409–432. CrossRefGoogle Scholar
  10. Bruhin, A., Fehr-Duda, H., & Epper, T. F. (2007). Risk and rationality: uncovering heterogeneity in probability distortion (Working Paper 0705). Socioeconomic Institute, University of Zurich. Google Scholar
  11. Camerer, C. F. (1995). Individual decision making. In J. H. Kagel & A. E. Roth (Eds.), The handbook of experimental economics. Princeton: Princeton University Press. Google Scholar
  12. Camerer, C. F., & Ho, T.-H. (1994). Violations of the betweeness axiom and nonlinearity in probability. Journal of Risk and Uncertainty, 8, 167–196. CrossRefGoogle Scholar
  13. Cherry, T. L., Frykblom, P., & Shogren, J. F. (2002). Hardnose the dictator. American Economic Review, 92(4), 1218–1221. CrossRefGoogle Scholar
  14. Clarke, K. A. (2003). Nonparametric model discrimination in international relations. Journal of Conflict Resolution, 47(1), 72–93. CrossRefGoogle Scholar
  15. Clarke, K. A. (2007). A simple distribution-free test for non-nested model selection. Political Analysis, 15(3), 347–363. CrossRefGoogle Scholar
  16. Cohen, J. D. (2005). The vulcanization of the human brain: a neural perspective on interactions between cognition and emotion. Journal of Economic Perspectives, 19(4), 3–24. CrossRefGoogle Scholar
  17. Conte, A., Hey, J. D., & Moffatt, P. G. (2007). Mixture models of choice under risk (Discussion Paper No. 2007/06). Department of Economics and Related Studies, University of York. Google Scholar
  18. Cox, D. R. (1961). Tests of separate families of hypotheses. In E. G. Charatsis (Ed.), Proceedings of the fourth Berkeley symposium on mathematical statistics and probability (Vol. 1, pp. 105–123). Berkeley: University of California Press. Google Scholar
  19. Cox, D. R. (1962). Further results on tests of separate families of hypotheses. Journal of the Royal Statistical Society, Series B, 24, 406–424. Google Scholar
  20. Cox, J. C., & Sadiraj, V. (2006). Small- and large-stakes risk aversion: implications of concavity calibration for decision theory. Games & Economic Behavior, 56(1), 45–60. CrossRefGoogle Scholar
  21. Davidson, R., & MacKinnon, J. G. (1993). Estimation and inference in econometrics. New York: Oxford University Press. Google Scholar
  22. El-Gamal, M. A., & Grether, D. M. (1995). Are people Bayesian? Uncovering behavioral strategies. Journal of the American Statistical Association, 90(432), 1137–1145. CrossRefGoogle Scholar
  23. Everitt, B. S. (1996). An introduction to finite mixture distributions. Statistical Methods in Medical Research, 5, 107–127. CrossRefGoogle Scholar
  24. Fudenberg, D., & Levine, D. K. (2006). A dual-self model of impulse control. American Economic Review, 96(5), 1449–1476. CrossRefGoogle Scholar
  25. George, J. G., Johnson, L. T., & Rutström, E. E. (2007). Social preferences in the face of regulatory change. In T. Cherry, S. Kroll, & J. F. Shogren (Eds.), Experimental methods, environmental economics. Oxford: Routledge. Google Scholar
  26. Geweke, J., & Keane, M. (1999). Mixture of normals probit models. In C. Hsio, K. Lahiri, L.-F. Lee, & M. H. Pesaran (Eds.), Analysis of panel and limited dependent variables: a volume in honor of G.S. Maddala. New York: Cambridge University Press. Google Scholar
  27. Goodman, L. A. (1974a). The analysis of systems of qualitative variables when some of the variables are unobservable: Part I. A modified latent structure approach. American Journal of Sociology, 79, 1179–1259. CrossRefGoogle Scholar
  28. Goodman, L. A. (1974b). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231. CrossRefGoogle Scholar
  29. Grether, D. M., & Plott, C. R. (1979). Economic theory of choice and the preference reversal phenomenon. American Economic Review, 69(4), 623–648. Google Scholar
  30. Haigh, M., & List, J. A. (2005). Do professional traders exhibit myopic loss aversion? An experimental analysis. Journal of Finance, 60(1), 523–534. CrossRefGoogle Scholar
  31. Harless, D. W., & Camerer, C. F. (1994). The predictive utility of generalized expected utility theories. Econometrica, 62, 1251–1289. CrossRefGoogle Scholar
  32. Harrison, G. W., & List, J. A. (2004). Field experiments. Journal of Economic Literature, 42(4), 1013–1059. CrossRefGoogle Scholar
  33. Harrison, G. W., & Rutström, E. E. (2008). Risk aversion in the laboratory. In J. C. Cox & G. W. Harrison (Eds.), Research in experimental economics : Vol. 12. Risk aversion in experiments. Bingley: Emerald. Google Scholar
  34. Harrison, G. W., Humphrey, S. J., & Verschoor, A. (2005). Choice under uncertainty: evidence from Ethiopia, India and Uganda (Working Paper 05-29). Department of Economics, College of Business Administration, University of Central Florida. Google Scholar
  35. Haruvy, E., Stahl, D. O., & Wilson, P. W. (2001). Modeling and testing for heterogeneity in observed strategic behavior. Review of Economics and Statistics, 83(1), 146–157. CrossRefGoogle Scholar
  36. Heckman, J., & Singer, B. (1984). A method for minimizing the impact of distributional assumptions in econometric models for duration data. Econometrica, 52(2), 271–320. CrossRefGoogle Scholar
  37. Hey, J. D., & Orme, C. (1994). Investigating generalizations of expected utility theory using experimental data. Econometrica, 62(6), 1291–1326. CrossRefGoogle Scholar
  38. Holt, C. A., & Laury, S. K. (2002). Risk aversion and incentive effects. American Economic Review, 92(5), 1644–1655. CrossRefGoogle Scholar
  39. Hosmer, D. W., & Lemeshow, S. (2000). Applied logistic regression (2nd edn.). New York: Wiley. Google Scholar
  40. Hurley, T. M., & Shogren, J. F. (2005). An experimental comparison of induced and elicited beliefs. Journal of Risk & Uncertainty, 30(2), 169–188. CrossRefGoogle Scholar
  41. Johnson, L. T., Rutström, E. E., & George, J. G. (2006). Income distribution preferences and regulatory change in social dilemmas. Journal of Economic Behavior & Organization, 61(2), 181–198. CrossRefGoogle Scholar
  42. Kahneman, D., & Tversky, A. (1979). Prospect theory: an analysis of decision under risk. Econometrica, 47(2), 263–291. CrossRefGoogle Scholar
  43. Kirman, A. P. (1992). Whom or what does the representative individual represent? Journal of Economic Perspectives, 6(2), 117–136. Google Scholar
  44. Köbberling, V., & Wakker, P. P. (2005). An index of loss aversion. Journal of Economic Theory, 122, 119–131. CrossRefGoogle Scholar
  45. Kumbhakar, S. C., & Lovell, C. A. K. (2000). Stochastic frontier analysis. New York: Cambridge University Press. Google Scholar
  46. Liang, K.-Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22. CrossRefGoogle Scholar
  47. List, J. A. (2002). Preference reversals of a different kind: the more is less phenomenon. American Economic Review, 92, 1636–1643. CrossRefGoogle Scholar
  48. List, J. A. (2003). Does market experience eliminate market anomalies. Quarterly Journal of Economics, 118, 41–71. CrossRefGoogle Scholar
  49. List, J. A. (2004). Neoclassical theory versus prospect theory: evidence from the marketplace. Econometrica, 72(2), 615–625. CrossRefGoogle Scholar
  50. Loomes, G., & Sugden, R. (1998). Testing different stochastic specifications of risky choice. Economica, 65, 581–598. CrossRefGoogle Scholar
  51. Lopes, L. L. (1995). Algebra and process in the modeling of risky choice. In J. R. Busemeyer, R. Hastie, & D. L. Medin (Eds.), Decision making from a cognitive perspective. San Diego: Academic Press. Google Scholar
  52. Lopes, L. L., & Oden, G. C. (1999). The role of aspiration level in risky choice: a comparison of cumulative prospect theory and SP/A theory. Journal of Mathematical Psychology, 43, 286–313. CrossRefGoogle Scholar
  53. Luce, R. D., & Suppes, P. (1965). Preference, utility, and subjective probability. In R. D. Luce, R. R. Bush, & E. Galanter (Eds.), Handbook of mathematical psychology (Vol. 3, pp. 249–410). New York: Wiley. Google Scholar
  54. Marschak, J. (1960). Binary choice constraints on random utility indications. In K. Arow (Ed.), Stanford symposium on mathematical models in the social sciences. Stanford: Stanford University Press. Google Scholar
  55. McLachlan, G., & Peel, D. (2000). Finite mixture models. New York: Wiley. CrossRefGoogle Scholar
  56. Oehlert, G. W. (1992). A note on the delta method. The American Statistician, 46(1), 27–29. CrossRefGoogle Scholar
  57. Papke, L. E., & Wooldridge, J. M. (1996). Econometric methods for fractional response variables with an application to 401(K) plan participation rates. Journal of Applied Econometrics, 11, 619–632. CrossRefGoogle Scholar
  58. Pearson, K. (1894). Contribution to the mathematical theory of evolution. Philosophical Transactions A, 185, 71–110. CrossRefGoogle Scholar
  59. Pesaran, M. H. (1981). Pitfalls of testing non-nested hypotheses by the Lagrange multiplier method. Journal of Econometrics, 17, 323–331. CrossRefGoogle Scholar
  60. Pollak, R. A., & Wales, T. J. (1991). The likelihood dominance criterion: a new approach to model selection. Journal of Econometrics, 47, 227–242. CrossRefGoogle Scholar
  61. Prelec, D. (1998). The probability weighting function. Econometrica, 66(3), 497–527. CrossRefGoogle Scholar
  62. Quandt, R. E. (1974). A comparison of methods for testing nonnested hypotheses. Review of Economics and Statistics, 56, 92–99. CrossRefGoogle Scholar
  63. Rogers, W. H. (1993). Regression standard errors in clustered samples. Stata Technical Bulletin, 13, 19–23. Google Scholar
  64. Schoemaker, P. (1982). The expected utility model: its variants, purposes, evidence and limitations. Journal of Economic Literature, 20(2), 529–563. Google Scholar
  65. Stahl, D. O. (1996). Boundedly rational rule learning in a guessing game. Games and Economic Behavior, 16, 303–330. CrossRefGoogle Scholar
  66. Stahl, D. O. (1998). Is step-j thinking an arbitrary modelling restriction or a fact of human nature? Journal of Economic Behavior & Organization, 37, 33–51. CrossRefGoogle Scholar
  67. Stahl, D. O., & Wilson, P. W. (1995). On players’ models of other players: theory and experimental evidence. Games and Economic Behavior, 10, 218–254. CrossRefGoogle Scholar
  68. Starmer, C. (2000). Developments in non-expected utility theory: the hunt for a descriptive theory of choice under risk. Journal of Economic Literature, 38, 332–382. Google Scholar
  69. Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1985). Statistical analysis of finite mixture distributions. New York: Wiley. Google Scholar
  70. Train, K. E. (2003). Discrete choice methods with simulation. New York: Cambridge University Press. Google Scholar
  71. Tversky, A., & Kahneman, D. (1992). Advances in prospect theory: cumulative representations of uncertainty. Journal of Risk & Uncertainty, 5, 297–323. CrossRefGoogle Scholar
  72. Vermunt, J. K., & Magidson, J. (2003). Latent class models for classification. Computational Statistics & Data Analysis, 41, 531–537. CrossRefGoogle Scholar
  73. Vuong, Q. H. (1989). Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica, 57(2), 307–333. CrossRefGoogle Scholar
  74. Wang, M., & Fischbeck, P. S. (2004). Incorporating framing into prospect theory modeling: a mixture-model approach. Journal of Risk & Uncertainty, 29(2), 181–197. CrossRefGoogle Scholar
  75. Werner, M. (1999). Allowing for zeros in dichotomous choice contingent valuation models. Journal of Business and Economic Statistics, 17, 479–486. CrossRefGoogle Scholar
  76. Williams, R. L. (2000). A note on robust variance estimation for cluster-correlated data. Biometrics, 56, 645–646. CrossRefGoogle Scholar
  77. Wooldridge, J. (2003). Cluster-sample methods in applied econometrics. American Economic Review (Papers & Proceedings), 93, 133–138. CrossRefGoogle Scholar
  78. Wu, G., & Gonzalez, R. (1996). Curvature of the probability weighting function. Management Science, 42, 1676–1690. CrossRefGoogle Scholar

Copyright information

© Economic Science Association 2008

Authors and Affiliations

  1. 1.Department of Economics, College of Business AdministrationUniversity of Central FloridaOrlandoUSA

Personalised recommendations