Journal of Risk and Uncertainty

, Volume 2, Issue 1, pp 61–104 | Cite as

An experimental test of several generalized utility theories

  • Colin F. Camerer


There is much evidence that people willingly violate expected utility theory when making choices. Several axiomatic theories have been proposed to explain some of this evidence, but there are few data that discriminate between the theories. To gather such data, an experiment was conducted using pairs of gambles with three levels of outcomes and many combinations of probabilities. Most typical findings were replicated, including the common consequence effect and different risk attitudes for gains and losses. There is evidence of both fanning out and fanning in of indifference curves, and both quasiconcavity and quasiconvexity of preferences. No theory can explain all the data, but prospect theory and the hypothesis that indifference curves fan out can explain most of them.

Key words

expected utility generalized utility nonexpected utility risky choice Allais paradox 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. AllaisMaurice. (1953). “Le Comportement de L'homme Rationel Devant le Risque, Critique des Postulates et Axiomes de L'ecole Americaine.” Econometrica 21, 503–546.Google Scholar
  2. AllaisMaurice. (1979). “The So-called Allais Paradox and Rational Decisions Under Uncertainty.” In MauriceAllais and O.Hagen (eds.), The Expected Utility Hypothesis and the Allais Paradox, Dordrecht: D. Reidel Publishing Company.Google Scholar
  3. BattalioRay C., John H.Kagel, and Don N.MacDonald. (1988). “Animals' Choices Over Uncertain Outcomes: Some Initial Experimental Evidence,” American Economic Review 75, 597–613.Google Scholar
  4. Battalio, Ray C., John H. Kagel, and Jiranyakul Komain. (1988). “Testing Between Alternative Models of Choice Under Uncertainty: Some Initial Results.” Texas A&M Department of Economics working paper.Google Scholar
  5. BeckerJoao L., and RakeshSarin. (1987). “Lottery Dependent Utility,” Management Science 33, 1367–1382.Google Scholar
  6. BellDavid. (1982). “Regret in Decision Making under Uncertainty,” Operations Research 30, 961–981.Google Scholar
  7. BellDavid. (1985). “Disappointment in Decision Making Under Uncertainty,” Operations Research 33, 1–27.Google Scholar
  8. ChewSoo Hong. (1983). “A Generalization of the Quasilinear Mean with Applications to the Measurement of Income Inequality and Decision Theory Resolving the Allais Paradox, Econometrica 51, 1065–1092.Google Scholar
  9. Chew, Soo Hong. (1984). “An Axiomatization of the Rank Dependent Quasilinear Mean Generalizing the Gini Mean and the Quasilinear Mean,” John Hopkins University Department of Political Economy working paper.Google Scholar
  10. Chew, Soo Hong. (1985). “Implicit-weighted and Semi-weighted Utility Theories, M-estimators, and Non-demand Revelation of Second-price Auctions for an Uncertain Auctioned Object,” Johns Hopkins University Department of Political Economy working paper #155.Google Scholar
  11. Chew, Soo Hong, and Kenneth R. MacCrimmon. (1979). “Alpha-nu Choice Theory: An Axiomatization of Expected Utility,” University of British Columbia Faculty of Commerce working paper #669.Google Scholar
  12. Chew, Soo Hong, and Larry G. Epstein. (1987a). “A Unifying Approach to Axiomatic Non-Expected Utility Theories,” John Hopkins University Department of Political Economy working paper.Google Scholar
  13. Chew, Soo Hong, and Larry G. Epstein. (1987b). “Non-Expected Utility Preferences in a Temporal Framework with an Application to Consumption-Savings Behavior,” John Hopkins University Department of Political Economy working paper.Google Scholar
  14. ChewSoo Hong, and William S.Waller. (1986). “Empirical Tests of Weighted Utility Theory,” Journal of Mathematical Psychology 30, 55–72.Google Scholar
  15. CoombsClyde, and LilyHuang. (1976). “Tests of the Betweenness Property of Expected Utility,” Journal of Mathematical Psychology 13, 323–337.Google Scholar
  16. Crawford, Vincent P. (forthcoming). “Equilibrium without Independence,” Journal of Economic Theory.Google Scholar
  17. DekelEddie. (1986). “An Axiomatic Characterization of Preferences under Uncertainty: Weakening the Independence Axiom,” Journal of Economic Theory 40, 304–318.Google Scholar
  18. EdwardsWard. (1954a). “The Theory of Decision Making,” Psychological Bulletin 51, 380–417.Google Scholar
  19. EdwardsWard. (1954b). “The Reliability of Probability Preferences,” American Journal of Psychology 67, 68–95.Google Scholar
  20. EdwardsWard. (1955). “The Prediction of Decisions Among Bets,” Journal of Experimental Psychology 51, 201–214.Google Scholar
  21. EinhornHillel J., and Robin M.Hogarth. (1985). “Ambiguity and Uncertainty in Probabilistic Inference,” Psychological Review 92, 433–461.Google Scholar
  22. EllsbergDaniel. (1961). “Risk, Ambiguity, and the Savage Axioms,” Quarterly Journal of Economics 75, 643–669.Google Scholar
  23. EncarnacionJ. (1987). “Preference Paradoxes and Lexicographic Choice,” Journal of Economic Behavior and Organization 8, 231–248.Google Scholar
  24. FishburnPeter. (1982). “Nontransitive Measurable Utility,” Journal of Mathematical Psychology 26, 31–67.Google Scholar
  25. FishburnPeter. (1983). “Transitive Measurable Utility,” Journal of Economic Theory 31, 293–317.Google Scholar
  26. FishburnPeter. (1984). “SSB Utility Theory: An Economic Perspective,” Mathematical Social Science 8, 63–94.Google Scholar
  27. Grether, David. (1981). “Financial Incentive Effects and Individual Decision Making”, California Institute of Technology working paper 401.Google Scholar
  28. GretherDavid, and Charles R.Plott. (1979). “Economic Theory of Choice and the Preference Reversal Phenomenon,” American Economic Review 69, 623–638.Google Scholar
  29. HandaJagdish. (1977). “Risk, Probabilities, and a New Theory of Cardinal Utility,” Journal of Political Economy 85, 97–122.Google Scholar
  30. Harless, David W. (1988). “Predictions about Indifference Curves in the Unit Triangle: A Test of Competing Decision Theories”, Grinnell College working paper.Google Scholar
  31. HersheyJohn, HowardKunreuther, and PaulSchoemaker. (1982). “Sources of Bias in Assessment Procedures for Utility Function,” Management Science 28, 936–954.Google Scholar
  32. HeyJohn D. (1984). “The Economics of Optimism and Pessimism: A Definition and Some Applications,” Kyklos 37, 181–205.Google Scholar
  33. Hey, John D. and Elisabetta Strazzera. (1988). “Estimation of Indifference Curves in the Marschak-Machina Triangle,” University of York Department of Economics working paper.Google Scholar
  34. Hogarth, Robin, and Hillel Einhorn. (1987). “Venture Theory: A Model of Decision Weights,” University of Chicago Center for Decision Research working paper.Google Scholar
  35. Hogarth, Robin, and Howard Kunreuther. (forthcoming). “Risk, Ambiguity, and Insurance,” Journal of Risk and Uncertainty.Google Scholar
  36. KahnemanDaniel, and AmosTversky. (1979). “Prospect Theory: An Analysis of Decision under Risk,” Econometrica 47, 263–291.Google Scholar
  37. KarmarkarUday S. (1978). “Subjectively Weighted Utility: A Descriptive Extension of the Expected Utility Model,” Organizational Behavior and Human Performance 21, 61–72.Google Scholar
  38. KellerRobin L. (1985). “The Effects of Problem Representation on the Sure-Thing and Substitution Principles,” Management Science 31, 738–751.Google Scholar
  39. LoomesGraham. (1988). “Further Evidence of the Impact of Regret and Disappointment in Choice under Uncertainty, Economica 55, 47–62.Google Scholar
  40. LoomesGraham, and RobertSugden. (1982). “Regret theory: An Alternative Theory of Rational Choice under Uncertainty”, Economic Journal 92, 805–824.Google Scholar
  41. LoomesGraham and RobertSugden. (1986). “Disappointment and Dynamic Consistency in Choice under Uncertainty,” Review of Economic Studies 53, 271–282.Google Scholar
  42. LoomesGraham, and RobertSugden. (1987a). “Some Implications of a More General Form of Regret Theory,” Journal of Economic Theory 41, 270–287.Google Scholar
  43. LoomesGraham, and RobertSugden. (1987b). “Testing for Regret and Disappointment in Choice under Uncertainty,” Economic Journal 97, 118–129.Google Scholar
  44. LuceR. Duncan, and LouisNarens. (1985). “Classification of Concatenation Measurement Structures According to Scale Type,” Journal of Mathematical Psychology 29, 1–72.Google Scholar
  45. MacCrimmon, Kenneth R. (1965). “An Experimental Study of the Decision Making Behavior of Business Executives,” unpublished dissertation, University of California, Los Angeles.Google Scholar
  46. MacCrimmonKenneth R. and StigLarsson. (1979). “Utility Theory: Axioms Versus Paradoxes.” In MauriceAllais and O.Hagen (eds.), The Expected Utility Hypothesis and the Allais Paradox, Dordrecht: D. Reidel Publishing Co..Google Scholar
  47. MacCrimmonKenneth R., and MasanaoToda. (1969). “The Experimental Determination of Indifference Curves,” Review of Economic Studies 36, 433–451.Google Scholar
  48. MachinaMark. (1982). “Expected Utility Analysis Without the Independence Axiom,” Econometrica 50, 277–323.Google Scholar
  49. Machina, Mark. (1983). “The Economic Theory of Individual Behavior Toward Risk,” Technical Report #433, Institute for Mathematical Studies in the Social Sciences, Stanford University.Google Scholar
  50. MarkowitzHarry. (1952). “The Utility of Wealth,” Journal of Political Economy 60, 151–158.Google Scholar
  51. MarschakJacob. (1950). “Rational Behavior, Uncertain Prospects, and Measurable Utility,” Econometrica 18, 111–141.Google Scholar
  52. McCordMark, and RicharddeNeufville. (1986). “Lottery Equivalents: Reduction of the Certainty Effect Problem in Utility Assessment,” Management Science, 32, 56–60.Google Scholar
  53. MoskowitzHerbert. (1974). “Effects of Problem Representation and Feedback on Rational Behavior in Allais and Morlat-type Problems, Decision Sciences 5, 225–242.Google Scholar
  54. PayneJohn W. (1973). “Alternative Approaches to Decision Making Under Risk: Moments versus Risk Dimensions,” Psychological Bulletin 80, 439–453.Google Scholar
  55. PrestonMalcolm G. and PhilipBaratta. (1948). “An Experimental Study of the Auction-Value of an Uncertain Outcome”, American Journal of Psychology 61, 183–193.Google Scholar
  56. QuigginJohn. (1982). “A Theory of Anticipated Utility,” Journal of Economic Behavior and Organization 3, 323–343.Google Scholar
  57. QuigginJohn. (1985). “Subjective Utility, Anticipated Utility, and the Allais Paradox,” Organizational Behavior and Human Decision Processes 35, 94–101.Google Scholar
  58. RoellAlissa. (1987). “Risk Aversion in Quiggin and Yaari's Rank-Order Model of Choice under Uncertainty,” Economic Journal 97, 143–159.Google Scholar
  59. Rubinstein, Ariel. (1986). “Similarity and Decision Making Under Risk (Is there a Utility Theory Resolution to the Allais Paradox?),” Hebrew University Department of Economics research report no. 156.Google Scholar
  60. SchoemakerPaul. (1982). “The Expected Utility Model: Its Variants, Purposes, Evidence and Limitations,” Journal of Economic Literature 20, 529–563.Google Scholar
  61. Segal, Uzi. (forthcoming). “The Ellsberg Paradox and Risk Aversion: An Anticipated Utility Approach,” International Economic Review.Google Scholar
  62. SlovicPaul, and SarahLichtenstein. (1983). “Preference Reversals: A Broader Perspective,” American Economic Review 73, 596–605.Google Scholar
  63. SlovicPaul, and AmosTversky. (1974). “Who Accepts Savage's Axiom?,” Behavioral Science 19, 368–373.Google Scholar
  64. SmithVernon L. (1982). “Microeconomic Systems as an Experimental Science,” American Economic Review 72, 923–955.Google Scholar
  65. Starmer, C., and Robert Sugden. (1987a). “Experimental Evidence of the Impact of Regret on Choice Under Uncertainity,” Economics Research Centre discussion paper no. 23, University of East Anglia.Google Scholar
  66. Starmer, C., and Robert Sugden. (1987b). ‘Violations of the Independence Axiom: An Experimental Test of Some Competing Hypotheses,” Economics Research Centre discussion paper no. 24, University of East Anglia.Google Scholar
  67. Starmer, C., and Robert Sugden. (1987c). “Testing Prospect Theory,” Economics Research Centre discussion paper no. 26, University of East Anglia.Google Scholar
  68. SugdenRobert. (1986). “New Developments in the Theory of Choice Under Uncertainty,” Bulletin of Economic Research 38, 1–24.Google Scholar
  69. ThalerRichard. (1985). “Mental Accounting and Consumer Choice,” Marketing Science 4, 199–214.Google Scholar
  70. TverskyAmos, and DanielKahneman. (1987). “Rational Choice and the Framing of Decisions,” Journal of Business 59, S251-S278. Reprinted in Robin Hogarth and M. Reder (eds.) Rational Choice: The Cantrast Between Economics and Psychology. Chicago: University of Chicago Press.Google Scholar
  71. WeberMartin and Colin F.Camerer. (1987). “Recent Developments in Modelling Preferences Under Risk,” OR Spektrum 9, 129–151.Google Scholar
  72. Weber, Robert J. (1982). “The Allais Paradox, Dutch Auctions, and Alpha-Utility Theory” Northwestern University MEDS Department discussion paper #536.Google Scholar
  73. YaariMenhem E. (1987). “The Dual Theory of Choice Under Risk,” Econometrica 55, 95–115.Google Scholar

Copyright information

© Kluwer Academic Publishers 1988

Authors and Affiliations

  • Colin F. Camerer

There are no affiliations available

Personalised recommendations