Skip to main content
Log in

Probability Weighting in Choice under Risk: An Empirical Test

  • Published:
Journal of Risk and Uncertainty Aims and scope Submit manuscript

Abstract

This paper reports a violation of rank-dependent utility with inverse S-shaped probability weighting for binary gambles. The paper starts with a violation of expected utility theory: one-stage gambles elicit systematically different utilities than theoretically equivalent two-stage gambles. This systematic disparity does not disappear, but becomes more pronounced after correction for inverse S-shaped probability weighting. The data are also inconsistent with configural weight theory and Machina's fanning out hypothesis. Possible explanations for the data are loss aversion and anchoring and insufficient adjustment.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Abdellaoui, M. (2000). “Parameter-Free Elicitation of Utilities and Probability Weighting Functions,” Management Science 46, 1497–1512.

    Google Scholar 

  • Allais, M. (1979). “The So-Called Allais Paradox and Rational Decisions under Uncertainty.” In M. Allais and O. Hagen (eds.), Expected Utility Hypotheses and the Allais Paradox. Dordrecht: D. Reidel.

    Google Scholar 

  • Birnbaum, M. H. and W. R. McIntosh. (1996). “Violations of Branch Independence in Choices between Gambles,” Organizational Behavior and Human Decision Processes 67, 91–110.

    Google Scholar 

  • Birnbaum, M. H. and J. B. Navarrete. (1998). “Testing Descriptive Utility Theories: Violations of Stochastic Dominance and Cumulative Independence,” Journal of Riskand Uncertainty 17, 49–78.

    Google Scholar 

  • Bleichrodt, H. and J.-L. Pinto. (2000). “A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis,” Management Science 46, 1485–1496.

    Google Scholar 

  • Bleichrodt, H., J. van Rijn, and M. Johannesson. (1999). “Probability Weighting and Utility Curvature in QALY Based Decision Making,” Journal of Mathematical Psychology 43, 238–260.

    Google Scholar 

  • Camerer, C. F. and T.-H. Ho. (1994). “Nonlinear Weighting of Probabilities and Violations of the Betweenness Axiom,” Journal of Risk and Uncertainty 8, 167–196.

    Google Scholar 

  • Dubourg, W. R., M. W. Jones-Lee, and G. Loomes. (1994). “Imprecise Preferences and the WTP-WTA Disparity,” Journal of Riskand Uncertainty 9, 115–133.

    Google Scholar 

  • The EuroQol Group. (1990). “EuroQol: A New Facility for the Measurement of Health Related Quality of Life,” Health Policy 16, 199–208.

    Google Scholar 

  • Farquhar, P. (1984). “Utility Assessment Methods,” Management Science 30, 1283–1300.

    Google Scholar 

  • Fellner, W. (1961). “Distortion of Subjective Probabilities as a Reaction to Uncertainty,” Quarterly Journal of Economics 75, 670–689.

    Google Scholar 

  • Gonzalez, R. and G. Wu. (1999). “On the Form of the Probability Weighting Function,” Cognitive Psychology 38, 129–166.

    Google Scholar 

  • Hershey, J. C. and P. J. H. Schoemaker. (1985). “Probability versus Certainty Equivalence Methods in Utility Measurement: Are They Equivalent?” Management Science 31, 1213–1231.

    Google Scholar 

  • Jensen, N. E. (1967). “An Introduction to Bernoullian Utility Theory: I. Utility Functions,” Scandinavian Journal of Economics 69, 163–183.

    Google Scholar 

  • Johnson, E. J. and D. A. Schkade. (1989). “Bias in Utility Assessments: Further Evidence and Explanations,” Management Science 35, 406–424.

    Google Scholar 

  • Kahneman, D. and A. Tversky. (1979). “ Prospect Theory: An Analysis of Decision Under Risk,” Econometrica 47, 263–291.

    Google Scholar 

  • Karmarkar, U. A. (1974). “The Effect of Probabilities on the Subjective Evaluation of Lotteries,” MIT Working Paper No. 698–74, MIT, Cambridge, MA.

    Google Scholar 

  • Karmarkar, U. A. (1978). “Subjectively Weighted Utility: A Descriptive Extension of the Expected Utility Model,” Organizational Behavior and Human Performance 21, 61–72.

    Google Scholar 

  • Lattimore, P. M., J. R. Baker, and A. D. Witte. (1992). “The Influence of Probability on Risky Choice,” Journal of Economic Behavior and Organization 17, 377–400.

    Google Scholar 

  • Llewellyn-Thomas, H., H. J. Sutherland, R. Tibshirani, A. Ciampi, J. E. Till, and N. F. Boyd. (1982). “The Measurement of Patients’ Values in Medicine,” Medical Decision Making 2, 449–462.

    Google Scholar 

  • Luce, R. D. (2000). Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.

    Google Scholar 

  • Machina, M. (1982). “ 'Expected Utility’ Analysis without the Independence Axiom,” Econometrica 50, 277–323.

    Google Scholar 

  • Machina, M. (1983). “Generalized Expected Utility Analysis and the Nature of Observed Violations of the Independence Axiom.” In B. P. Stigum and F. Wenstop (eds.), Foundations of Utility and RiskTheory with Applications. Dordrecht: D. Reidel.

    Google Scholar 

  • Machina, M. (1987). “Choice Under Uncertainty: Problems Solved and Unsolved,” Journal of Economic Perspectives 1, 121–154.

    Google Scholar 

  • McCord, M. R. and R. de Neufville. (1983). “Empirical Demonstration that Expected Utility Decision Analysis Is Not Operational.” In B. P. Stigum and F. Wenstop (eds.), Foundations of Utility and RiskTheory with Applications. Dordrecht: D. Reidel.

    Google Scholar 

  • McCord, M. R. and R. de Neufville. (1984). “Utility Dependence on Probability: An Empirical Demonstration,” Journal of Large Scale Systems 6, 91–103.

    Google Scholar 

  • Prelec, D. (1998). “The Probability Weighting Function,” Econometrica 66, 497–528.

    Google Scholar 

  • Quiggin, J. (1982). “A Theory of Anticipated Utility,” Journal of Economic Behavior and Organization 3, 323–343.

    Google Scholar 

  • Rutten-van Mölken, M. P., C. H. Bakker, E. K. A. van Doorslaer, and S. van der Linden. (1995). “Methodological Issues of Patient Utility Measurement. Experience from Two Clinical Trials,” Medical Care 33, 922–937.

    Google Scholar 

  • Tversky, A. and C. Fox. (1995). “Weighting Risk and Uncertainty,” Psychological Review 102, 269–283.

    Google Scholar 

  • Tversky, A. and D. Kahneman. (1992). “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Riskand Uncertainty 5, 297–323.

    Google Scholar 

  • Tversky, A. S. Sattath, and P. Slovic. (1988). “Contingent Weighting in Judgment and Choice,” Psychological Review 95, 371–384.

    Google Scholar 

  • Wakker, P. P., I. Erev, and E. U. Weber. (1994). ”Comonotonic Independence: The Critical Test between Classical and Rank-Dependent Utility,” Journal of Riskand Uncertainty 9, 195–230.

    Google Scholar 

  • Wakker, P. P. and A. M. Stiggelbout. (1995). “Explaining Distortions in Utility Elicitation Through the Rank-Dependent Model for Risky Choices,” Medical Decision Making 15, 180–186.

    Google Scholar 

  • Wu, G. (1994). “An Empirical Test of Ordinal Independence,” Journal of Risk and Uncertainty 9, 39–60.

    Google Scholar 

  • Wu, G. and R. Gonzalez. (1996). “Curvature of the Probability Weighting Function,” Management Science 42, 1676–1690.

    Google Scholar 

  • Yaari, M. E. (1987). “The Dual Theory of Choice under Risk,” Econometrica 55, 95–115.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bleichrodt, H. Probability Weighting in Choice under Risk: An Empirical Test. Journal of Risk and Uncertainty 23, 185–198 (2001). https://doi.org/10.1023/A:1011136203223

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1011136203223

Navigation