Advertisement

Journal of Risk and Uncertainty

, Volume 23, Issue 2, pp 185–198 | Cite as

Probability Weighting in Choice under Risk: An Empirical Test

  • Han Bleichrodt
Article

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.

nonexpected utility probability weighting health 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdellaoui, M. (2000). “Parameter-Free Elicitation of Utilities and Probability Weighting Functions,” Management Science 46, 1497–1512.Google Scholar
  2. 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
  3. 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
  4. 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
  5. 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
  6. 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
  7. 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
  8. 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
  9. The EuroQol Group. (1990). “EuroQol: A New Facility for the Measurement of Health Related Quality of Life,” Health Policy 16, 199–208.Google Scholar
  10. Farquhar, P. (1984). “Utility Assessment Methods,” Management Science 30, 1283–1300.Google Scholar
  11. Fellner, W. (1961). “Distortion of Subjective Probabilities as a Reaction to Uncertainty,” Quarterly Journal of Economics 75, 670–689.Google Scholar
  12. Gonzalez, R. and G. Wu. (1999). “On the Form of the Probability Weighting Function,” Cognitive Psychology 38, 129–166.Google Scholar
  13. 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
  14. Jensen, N. E. (1967). “An Introduction to Bernoullian Utility Theory: I. Utility Functions,” Scandinavian Journal of Economics 69, 163–183.Google Scholar
  15. Johnson, E. J. and D. A. Schkade. (1989). “Bias in Utility Assessments: Further Evidence and Explanations,” Management Science 35, 406–424.Google Scholar
  16. Kahneman, D. and A. Tversky. (1979). “ Prospect Theory: An Analysis of Decision Under Risk,” Econometrica 47, 263–291.Google Scholar
  17. 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
  18. 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
  19. 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
  20. 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
  21. Luce, R. D. (2000). Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.Google Scholar
  22. Machina, M. (1982). “ 'Expected Utility’ Analysis without the Independence Axiom,” Econometrica 50, 277–323.Google Scholar
  23. 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
  24. Machina, M. (1987). “Choice Under Uncertainty: Problems Solved and Unsolved,” Journal of Economic Perspectives 1, 121–154.Google Scholar
  25. 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
  26. 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
  27. Prelec, D. (1998). “The Probability Weighting Function,” Econometrica 66, 497–528.Google Scholar
  28. Quiggin, J. (1982). “A Theory of Anticipated Utility,” Journal of Economic Behavior and Organization 3, 323–343.Google Scholar
  29. 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
  30. Tversky, A. and C. Fox. (1995). “Weighting Risk and Uncertainty,” Psychological Review 102, 269–283.Google Scholar
  31. Tversky, A. and D. Kahneman. (1992). “Advances in Prospect Theory: Cumulative Representation of Uncertainty,” Journal of Riskand Uncertainty 5, 297–323.Google Scholar
  32. Tversky, A. S. Sattath, and P. Slovic. (1988). “Contingent Weighting in Judgment and Choice,” Psychological Review 95, 371–384.Google Scholar
  33. 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
  34. 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
  35. Wu, G. (1994). “An Empirical Test of Ordinal Independence,” Journal of Risk and Uncertainty 9, 39–60.Google Scholar
  36. Wu, G. and R. Gonzalez. (1996). “Curvature of the Probability Weighting Function,” Management Science 42, 1676–1690.Google Scholar
  37. Yaari, M. E. (1987). “The Dual Theory of Choice under Risk,” Econometrica 55, 95–115.Google Scholar

Copyright information

© Kluwer Academic Publishers 2001

Authors and Affiliations

  • Han Bleichrodt
    • 1
  1. 1.iMTA/iBMGErasmus UniversityRotterdamThe Netherlands

Personalised recommendations