Theory and Decision

, Volume 60, Issue 2–3, pp 315–334 | Cite as

Error Propagation in the Elicitation of Utility and Probability Weighting Functions

  • Pavlo BlavatskyyEmail author


Elicitation methods in decision-making under risk allow us to infer the utilities of outcomes as well as the probability weights from the observed preferences of an individual. An optimally efficient elicitation method is proposed, which takes the inevitable distortion of preferences by random errors into account and minimizes the effect of such errors on the inferred utility and probability weighting functions. Under mild assumptions, the optimally efficient method for eliciting utilities and probability weights is the following three-stage procedure. First, a probability is elicited whose subjective weight is one half. Second, the utility function is elicited through the midpoint chaining certainty equivalent method using the probability elicited at the first stage. Finally, the probability weighting function is elicited through the probability equivalent method.


cumulative prospect theory decision theory elicitation von Neumann–Morgenstern utility probability weighting rank-dependent expected utility 

Jel classification

C91 D81 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Abdellaoui, M. 2000Parameter-free elicitation of utility and probabilitity weighting functionsManagement Science4614971512CrossRefGoogle Scholar
  2. Abdellaoui, M., Bleichrodt, H. and Paraschiv, C. (2004). Measuring loss aversion under prospect theory: parameter-free approach, GRID, ESTP & ENSAM Working Paper.Google Scholar
  3. Bleichrodt, H., Pinto, J.L. 2000A parameter-free elicitation of the probability weighting function in medical decision analysisManagement Science4614851496CrossRefGoogle Scholar
  4. Camerer, C. 1989An experimental test of several generalized utility theoriesJournal of Risk and Uncertainty261104CrossRefGoogle Scholar
  5. Etchart-Vincent, N. 2004Is probability weighting sensitive to the magnitude of consequences? An experimental investigation on lossesJournal of Risk and Uncertainty28217235CrossRefGoogle Scholar
  6. Farquhar, P. 1984Utility assessment methodsManagement Science3012831300Google Scholar
  7. Fennema, H., assen, M. 1998Measuring the utility of losses by means of the trade-off methodJournal of Risk and Uncertainty17277296CrossRefGoogle Scholar
  8. Gonzalez, R., Wu, G. 1999On the shape of the probability weighting functionCognitive Psychology38129166CrossRefGoogle Scholar
  9. Ghirardato, P., Maccheroni, F., Marinacci, M., Siniscalchi, M. 2003A subjective spin on roulette wheelsEconometrica7118971908CrossRefGoogle Scholar
  10. Harless, D., Camerer, C. 1994The predictive utility of generalized expected utility theoriesEconometrica6212511289Google Scholar
  11. Hershey, J., Schoemaker, P. 1985Probability versus certainty equivalence methods in utility measurement: Are they equivalent?Management Science3112131231Google Scholar
  12. Hey, J.D., Orme, C. 1994Investigating generalisations of expected utility theory using experimental dataEconometrica6212911326Google Scholar
  13. Karmarkar, U. 1978Subjectively weighted utility: A descriptive extension of the expected utility modelOrganizational Behavior and Human Performance216172CrossRefGoogle Scholar
  14. Keeney, R., Raiffa, H. 1976Decisions with Multiple Objectives: Preferences and Value TradeoffsWileyNew YorkGoogle Scholar
  15. Krzysztofowicz, R., Duckstein, L. 1980Strength of preference and risk attitude in utility measurementOrganizational Behavior and Human Performance3188113CrossRefGoogle Scholar
  16. McCord, M., Neufville, R. 1986‘Lottery Equivalents’: Reduction of the certainty effect problem in utility assessmentManagement Science325660Google Scholar
  17. Quiggin, J. 1982A theory of anticipated utilityJournal of Economic Behavior and Organization3323343CrossRefGoogle Scholar
  18. Ronen, J. 1973Effects of some probability displays on choicesOrganizational Behavior and Human Performance9115CrossRefGoogle Scholar
  19. Smith, V.L., Walker, J. 1993Monetary rewards and decision cost in experimental economicsEconomic Inquiry31245261CrossRefGoogle Scholar
  20. Starmer, Ch., Sugden, R. 1989Probability and juxtaposition effects: An experimental investigation of the common ratio effectJournal of Risk and Uncertainty2159178CrossRefGoogle Scholar
  21. Tversky, A., Kahneman, D. 1992Advances in prospect theory: Cumulative representation of uncertaintyJournal of Risk and Uncertainty5297323CrossRefGoogle Scholar
  22. Winterfeldt, D., Edwards, W. 1986Decision Analysis and Behavioral ResearchCambridge University PressCambridgeGoogle Scholar
  23. Wakker, P.P., Deneffe, D. 1996Eliciting von Neumann–Morgenstern utilities when probabilities are distorted or unknownManagement Science4211311150CrossRefGoogle Scholar
  24. Wu, G. 1994An Empirical Test of Ordinal IndependenceJournal of Risk and Uncertainty93960CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  1. 1.Institute for Empirical Research in EconomicsUniversity of ZurichZurichSwitzerland

Personalised recommendations