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Random Expected Utility and Certainty Equivalents: Mimicry of Probability Weighting Functions

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  • Nathaniel T. Wilcox

    (Economic Science Institute, Chapman University)

Abstract

For simple prospects routinely used for certainty equivalent elicitation, random expected utility preferences imply a conditional expectation function that can mimic deterministic rank dependent preferences. That is, a subject with random expected utility preferences can have expected certainty equivalents exactly like those predicted by rank dependent probability weighting functions of the inverse-s shape discussed by Quiggin (1982) and advocated by Tversky and Kahneman (1992), Prelec (1998) and other scholars. Certainty equivalents may not nonparametrically identify preferences: Their conditional expectation (and critically, their interpretation) depends on assumptions concerning the source of their variability.

Suggested Citation

  • Nathaniel T. Wilcox, 2017. "Random Expected Utility and Certainty Equivalents: Mimicry of Probability Weighting Functions," Working Papers 16-14, Chapman University, Economic Science Institute.
    • Handle: RePEc:chu:wpaper:16-14
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    References listed on IDEAS

    as
    1. Loomes, Graham & Moffatt, Peter G & Sugden, Robert, 2002. "A Microeconometric Test of Alternative Stochastic Theories of Risky Choice," Journal of Risk and Uncertainty, Springer, vol. 24(2), pages 103-130, March.
    2. repec:bla:econom:v:65:y:1998:i:260:p:581-98 is not listed on IDEAS
    3. Grant, Simon & Polak, Ben, 2013. "Mean-dispersion preferences and constant absolute uncertainty aversion," Journal of Economic Theory, Elsevier, vol. 148(4), pages 1361-1398.
    4. Camerer, Colin F & Hogarth, Robin M, 1999. "The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework," Journal of Risk and Uncertainty, Springer, vol. 19(1-3), pages 7-42, December.
    5. Mohammed Abdellaoui & Han Bleichrodt & Olivier L’Haridon, 2008. "A tractable method to measure utility and loss aversion under prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 245-266, June.
    6. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    7. Jehoshua Eliashberg & John R. Hauser, 1985. "A Measurement Error Approach for Modeling Consumer Risk Preference," Management Science, INFORMS, vol. 31(1), pages 1-25, January.
    8. Alex Voorhoeve & Ken Binmore & Arnaldur Stefansson & Lisa Stewart, 2016. "Ambiguity attitudes, framing, and consistency," Theory and Decision, Springer, vol. 81(3), pages 313-337, September.
    9. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2012. "Salience Theory of Choice Under Risk," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(3), pages 1243-1285.
    10. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    11. Pedro Bordalo & Nicola Gennaioli & Andrei Shleifer, 2013. "Salience and Consumer Choice," Journal of Political Economy, University of Chicago Press, vol. 121(5), pages 803-843.
    12. Michael H. Birnbaum & Ulrich Schmidt, 2015. "The Impact of Learning by Thought on Violations of Independence and Coalescing," Decision Analysis, INFORMS, vol. 12(3), pages 144-152.
    13. Ghirardato, Paolo & Maccheroni, Fabio & Marinacci, Massimo, 2004. "Differentiating ambiguity and ambiguity attitude," Journal of Economic Theory, Elsevier, vol. 118(2), pages 133-173, October.
    14. Nathaniel T. Wilcox, 2023. "Unusual Estimates of Probability Weighting Functions," Research in Experimental Economics, in: Models of Risk Preferences: Descriptive and Normative Challenges, volume 22, pages 69-106, Emerald Group Publishing Limited.
    15. David S. Ahn & Todd Sarver, 2013. "Preference for Flexibility and Random Choice," Econometrica, Econometric Society, vol. 81(1), pages 341-361, January.
    16. Yoram Halevy, 2007. "Ellsberg Revisited: An Experimental Study," Econometrica, Econometric Society, vol. 75(2), pages 503-536, March.
    17. Karni, Edi & Safra, Zvi, 1987. ""Preference Reversal' and the Observability of Preferences by Experimental Methods," Econometrica, Econometric Society, vol. 55(3), pages 675-685, May.
    18. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    19. Nathaniel T Wilcox, 2006. "Theories of Learning in Games and Heterogeneity Bias," Econometrica, Econometric Society, vol. 74(5), pages 1271-1292, September.
    20. Wilcox, Nathaniel T., 2011. "'Stochastically more risk averse:' A contextual theory of stochastic discrete choice under risk," Journal of Econometrics, Elsevier, vol. 162(1), pages 89-104, May.
    21. Harrison, Glenn W. & Rutström, E. Elisabet, 2008. "Experimental Evidence on the Existence of Hypothetical Bias in Value Elicitation Methods," Handbook of Experimental Economics Results, in: Charles R. Plott & Vernon L. Smith (ed.), Handbook of Experimental Economics Results, edition 1, volume 1, chapter 81, pages 752-767, Elsevier.
    22. Graham Loomes & Ganna Pogrebna, 2014. "Measuring Individual Risk Attitudes when Preferences are Imprecise," Economic Journal, Royal Economic Society, vol. 0(576), pages 569-593, May.
    23. David J. Butler & Graham C. Loomes, 2007. "Imprecision as an Account of the Preference Reversal Phenomenon," American Economic Review, American Economic Association, vol. 97(1), pages 277-297, March.
    24. Daniel Navarro-Martinez & Graham Loomes & Andrea Isoni & David Butler & Larbi Alaoui, 2018. "Boundedly rational expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 57(3), pages 199-223, December.
    25. Jonathan W. Leland & Mark Schneider, 2016. "Salience, Framing, and Decisions under Risk, Uncertainty, and Time," Working Papers 16-08, Chapman University, Economic Science Institute.
    26. Mohammed Abdellaoui & Han Bleichrodt & Corina Paraschiv, 2007. "Loss Aversion Under Prospect Theory: A Parameter-Free Measurement," Management Science, INFORMS, vol. 53(10), pages 1659-1674, October.
    27. George Wu & Richard Gonzalez, 1999. "Nonlinear Decision Weights in Choice Under Uncertainty," Management Science, INFORMS, vol. 45(1), pages 74-85, January.
    28. Pavlo R. Blavatskyy & Ganna Pogrebna, 2010. "Models of stochastic choice and decision theories: why both are important for analyzing decisions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(6), pages 963-986.
    29. Faruk Gul & Wolfgang Pesendorfer, 2006. "Random Expected Utility," Econometrica, Econometric Society, vol. 74(1), pages 121-146, January.
    30. Karni, Edi & Safra, Zvi, 2016. "A theory of stochastic choice under uncertainty," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 164-173.
    31. Voorhoeve, Alex & Binmore, Ken G & Stefansson, Arnaldur & Stewart, Lisa, 2016. "Ambiguity attitudes, framing, and consistency," LSE Research Online Documents on Economics 65577, London School of Economics and Political Science, LSE Library.
    32. Daniel Ellsberg, 1961. "Risk, Ambiguity, and the Savage Axioms," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 75(4), pages 643-669.
    33. Krahnen, Jan Pieter & Rieck, Christian & Theissen, Erik, 1997. "Inferring risk attitudes from certainty equivalents: Some lessons from an experimental study," Journal of Economic Psychology, Elsevier, vol. 18(5), pages 469-486, September.
    34. Leland, Jonathan, 2010. "The hunt for a descriptive theory of choice under risk--A view from the road not taken," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 39(5), pages 568-577, October.
    35. Adrian Bruhin & Helga Fehr-Duda & Thomas Epper, 2010. "Risk and Rationality: Uncovering Heterogeneity in Probability Distortion," Econometrica, Econometric Society, vol. 78(4), pages 1375-1412, July.
    36. Joost M.E. Pennings & Ale Smidts, 2000. "Assessing the Construct Validity of Risk Attitude," Management Science, INFORMS, vol. 46(10), pages 1337-1348, October.
    37. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
    38. Loewenstein, George, 1999. "Experimental Economics from the Vantage-Point of Behavioural Economics," Economic Journal, Royal Economic Society, vol. 109(453), pages 23-34, February.
    39. Ferdinand M. Vieider & Mathieu Lefebvre & Ranoua Bouchouicha & Thorsten Chmura & Rustamdjan Hakimov & Michal Krawczyk & Peter Martinsson, 2015. "Common Components Of Risk And Uncertainty Attitudes Across Contexts And Domains: Evidence From 30 Countries," Journal of the European Economic Association, European Economic Association, vol. 13(3), pages 421-452, June.
    40. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
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    Cited by:

    1. Daniel Navarro-Martinez & Graham Loomes & Andrea Isoni & David Butler & Larbi Alaoui, 2018. "Boundedly rational expected utility theory," Journal of Risk and Uncertainty, Springer, vol. 57(3), pages 199-223, December.
    2. Charles-Cadogan, G., 2018. "Probability interference in expected utility theory," Journal of Mathematical Economics, Elsevier, vol. 78(C), pages 163-175.

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    More about this item

    Keywords

    Certainty Equivalence; Identification; Preference Estimation; Preference Measurement; Random Preference; Choice Under Risk and Uncertainty;
    All these keywords.

    JEL classification:

    • C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
    • C91 - Mathematical and Quantitative Methods - - Design of Experiments - - - Laboratory, Individual Behavior
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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