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Resolving Rabin’s paradox

Author

Listed:
  • Han Bleichrodt

    (Erasmus University Rotterdam
    Australian National University)

  • Jason N. Doctor

    (University of Southern California)

  • Yu Gao

    (Peking University)

  • Chen Li

    (Erasmus University Rotterdam)

  • Daniella Meeker

    (University of South California)

  • Peter P. Wakker

    () (Erasmus University Rotterdam)

Abstract

We present a theoretical model of Rabin’s famous calibration paradox that resolves confusions in the literature and that makes it possible to identify the causes of the paradox. Using suitable experimental stimuli, we show that the paradox truly violates expected utility and that it is caused by reference dependence. Rabin already showed that utility curvature alone cannot explain his paradox. We, more strongly, do not find any contribution of utility curvature to the explanation of the paradox. We find no contribution of probability weighting either. We conclude that Rabin’s paradox underscores the importance of reference dependence.

Suggested Citation

  • Han Bleichrodt & Jason N. Doctor & Yu Gao & Chen Li & Daniella Meeker & Peter P. Wakker, 2019. "Resolving Rabin’s paradox," Journal of Risk and Uncertainty, Springer, vol. 59(3), pages 239-260, December.
  • Handle: RePEc:kap:jrisku:v:59:y:2019:i:3:d:10.1007_s11166-019-09318-0
    DOI: 10.1007/s11166-019-09318-0
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    1. Mohammed Abdellaoui & Han Bleichrodt & Olivier L’Haridon & Dennie Dolder, 2016. "Measuring Loss Aversion under Ambiguity: A Method to Make Prospect Theory Completely Observable," Journal of Risk and Uncertainty, Springer, vol. 52(1), pages 1-20, February.
    2. Zvi Safra & Uzi Segal, 2008. "Calibration Results for Non-Expected Utility Theories," Econometrica, Econometric Society, vol. 76(5), pages 1143-1166, September.
    3. Harrison, Glenn W. & Lau, Morten I. & Ross, Don & Swarthout, J. Todd, 2017. "Small stakes risk aversion in the laboratory: A reconsideration," Economics Letters, Elsevier, vol. 160(C), pages 24-28.
    4. Levon Barseghyan & Francesca Molinari & Ted O'Donoghue & Joshua C. Teitelbaum, 2013. "The Nature of Risk Preferences: Evidence from Insurance Choices," American Economic Review, American Economic Association, vol. 103(6), pages 2499-2529, October.
    5. Freeman, David, 2015. "Calibration without reduction for non-expected utility," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 21-32.
    6. Cox, James C. & Sadiraj, Vjollca, 2006. "Small- and large-stakes risk aversion: Implications of concavity calibration for decision theory," Games and Economic Behavior, Elsevier, vol. 56(1), pages 45-60, July.
    7. Ulrich Schmidt & Chris Starmer & Robert Sugden, 2008. "Third-generation prospect theory," Journal of Risk and Uncertainty, Springer, vol. 36(3), pages 203-223, June.
    8. Jose Apesteguia & Miguel Ballester, 2009. "A theory of reference-dependent behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 40(3), pages 427-455, September.
    9. Mohammed Abdellaoui & Cédric Gutierrez & Emmanuel Kemel, 2018. "Temporal discounting of gains and losses of time: An experimental investigation," Journal of Risk and Uncertainty, Springer, vol. 57(1), pages 1-28, August.
    10. Botond Kőszegi & Matthew Rabin, 2006. "A Model of Reference-Dependent Preferences," The Quarterly Journal of Economics, Oxford University Press, vol. 121(4), pages 1133-1165.
    11. 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.
    12. Ar. Rubinstein., 2008. "Dilemmas of an Economic Theorist," VOPROSY ECONOMIKI, N.P. Redaktsiya zhurnala "Voprosy Economiki", vol. 11.
    13. Vjollca Sadiraj, 2014. "Probabilistic risk attitudes and local risk aversion: a paradox," Theory and Decision, Springer, vol. 77(4), pages 443-454, December.
    14. 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.
    15. Peters, Hans, 2012. "A preference foundation for constant loss aversion," Journal of Mathematical Economics, Elsevier, vol. 48(1), pages 21-25.
    16. Jianying Qiu & Eva-Maria Steiger, 2011. "Understanding the Two Components of Risk Attitudes: An Experimental Analysis," Management Science, INFORMS, vol. 57(1), pages 193-199, January.
    17. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151-151.
    18. Nicholas Barberis & Ming Huang & Richard H. Thaler, 2006. "Individual Preferences, Monetary Gambles, and Stock Market Participation: A Case for Narrow Framing," American Economic Review, American Economic Association, vol. 96(4), pages 1069-1090, September.
    19. Ulrich Schmidt & Horst Zank, 2005. "What is Loss Aversion?," Journal of Risk and Uncertainty, Springer, vol. 30(2), pages 157-167, January.
    20. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    21. Charles R. Plott & Kathryn Zeiler, 2005. "The Willingness to Pay–Willingness to Accept Gap, the "Endowment Effect," Subject Misconceptions, and Experimental Procedures for Eliciting Valuations," American Economic Review, American Economic Association, vol. 95(3), pages 530-545, June.
    22. Helga Fehr-Duda & Thomas Epper, 2012. "Probability and Risk: Foundations and Economic Implications of Probability-Dependent Risk Preferences," Annual Review of Economics, Annual Reviews, vol. 4(1), pages 567-593, July.
    23. Harrell Chesson & W. Viscusi, 2003. "Commonalities in Time and Ambiguity Aversion for Long-Term Risks ," Theory and Decision, Springer, vol. 54(1), pages 57-71, February.
    24. Yusufcan Masatlioglu & Collin Raymond, 2016. "A Behavioral Analysis of Stochastic Reference Dependence," American Economic Review, American Economic Association, vol. 106(9), pages 2760-2782, September.
    25. Helga Fehr-Duda & Adrian Bruhin & Thomas Epper & Renate Schubert, 2010. "Rationality on the rise: Why relative risk aversion increases with stake size," Journal of Risk and Uncertainty, Springer, vol. 40(2), pages 147-180, April.
    26. W. Kip Viscusi & Clayton Masterman, 2017. "Anchoring biases in international estimates of the value of a statistical life," Journal of Risk and Uncertainty, Springer, vol. 54(2), pages 103-128, April.
    27. Todd Sarver, 2018. "Dynamic Mixture‐Averse Preferences," Econometrica, Econometric Society, vol. 86(4), pages 1347-1382, July.
    28. Matthew Rabin & Richard H. Thaler, 2001. "Anomalies: Risk Aversion," Journal of Economic Perspectives, American Economic Association, vol. 15(1), pages 219-232, Winter.
    29. Eyal Ert & Ido Erev, 2013. "On the descriptive value of loss aversion in decisions under risk: Six clarifications," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 8(3), pages 214-235, May.
    30. Sayman, Serdar & Onculer, Ayse, 2005. "Effects of study design characteristics on the WTA-WTP disparity: A meta analytical framework," Journal of Economic Psychology, Elsevier, vol. 26(2), pages 289-312, April.
    31. Mohammed Abdellaoui & Emmanuel Kemel, 2014. "Eliciting Prospect Theory When Consequences Are Measured in Time Units: “Time Is Not Money”," Management Science, INFORMS, vol. 60(7), pages 1844-1859, July.
    32. Adam Oliver, 2018. "Your money and your life: Risk attitudes over gains and losses," Journal of Risk and Uncertainty, Springer, vol. 57(1), pages 29-50, August.
    33. Gul, Faruk, 1991. "A Theory of Disappointment Aversion," Econometrica, Econometric Society, vol. 59(3), pages 667-686, May.
    34. Luke Lindsay, 2013. "The arguments of utility: Preference reversals in expected utility of income models," Journal of Risk and Uncertainty, Springer, vol. 46(2), pages 175-189, April.
    35. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    36. Oliver, Adam, 2018. "Your money and your life: risk attitudes over gains and losses," LSE Research Online Documents on Economics 88583, London School of Economics and Political Science, LSE Library.
    37. Julius Pahlke & Sebastian Strasser & Ferdinand Vieider, 2015. "Responsibility effects in decision making under risk," Journal of Risk and Uncertainty, Springer, vol. 51(2), pages 125-146, October.
    38. W. Viscusi & Joel Huber, 2012. "Reference-dependent valuations of risk: Why willingness-to-accept exceeds willingness-to-pay," Journal of Risk and Uncertainty, Springer, vol. 44(1), pages 19-44, February.
    39. Hong Chao & Chun-Yu Ho & Xiangdong Qin, 2017. "Risk taking after absolute and relative wealth changes: The role of reference point adaptation," Journal of Risk and Uncertainty, Springer, vol. 54(2), pages 157-186, April.
    40. James Cox & Vjollca Sadiraj & Bodo Vogt & Utteeyo Dasgupta, 2013. "Is there a plausible theory for decision under risk? A dual calibration critique," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(2), pages 305-333, October.
    41. Steffen Andersen & James C. Cox & Glenn W. Harrison & Morten I. Lau & E. Elisabet Rutström & Vjollca Sadiraj, 2018. "Asset Integration and Attitudes toward Risk: Theory and Evidence," The Review of Economics and Statistics, MIT Press, vol. 100(5), pages 816-830, December.
    42. Laura Schechter, 2007. "Risk aversion and expected-utility theory: A calibration exercise," Journal of Risk and Uncertainty, Springer, vol. 35(1), pages 67-76, August.
    43. William Neilson, 2001. "Calibration results for rank-dependent expected utility," Economics Bulletin, AccessEcon, vol. 4(10), pages 1-5.
    44. Andrea Isoni & Graham Loomes & Robert Sugden, 2011. "The Willingness to Pay—Willingness to Accept Gap, the "Endowment Effect," Subject Misconceptions, and Experimental Procedures for Eliciting Valuations: Comment," American Economic Review, American Economic Association, vol. 101(2), pages 991-1011, April.
    45. Bateman, Ian & Kahneman, Daniel & Munro, Alistair & Starmer, Chris & Sugden, Robert, 2005. "Testing competing models of loss aversion: an adversarial collaboration," Journal of Public Economics, Elsevier, vol. 89(8), pages 1561-1580, August.
    46. David A. Chapman & Valery Polkovnichenko, 2011. "Risk Attitudes Toward Small and Large Bets in the Presence of Background Risk," Review of Finance, European Finance Association, vol. 15(4), pages 909-927.
    47. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.
    48. Justin Sydnor, 2010. "(Over)insuring Modest Risks," American Economic Journal: Applied Economics, American Economic Association, vol. 2(4), pages 177-199, October.
    49. repec:lmu:muenar:20868 is not listed on IDEAS
    50. Camerer, Colin F, 1989. "An Experimental Test of Several Generalized Utility Theories," Journal of Risk and Uncertainty, Springer, vol. 2(1), pages 61-104, April.
    51. Ballinger, T Parker & Wilcox, Nathaniel T, 1997. "Decisions, Error and Heterogeneity," Economic Journal, Royal Economic Society, vol. 107(443), pages 1090-1105, July.
    52. Guido Baltussen & G. Post & Martijn Assem & Peter Wakker, 2012. "Random incentive systems in a dynamic choice experiment," Experimental Economics, Springer;Economic Science Association, vol. 15(3), pages 418-443, September.
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