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The gain-loss asymmetry and single-self preferences

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Abstract

Kahneman and Tversky asserted a fundamental asymmetry between gains and losses, namely a “reflection effect” which occurs when an individual prefers a sure gain of $ pz to an uncertain gain of $ z with probability p, while preferring an uncertain loss of $z with probability p to a certain loss of $ pz. We focus on this class of choices (actuarially fair), and explore the extent to which the reflection effect, understood as occurring at a range of wealth levels, is compatible with single-self preferences. We decompose the reflection effect into two components, a “probability switch” effect, which is compatible with single-self preferences, and a “translation effect,” which is not. To argue the first point, we analyze two classes of single-self, nonexpected utility preferences, which we label “homothetic” and “weakly homothetic.” In both cases, we characterize the switch effect as well as the dependence of risk attitudes on wealth. We also discuss two types of utility functions of a form reminiscent of expected utility but with distorted probabilities. Type I always distorts the probability of the worst outcome downwards, yielding attraction to small risks for all probabilities. Type II distorts low probabilities upwards, and high probabilities downwards, implying risk aversion when the probability of the worst outcome is low. By combining homothetic or weak homothetic preferences with Type I or Type II distortion functions, we present four explicit examples: All four display a switch effect and, hence, a form of reflection effect consistent a single self preferences.

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Paper provided by Department of Economics and Business, Universitat Pompeu Fabra in its series Economics Working Papers with number 885.

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Date of creation: Sep 2005
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Handle: RePEc:upf:upfgen:885

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Keywords: Reflection; gains; losses; experiments; risk attitude; Leex;

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  1. Hanemann, W Michael, 1991. "Willingness to Pay and Willingness to Accept: How Much Can They Differ?," American Economic Review, American Economic Association, vol. 81(3), pages 635-47, June.
  2. 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.
  3. Sugden, Robert, 2003. "Reference-dependent subjective expected utility," Journal of Economic Theory, Elsevier, vol. 111(2), pages 172-191, August.
  4. Horowitz, John K. & McConnell, K. E., 2003. "Willingness to accept, willingness to pay and the income effect," Journal of Economic Behavior & Organization, Elsevier, vol. 51(4), pages 537-545, August.
  5. Knetsch, Jack L, 1989. "The Endowment Effect and Evidence of Nonreversible Indifference Curves," American Economic Review, American Economic Association, vol. 79(5), pages 1277-84, December.
  6. Antoni Bosch-Domènech & Joaquim Silvestre, 2003. "Do the eealthy risk more money? An experimental comparison," Economics Working Papers 692, Department of Economics and Business, Universitat Pompeu Fabra, revised Jan 2005.
  7. Matthew Rabin, 2001. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Method and Hist of Econ Thought 0012001, EconWPA.
  8. Bosch-Domenech, Antoni & Silvestre, Joaquim, 1999. "Does risk aversion or attraction depend on income? An experiment," Economics Letters, Elsevier, vol. 65(3), pages 265-273, December.
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  10. Shogren, Jason F. & Seung Y. Shin & Dermot J. Hayes & James B. Kliebenstein, 1994. "Resolving Differences in Willingness to Pay and Willingness to Accept," American Economic Review, American Economic Association, vol. 84(1), pages 255-70, March.
  11. Tversky, Amos & Kahneman, Daniel, 1991. "Loss Aversion in Riskless Choice: A Reference-Dependent Model," The Quarterly Journal of Economics, MIT Press, vol. 106(4), pages 1039-61, November.
  12. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60, pages 151.
  13. Munro, Alistair & Sugden, Robert, 2003. "On the theory of reference-dependent preferences," Journal of Economic Behavior & Organization, Elsevier, vol. 50(4), pages 407-428, April.
  14. Bateman, Ian J, et al, 1997. "A Test of the Theory of Reference-Dependent Preferences," The Quarterly Journal of Economics, MIT Press, vol. 112(2), pages 479-505, May.
  15. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-91, March.
  16. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  17. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56, pages 279.
  18. Robson, Arthur J, 1992. "Status, the Distribution of Wealth, Private and Social Attitudes to Risk," Econometrica, Econometric Society, vol. 60(4), pages 837-57, July.
  19. Sugden Robert, 1993. "An Axiomatic Foundation for Regret Theory," Journal of Economic Theory, Elsevier, vol. 60(1), pages 159-180, June.
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Cited by:
  1. Antoni Bosch-Domènech & Joaquim Silvestre, 2006. "Reflections on gains and losses: A 2 × 2 × 7 experiment," Journal of Risk and Uncertainty, Springer, vol. 33(3), pages 217-235, December.

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