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Accounting for Optimism and Pessimism in Expected Utility

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  • Craig Webb
  • Horst Zank

Abstract

We provide a preference foundation for decision under risk resulting in a model where probability weighting is linear as long as the corresponding probabilities are not extreme (i.e., 0 or 1). This way, most of the elegance and mathematical tractability of expected utility is maintained and also much of its normative foundation. Yet, the new model can accommodate the extreme sensitivity towards changes from 0 to almost impossible and from almost certain to 1 that has widely been documented in the experimental literature. The model can be viewed as “expected utility with the best and worst in mind” as suggested by Chateauneuf, Eichberger and Grant (Chateauneuf, Alain, Eichberger, Jürgen, Grant, Simon, 2007. Choice under uncertainty with the best and worst in mind: NEO-Additive capacities. Journal of Economic Theory 137, 538–567) or, following our preference foundation, interpreted as “expected utility with consistent optimism and pessimism”.

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Bibliographic Info

Paper provided by Economics, The University of Manchester in its series The School of Economics Discussion Paper Series with number 1111.

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Date of creation: 2011
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Handle: RePEc:man:sespap:1111

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  1. Chateauneuf, Alain & Eichberger, Jurgen & Grant, Simon, 2007. "Choice under uncertainty with the best and worst in mind: Neo-additive capacities," Journal of Economic Theory, Elsevier, vol. 137(1), pages 538-567, November.
  2. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  3. Mohammed Abdellaoui & Frank Vossmann & Martin Weber, 2005. "Choice-Based Elicitation and Decomposition of Decision Weights for Gains and Losses Under Uncertainty," Management Science, INFORMS, vol. 51(9), pages 1384-1399, September.
  4. 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.
  5. Drazen Prelec, 1998. "The Probability Weighting Function," Econometrica, Econometric Society, vol. 66(3), pages 497-528, May.
  6. Daniel Ellsberg, 2000. "Risk, Ambiguity and the Savage Axioms," Levine's Working Paper Archive 7605, David K. Levine.
  7. Machina, Mark J, 1989. "Dynamic Consistency and Non-expected Utility Models of Choice under Uncertainty," Journal of Economic Literature, American Economic Association, vol. 27(4), pages 1622-68, December.
  8. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
  9. Enrico Diecidue & Ulrich Schmidt & Horst Zank, 2006. "Parametric Weighting Functions," The School of Economics Discussion Paper Series 0622, Economics, The University of Manchester.
  10. Mohammed Abdellaoui, 2000. "Parameter-Free Elicitation of Utility and Probability Weighting Functions," Management Science, INFORMS, vol. 46(11), pages 1497-1512, November.
  11. Wakker, Peter P, 2001. "Testing and Characterizing Properties of Nonadditive Measures through Violations of the Sure-Thing Principle," Econometrica, Econometric Society, vol. 69(4), pages 1039-59, July.
  12. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
  13. Michael Kilka & Martin Weber, 2001. "What Determines the Shape of the Probability Weighting Function Under Uncertainty?," Management Science, INFORMS, vol. 47(12), pages 1712-1726, December.
  14. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  15. Enrico Diecidue & Jeroen van de Ven, 2008. "Aspiration Level, Probability Of Success And Failure, And Expected Utility," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(2), pages 683-700, 05.
  16. Horst Zank, 2010. "Consistent probability attitudes," Economic Theory, Springer, vol. 44(2), pages 167-185, August.
  17. Chateauneuf, Alain, 1999. "Comonotonicity axioms and rank-dependent expected utility theory for arbitrary consequences," Journal of Mathematical Economics, Elsevier, vol. 32(1), pages 21-45, August.
  18. Wakker, Peter, 1993. "Additive representations on rank-ordered sets : II. The topological approach," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 1-26.
  19. Peter Wakker & Daniel Deneffe, 1996. "Eliciting von Neumann-Morgenstern Utilities When Probabilities Are Distorted or Unknown," Management Science, INFORMS, vol. 42(8), pages 1131-1150, August.
  20. Mohammed Abdellaoui & Olivier L’Haridon & Horst Zank, 2010. "Separating curvature and elevation: A parametric probability weighting function," Journal of Risk and Uncertainty, Springer, vol. 41(1), pages 39-65, August.
  21. Han Bleichrodt & Jose Luis Pinto, 2000. "A Parameter-Free Elicitation of the Probability Weighting Function in Medical Decision Analysis," Management Science, INFORMS, vol. 46(11), pages 1485-1496, November.
  22. 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.
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Cited by:
  1. Ulrich Schmidt & Horst Zank, 2013. "Chance Theory: A Separation of Riskless and Risky Utility," The School of Economics Discussion Paper Series 1324, Economics, The University of Manchester.

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