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Chance Theory: A Separation of Riskless and Risky Utility

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  • Ulrich Schmidt
  • Horst Zank

Abstract

We present a preference foundation for Chance Theory (CT), a model of decision making under uncertainty where the evaluation of an act depends distinctively on its lowest outcome. This outcome is evaluated with the riskless value function u and the potential increments over it are evaluated by subjective expected utility with a risky utility function u. In contrast to earlier approaches with models that aimed at separating riskless and risky utility, CT does not violate basic rationality principles like first-order stochastic dominance or transitivity. Decision makers with CT-preferences always prefer the expected value of a lottery to the latter, so they are weakly risk averse. Besides explaining behavioral irregularities like the expected utility paradoxes of Allais and Rabin, CT also separates risk attitude in the strong sense from attitude towards wealth. Risk attitude is completely determined by the curvature of vuand is independent of the value function v. Conversely, attitude towards wealth is reflected solely through the curvature of v without imposing constraints on u.
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  • Ulrich Schmidt & Horst Zank, 2013. "Chance Theory: A Separation of Riskless and Risky Utility," Economics Discussion Paper Series 1324, Economics, The University of Manchester.
    • Handle: RePEc:man:sespap:1324
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    References listed on IDEAS

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    1. Dillenberger, David, 2008. "Preferences for One-Shot Resolution of Uncertainty and Allais-Type Behavior," MPRA Paper 8342, University Library of Munich, Germany.
    2. Kimball, Miles S, 1990. "Precautionary Saving in the Small and in the Large," Econometrica, Econometric Society, vol. 58(1), pages 53-73, January.
    3. Simone Cerreia‐Vioglio & David Dillenberger & Pietro Ortoleva, 2015. "Cautious Expected Utility and the Certainty Effect," Econometrica, Econometric Society, vol. 83, pages 693-728, March.
    4. 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.
    5. Fishburn, Peter C, 1977. "Mean-Risk Analysis with Risk Associated with Below-Target Returns," American Economic Review, American Economic Association, vol. 67(2), pages 116-126, March.
    6. Uri Gneezy & John A. List & George Wu, 2006. "The Uncertainty Effect: When a Risky Prospect is Valued Less than its Worst Possible Outcome," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 121(4), pages 1283-1309.
    7. 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.
    8. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    9. James Andreoni & Charles Sprenger, 2010. "Certain and Uncertain Utility: The Allais Paradox and Five Decision Theory Phenomena," Levine's Working Paper Archive 814577000000000447, David K. Levine.
    10. Conlisk, John, 1989. "Three Variants on the Allais Example," American Economic Review, American Economic Association, vol. 79(3), pages 392-407, June.
    11. Peter Fishburn, 1980. "A simple model for the utility of gambling," Psychometrika, Springer;The Psychometric Society, vol. 45(4), pages 435-448, December.
    12. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    13. Webb, Craig S. & Zank, Horst, 2011. "Accounting for optimism and pessimism in expected utility," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 706-717.
    14. Daniel Kahneman & Amos Tversky, 2013. "Prospect Theory: An Analysis of Decision Under Risk," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 6, pages 99-127, World Scientific Publishing Co. Pte. Ltd..
    15. Chris Starmer, 2000. "Developments in Non-expected Utility Theory: The Hunt for a Descriptive Theory of Choice under Risk," Journal of Economic Literature, American Economic Association, vol. 38(2), pages 332-382, June.
    16. 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.
    17. Enrico Diecidue & Ulrich Schmidt & Peter P. Wakker, 2004. "The Utility of Gambling Reconsidered," Journal of Risk and Uncertainty, Springer, vol. 29(3), pages 241-259, December.
    18. Wakker,Peter P., 2010. "Prospect Theory," Cambridge Books, Cambridge University Press, number 9780521765015, October.
    19. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    20. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
    21. Veronika Köbberling & Peter P. Wakker, 2003. "Preference Foundations for Nonexpected Utility: A Generalized and Simplified Technique," Mathematics of Operations Research, INFORMS, vol. 28(3), pages 395-423, August.
    22. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    23. Wakker, Peter, 1993. "Additive representations on rank-ordered sets : II. The topological approach," Journal of Mathematical Economics, Elsevier, vol. 22(1), pages 1-26.
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    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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