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The Markowitz model of utility supplemented with a small degree of probability distortion as an explanation of outcomes of Allais experiments over large and small payoffs and gambling on unlikely outcomes

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  • D. A. Peel
  • Jie Zhang
  • D. Law

Abstract

We show that in principal only a small degree of probability distortion is necessary for agents to exhibit the Allais paradox. We also show that the choices observed in the Allais experiments employing small real payoffs cannot be explained by Cumulative Prospect Theory without the assumption of low degrees of probability distortion that rule out gambling at unfair odds on all but the most extreme longshots in CPT. Given these points we show that the Markowitz model of utility supplemented by a small degree of probability distortion can explain the majority choices involved Allais experiments and other experiments as well as gambling at actuarially unfair odds.

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  • D. A. Peel & Jie Zhang & D. Law, 2008. "The Markowitz model of utility supplemented with a small degree of probability distortion as an explanation of outcomes of Allais experiments over large and small payoffs and gambling on unlikely outc," Applied Economics, Taylor & Francis Journals, vol. 40(1), pages 17-26.
    • Handle: RePEc:taf:applec:v:40:y:2008:i:1:p:17-26
    DOI: 10.1080/00036840701728781
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    1. Hans P. Binswanger, 1980. "Attitudes Toward Risk: Experimental Measurement in Rural India," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 62(3), pages 395-407.
    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. Harry Markowitz, 1952. "The Utility of Wealth," Journal of Political Economy, University of Chicago Press, vol. 60(2), pages 151-151.
    4. Michael Cain & David Law & David A. Peel, 2001. "The Incidence of Insider Trading in Betting Markets and the Gabriel and Marsden Anomaly," Manchester School, University of Manchester, vol. 69(2), pages 197-207, March.
    5. Charles A. Holt & Susan K. Laury, 2002. "Risk Aversion and Incentive Effects," American Economic Review, American Economic Association, vol. 92(5), pages 1644-1655, December.
    6. Camerer, Colin F & Ho, Teck-Hua, 1994. "Violations of the Betweenness Axiom and Nonlinearity in Probability," Journal of Risk and Uncertainty, Springer, vol. 8(2), pages 167-196, March.
    7. 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..
    8. Matthew Rabin, 2000. "Risk Aversion and Expected-Utility Theory: A Calibration Theorem," Econometrica, Econometric Society, vol. 68(5), pages 1281-1292, September.
    9. Shlomo Benartzi & Richard H. Thaler, 1995. "Myopic Loss Aversion and the Equity Premium Puzzle," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 110(1), pages 73-92.
    10. Kachelmeier, Steven J & Shehata, Mohamed, 1992. "Examining Risk Preferences under High Monetary Incentives: Experimental Evidence from the People's Republic of China," American Economic Review, American Economic Association, vol. 82(5), pages 1120-1141, December.
    11. Harrison, Glenn W, 1994. "Expected Utility Theory and the Experimentalists," Empirical Economics, Springer, vol. 19(2), pages 223-253.
    12. Kagel, John H & MacDonald, Don N & Battalio, Raymond C, 1990. "Tests of "Fanning Out" of Indifference Curves: Results from Animal and Human Experiments," American Economic Review, American Economic Association, vol. 80(4), pages 912-921, September.
    13. Atanu Saha, 1993. "Expo-Power Utility: A ‘Flexible’ Form for Absolute and Relative Risk Aversion," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 75(4), pages 905-913.
    14. Starmer, Chris & Sugden, Robert, 1989. "Probability and Juxtaposition Effects: An Experimental Investigation of the Common Ratio Effect," Journal of Risk and Uncertainty, Springer, vol. 2(2), pages 159-178, June.
    15. Neilson, William S & Stowe, Jill, 2002. "A Further Examination of Cumulative Prospect Theory Parameterizations," Journal of Risk and Uncertainty, Springer, vol. 24(1), pages 31-46, January.
    16. Quiggin, John, 1993. "Testing between Alternative Models of Choice under Uncertainty: Comment," Journal of Risk and Uncertainty, Springer, vol. 6(2), pages 161-164, April.
    17. George Wu & Richard Gonzalez, 1996. "Curvature of the Probability Weighting Function," Management Science, INFORMS, vol. 42(12), pages 1676-1690, December.
    18. Kobberling, Veronika & Wakker, Peter P., 2005. "An index of loss aversion," Journal of Economic Theory, Elsevier, vol. 122(1), pages 119-131, May.
    19. 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.
    20. Battalio, Raymond C & Kagel, John H & Jiranyakul, Komain, 1990. "Testing between Alternative Models of Choice under Uncertainty: Some Initial Results," Journal of Risk and Uncertainty, Springer, vol. 3(1), pages 25-50, March.
    21. Ballinger, T Parker & Wilcox, Nathaniel T, 1997. "Decisions, Error and Heterogeneity," Economic Journal, Royal Economic Society, vol. 107(443), pages 1090-1105, July.
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    1. Niko Suhonen & Jani Saastamoinen & Mika Linden, 2018. "A dual theory approach to estimating risk preferences in the parimutuel betting market," Empirical Economics, Springer, vol. 54(3), pages 1335-1351, May.

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