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It is Whether You Win or Lose: The Importance of the Overall Probabilities of Winning or Losing in Risky Choice

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  • John Payne

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    Abstract

    Imagine that you own a five-outcome gamble with the following payoffs and probabilities: ($100, .20; $50, .20; $0, .20; −$25, .20; −$50, .20). What happens when the opportunity to improve such a gamble is provided by a manipulation that adds value to one outcome versus another outcome, particularly when the opportunity to add value to one outcome versus another outcome changes the overall probability of a gain or the overall probability of a loss? Such a choice provides a simple test of the expected utility model (EU), original prospect theory (OPT), and cumulative prospect theory (CPT). A study of risky choices involving 375 respondents indicates that respondents were most sensitive to changes in outcome values that either increased the overall probability of a strict gain or decreased the overall probability of a strict loss. These results indicate more support for OPT rather than CPT and EU under various assumptions about the shape of the utility and value and weighting functions. Most importantly, the main difference between the various expectation models of risky choice occurs for outcomes near the reference value. A second study of risky choice involving 151 respondents again demonstrated the sensitivity of subjects to reducing the probability of a strict loss even at the cost of reduced expected value. Consequently, we argue that theories of how people choose among gambles that involve three or more consequences with both gains and losses need to include measures of the overall probabilities of a gain and of a loss. Copyright Springer Science + Business Media, Inc. 2005

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    File URL: http://hdl.handle.net/10.1007/s11166-005-5831-x
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    Bibliographic Info

    Article provided by Springer in its journal Journal of Risk and Uncertainty.

    Volume (Year): 30 (2005)
    Issue (Month): 1 (January)
    Pages: 5-19

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    Handle: RePEc:kap:jrisku:v:30:y:2005:i:1:p:5-19

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    Web page: http://www.springerlink.com/link.asp?id=100299

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    Keywords: decision; risk; preference;

    References

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    1. Diecidue, E. & Wakker, P.P., 2000. "On the Intuition of Rank-Dependent Utility," Discussion Paper 2000-74, Tilburg University, Center for Economic Research.
    2. John W. Payne & Dan J. Laughhunn & Roy Crum, 1980. "Translation of Gambles and Aspiration Level Effects in Risky Choice Behavior," Management Science, INFORMS, vol. 26(10), pages 1039-1060, October.
    3. Amos Tversky & Daniel Kahneman, 1979. "Prospect Theory: An Analysis of Decision under Risk," Levine's Working Paper Archive 7656, David K. Levine.
    4. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    5. 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.
    6. Camerer, Colin F. & Hogarth, Robin M., 1999. "The Effects of Financial Incentives in Experiments: A Review and Capital-Labor-Production Framework," Working Papers 1059, California Institute of Technology, Division of the Humanities and Social Sciences.
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    Citations

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    Cited by:
    1. Bethany Weber, 2007. "The effects of losses and event splitting on the Allais paradox," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 2, pages 115-125, April.
    2. Kocher, Martin G. & Pahlke, Julius & Trautmann, Stefan T., 2011. "Tempus Fugit: Time Pressure in Risky Decisions," Discussion Papers in Economics 12221, University of Munich, Department of Economics.
    3. 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.
    4. Ulrich Schmidt & Horst Zank, 2011. "A Genuine Foundation for Prospect Theory," The School of Economics Discussion Paper Series 1114, Economics, The University of Manchester.
    5. Shaul Shalvi, 2012. "Dishonestly increasing the likelihood of winning," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 7(3), pages 292-303, May.
    6. David B. Brown & Enrico G. De Giorgi & Melvyn Sim, 2009. "A Satisficing Alternative to Prospect Theory," University of St. Gallen Department of Economics working paper series 2009 2009-09, Department of Economics, University of St. Gallen.
    7. Geiger, Gebhard, 2008. "An axiomatic account of status quo-dependent non-expected utility: Pragmatic constraints on rational choice under risk," Mathematical Social Sciences, Elsevier, vol. 55(2), pages 116-142, March.
    8. Chung, Chia-Shin & Flynn, James & Kuik, Roelof & Staliński, Piotr, 2013. "A single-period inventory placement problem for a supply system with the satisficing objective," European Journal of Operational Research, Elsevier, vol. 224(3), pages 520-529.
    9. Keith Blackburn & David Chivers, 2013. "Fearing the Worst: The Importance of Uncertainty for Inequality," Centre for Growth and Business Cycle Research Discussion Paper Series 182, Economics, The Univeristy of Manchester.
    10. E. Diecidue & Jeroen van de Ven & G.U. Weitzel, 2008. "Shareholders’ expectations, aspiration levels, and mergers," Working Papers 08-06, Utrecht School of Economics.
    11. Enrico G. De Giorgi & David B. Brown & Melvyn Sim, 2010. "Dual representation of choice and aspirational preferences," University of St. Gallen Department of Economics working paper series 2010 2010-07, Department of Economics, University of St. Gallen.
    12. Birnbaum, Michael H., 2007. "Tests of branch splitting and branch-splitting independence in Allais paradoxes with positive and mixed consequences," Organizational Behavior and Human Decision Processes, Elsevier, vol. 102(2), pages 154-173, March.
    13. Peter Brooks & Horst Zank, 2005. "Loss Averse Behavior," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 301-325, December.
    14. Stefan Zeisberger & Thomas Langer & Martin Weber, 2012. "Why does myopia decrease the willingness to invest? Is it myopic loss aversion or myopic loss probability aversion?," Theory and Decision, Springer, vol. 72(1), pages 35-50, January.

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