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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

Suggested Citation

  • John Payne, 2005. "It is Whether You Win or Lose: The Importance of the Overall Probabilities of Winning or Losing in Risky Choice," Journal of Risk and Uncertainty, Springer, vol. 30(1), pages 5-19, January.
  • Handle: RePEc:kap:jrisku:v:30:y:2005:i:1:p:5-19
    DOI: 10.1007/s11166-005-5831-x
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    References listed on IDEAS

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    Cited by:

    1. Geiger, Gebhard, 2015. "Risk pricing in a non-expected utility framework," European Journal of Operational Research, Elsevier, vol. 246(3), pages 944-948.
    2. 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.
    3. David B. BROWN & Enrico G. DE GIORGI & Melvyn SIM, "undated". "A Satiscing Alternative to Prospect Theory," Swiss Finance Institute Research Paper Series 09-19, Swiss Finance Institute.
    4. 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.
    5. 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.
    6. 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.
    7. Keith Blackburn & David Chivers, 2015. "Fearing the worst: the importance of uncertainty for inequality," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 345-370, October.
    8. Enrico Diecidue & Moshe Levy & Jeroen Ven, 2015. "No aspiration to win? An experimental test of the aspiration level model," Journal of Risk and Uncertainty, Springer, vol. 51(3), pages 245-266, December.
    9. Peter Brooks & Horst Zank, 2005. "Loss Averse Behavior," Journal of Risk and Uncertainty, Springer, vol. 31(3), pages 301-325, December.
    10. Martin G. Kocher & Julius Pahlke & Stefan T. Trautmann, 2013. "Tempus Fugit : Time Pressure in Risky Decisions," Management Science, INFORMS, vol. 59(10), pages 2380-2391, October.
    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. Peter Brooks & Simon Peters & Horst Zank, 2014. "Risk behavior for gain, loss, and mixed prospects," Theory and Decision, Springer, vol. 77(2), pages 153-182, August.
    13. George Wu & Alex B. Markle, 2008. "An Empirical Test of Gain-Loss Separability in Prospect Theory," Management Science, INFORMS, vol. 54(7), pages 1322-1335, July.
    14. Katarzyna Werner & Horst Zank, 2012. "Foundations for Prospect Theory Through Probability Midpoint Consistency," The School of Economics Discussion Paper Series 1210, Economics, The University of Manchester.
    15. Ulrich Schmidt & Horst Zank, 2012. "A genuine foundation for prospect theory," Journal of Risk and Uncertainty, Springer, vol. 45(2), pages 97-113, October.
    16. Manel Baucells & Franz H. Heukamp, 2006. "Stochastic Dominance and Cumulative Prospect Theory," Management Science, INFORMS, vol. 52(9), pages 1409-1423, September.
    17. 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.
    18. David B. Brown & Enrico De Giorgi & Melvyn Sim, 2012. "Aspirational Preferences and Their Representation by Risk Measures," Management Science, INFORMS, vol. 58(11), pages 2095-2113, November.
    19. Chivers, David, 2017. "Success, survive or escape? Aspirations and poverty traps," Journal of Economic Behavior & Organization, Elsevier, vol. 143(C), pages 116-132.
    20. 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.
    21. Venkatraman, Vinod & Payne, John W. & Huettel, Scott A., 2014. "An overall probability of winning heuristic for complex risky decisions: Choice and eye fixation evidence," Organizational Behavior and Human Decision Processes, Elsevier, vol. 125(2), pages 73-87.
    22. E. Diecidue & J. van de Ven & U. Weitzel, 2008. "Shareholders’ expectations, aspiration levels, and mergers," Working Papers 08-06, Utrecht School of Economics.
    23. 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.

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    decision; risk; preference;

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