Valuation of Vague Prospects with Mixed Outcomes

  • David V. Budescu
  • Sara Templin
Part of the Springer Optimization and Its Applications book series (SOIA, volume 21)

Previous work on the joint effects of vagueness in probabilities and outcomes in decisions about risky prospects has documented the decision-makers' (DMs) differential sensitivity to these two sources of imprecision. Budescu et al. [6] report two studies in which DMs provided certainty equivalents (CEs) for precise and vague prospects involving gains or losses. They found (a) higher concern for the precision of the outcomes than that of the probabilities, (b) vagueness seeking for positive outcomes, (c) vagueness avoidance for negative outcomes, and (d) stronger attitudes towards vague gains than for vague losses (see also, [13]). They proposed and tested a new generalization of prospect theory (PT) for options with vaguely specified attributes.

The present work extends this model to the case of vague mixed prospects.We report results of a new experiment where 40 DMs used two methods (direct judgments of numerical CEs, and inferred CEs from a series of pairwise comparisons) of valuation of positive (gains), negative (losses), and mixed (gains and losses) prospects with vague outcomes. The results confirm the previous findings of vagueness seeking in the domain of gains, vagueness avoidance for losses, and stronger effects of vagueness in the domain of gains. The CEs of mixed prospects are also consistent with this pattern. The DMs overvalue prospects with vaguely specified gains and precise losses, and undervalue prospects with precisely specified gains and imprecise losses, relative to mixed prospects with precise parameters. Parameter estimates of the generalized model indicate that in the mixed cases the attitudes to vagueness in the two domains are slightly less pronounced, and they are treated more similarly to each other than in the strictly positive, or negative, cases.


Prospect Theory Negative Component Ambiguity Aversion Certainty Equivalent Elicitation Method 
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  1. 1.
    M. Baucells and F. H. Heukamp. Reevaluation of the results of Levy and Levy (2002a). Organizational Behavior and Human Decision Processes, 94:15–21, 2004.CrossRefGoogle Scholar
  2. 2.
    S. W. Becker and F. O. Brownson. What price ambiguity? On the role of ambiguity in decision making. Journal of Political Economy, 72:62–73, 1964.CrossRefGoogle Scholar
  3. 3.
    M. H. Birnbaum. Evidence against prospect theories in gambles with positive, negative and mixed consequences. Journal of Economic Psychology, 27:737–761, 2006.CrossRefGoogle Scholar
  4. 4.
    H. Bleichrodt, J. L. Pinto, and P. P. Wakker. Making descriptive use of prospect theory to improve the prescriptive use of expected utility. Management Science, 47:1498–1514, 2001.CrossRefGoogle Scholar
  5. 5.
    R. Bostic, R. J. Herrnstein, and R. D. Luce. The effect on the preference-reversal phenomenon of using choice indifferences. Journal of Economic Behavior and Organization, 13:193–212, 1990.CrossRefGoogle Scholar
  6. 6.
    D. V. Budescu, K. M. Kuhn, K. M. Kramer, and T. Johnson. Modeling certainty equivalents for imprecise gambles. Organizational Behavior and Human Decision Processes, 88:748–768, 2002.CrossRefGoogle Scholar
  7. 7.
    D. V. Budescu and T. S. Wallsten. Processing linguistic probabilities: General principles and empirical evidence. In J. R. Busemeyer, R. Hastie, and D. Medin, editors, Decision Making from a Cognitive Perspective, volume 32 of Psychology of Learning and Motivation: Advances in Research and Theory, pages 275–318. Academic Press, San Diego, 1995.Google Scholar
  8. 8.
    D. V. Budescu, S. Weinberg, and T. S. Wallsten. Decisions based on numerically and verbally expressed uncertainties. Journal of Experimental Psychology: Human Performance and Perception, 14:281–294, 1988.CrossRefGoogle Scholar
  9. 9.
    C. Camerer and M. Weber. Recent developments in modeling preferences: Uncertainty and ambiguity. Journal of Risk and Uncertainty, 5:325–370, 1992.MATHCrossRefGoogle Scholar
  10. 10.
    J. T. Casey and J. T. Scholz. Boundary effects of vague risk information on taxpayer decisions. Organizational Behavior and Human Decision Processes, 50:360–394, 1991.CrossRefGoogle Scholar
  11. 11.
    R. A. Chechile and S. F. Butler. Reassessing the testing of generic utility models for mixed gambles. Journal of Risk and Uncertainty, 26:55–76, 2003.MATHCrossRefGoogle Scholar
  12. 12.
    S. P. Curley and J. F. Yates. The center and range of the probability interval as factors affecting ambiguity preferences. Organizational Behavior and Human Decision Processes, 36:273–287, 1985.CrossRefGoogle Scholar
  13. 13.
    N. Du and D. V. Budescu. The effects of imprecise probabilities and outcomes in evaluating investment options. Management Science, 51:1791–1803, 2005.CrossRefGoogle Scholar
  14. 14.
    H. J. Einhorn and R. M. Hogarth. Ambiguity and uncertainty in probabilistic inference. Psychological Review, 92:433–461, 1985.CrossRefGoogle Scholar
  15. 15.
    D. Ellsberg. Risk, ambiguity, and the Savage axioms. Quarterly Journal of Economics, 75:643–669, 1961.CrossRefGoogle Scholar
  16. 16.
    P. Farqhuar. Utility assessment methods. Management Science, 30:1283–1300, 1984.CrossRefMathSciNetGoogle Scholar
  17. 17.
    W. Fellner. Distortion of subjective probabilities as a reaction to uncertainty. Quarterly Journal of Economics, 75:670–694, 1961.CrossRefGoogle Scholar
  18. 18.
    G. W. Fischer and S. A. Hawkins. Strategy compatibility, scale compatibility and the prominence effect. Journal of Experimental Psychology: Human Perception and Performance, 19:580–597, 1993.CrossRefGoogle Scholar
  19. 19.
    P. Gardenfors and N. E. Sahlin. Decision making with unreliable probabilities. British Journal of Mathematical and Statistical Psychology, 36:240–251, 1983.Google Scholar
  20. 20.
    C. González-Vallejo, A. Bonazzi, and A. J. Shapiro. Effects of vague probabilities and of vague payoffs on preference: A model comparison analysis. Journal of Mathematical Psychology, 40:130–140, 1996.MATHCrossRefGoogle Scholar
  21. 21.
    J. Hershey, H. C. Kunreuther, and P. J. Schoemaker. Sources of bias in assessment of utility functions. Management Science, 28:936–954, 1982.MATHCrossRefGoogle Scholar
  22. 22.
    J. Hershey and P. J. Schoemaker. Probability versus certainty equivalence methods in utility measurement: Are they equivalent? Management Science, 31:1213–1231, 1985.CrossRefGoogle Scholar
  23. 23.
    R. M. Hogarth and H. Kunreuther. Risk, ambiguity and insurance. Journal of Risk and Uncertainty, 2:5–35, 1989.CrossRefGoogle Scholar
  24. 24.
    D. Kahneman and A. Tversky. Prospect theory: An analysis of decision under risk. Econometrica, 47:263–291, 1979.MATHCrossRefGoogle Scholar
  25. 25.
    G. Keren and L. E. M. Gerritsen. On the robustness and possible accounts of ambiguity aversion. Acta Psychologica, 103:149–172, 1999.CrossRefGoogle Scholar
  26. 26.
    K. M. Kuhn and D. V. Budescu. The relative importance of probabilities, outcomes, and vagueness in hazard risk decisions. Organizational Behavior and Human Decision Processes, 68:301–317, 1996.CrossRefGoogle Scholar
  27. 27.
    K. M. Kuhn, D. V. Budescu, J. R. Hershey, K. M. Kramer, and A. K. Rantilla. Attribute tradeoffs in low probability/high consequence risks: The joint effects of dimension preference and vagueness. Risk, Decision, and Policy, 4:31–46, 1999.CrossRefGoogle Scholar
  28. 28.
    H. Kunreuther, J. Meszaros, R. M. Hogarth, and M. Spranca. Ambiguity and underwriter decision processes. Journal of Economic Behavior and Organization, 26:337–352, 1995.CrossRefGoogle Scholar
  29. 29.
    I. P. Levin, S. L. Schneider, and G. J. Gaeth. All frames are not created equal: A typology and critical analysis of framing effects. Organizational Behavior and Human Decision Processes, 76:149–188, 1998.CrossRefGoogle Scholar
  30. 30.
    H. Levy and M. Levy. Experimental tests of prospect theory value function: A stochastic dominance approach. Organizational Behavior and Human Decision Processes, 89:1058–1081, 2002.CrossRefGoogle Scholar
  31. 31.
    M. Levy and H. Levy. Prospect theory: Much ado about nothing? Management Science, 48:1334–1349, 2002.CrossRefGoogle Scholar
  32. 32.
    G. Loomes. Different experimental procedures for obtaining valuations of risky actions: Implications for utility theory. Theory and Decision, 25:1–23, 1988.CrossRefMathSciNetGoogle Scholar
  33. 33.
    L. L. Lopes and G. C. Oden. The role of aspiration level in risky choice: A comparison of cumulative prospect theory and SP/A theory. Journal of Mathematical Psychology, 43:286–313, 1999.MATHCrossRefGoogle Scholar
  34. 34.
    R. D. Luce. Utility of Gains and Losses: Measurement-Theoretical and Experimental Approaches. Erlbaum, Mahwah, NJ, 2000.MATHGoogle Scholar
  35. 35.
    M. McCord and R. de Neufville. Lottery equivalents: Reduction of the certainty effect problem in utility assessment. Management Science, 32:56–60, 1986.MATHCrossRefGoogle Scholar
  36. 36.
    B. A. Mellers, S. Chang, M. H. Birnbaum, and L. D. Ordóñez. Preferences, prices, and ratings in risky decision making. Journal of Experimental Psychology: Human Perception and Performance, 18:347–361, 1992.CrossRefGoogle Scholar
  37. 37.
    B. A. Mellers, E. U. Weber, L. D. Ordóñez, and A. D. J. Cooke. Utility invariance despite labile preferences. The Psychology of Learning and Motivation, 32:221–246, 1995.CrossRefGoogle Scholar
  38. 38.
    J. W. Payne. It’s whether you win or lose: The importance of the overall probabilities of winning or losing in risky choice. Journal of Risk and Uncertainty, 30:5–19, 2005.MATHCrossRefGoogle Scholar
  39. 39.
    S. L. Schneider and L. L. Lopes. Reflection in preferences under risk: Who and when may suggest why. Journal of Experimental Psychology: Human Perception and Performance, 12:535–548, 1986.CrossRefGoogle Scholar
  40. 40.
    P. J. H. Schoemaker. Preference for information on probabilities versus prizes: The role of risk-taking attitudes. Journal of Risk and Uncertainty, 2:37–60, 1989.CrossRefGoogle Scholar
  41. 41.
    P. Slovic. Relative importance of probabilities and payoffs in risk taking. Journal of Experimental Psychology, 78:18–27, 1968.Google Scholar
  42. 42.
    P. Slovic. The construction of preferences. American Psychologist, 50:364–371, 1995.CrossRefGoogle Scholar
  43. 43.
    A. Tversky and D. Kahneman. Advances in prospect theory: Cumulative representation of uncertainty. Journal of Risk and Uncertainty, 26:297–323, 1992.CrossRefGoogle Scholar
  44. 44.
    A. Tversky, S. Sattath, and P. Slovic. Contingent weighting in judgment and choice. Psychological Review, 95:371–84, 1988.CrossRefGoogle Scholar
  45. 45.
    A. Tversky, P. Slovic, and D. Kahneman. The causes of preference reversal. The American Economic Review, 80:204–217, 1990.Google Scholar
  46. 46.
    P. P. Wakker. The data of Levy & Levy (2002) “Prospect theory: Much ado about nothing?” actually support prospect theory. Management Science, 49:979–981, 2003.CrossRefGoogle Scholar
  47. 47.
    G. Wu and A. B. Markle. An empirical test of gain-loss separability in prospect theory. Working paper, Graduate School of Business, University of Chicago, IL, 2005.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • David V. Budescu
    • 1
  • Sara Templin
    • 2
  1. 1.Department of PsychologyUniversity of Illinois at Urbana-ChampaignChampaignUSA
  2. 2.Department of PsychologyUniversity of KansasLawrenceUSA

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