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Simplifying the Choice between Uncertain Prospects Where Preference is Nonlinear


  • John S. Hammond, III

    (Harvard Business School)


This work makes analytical progress in reducing or avoiding two practical difficulties in using preference or utility theory in the analysis of decisions involving uncertainty: (1) assessing the preference curve, and (2) doing calculations with the resultant curve, which may not have an analytically-convenient functional form. The paper identifies circumstances under which simplifications can be found which overcome these difficulties, while at the same time properly reflecting attitude towards risk in the analysis. It is assumed that a decision-maker must choose between risks w\~ 1 and w\~ 2 . He wishes to make decisions consistent with a preference curve u(\cdot) which exists, but has not necessarily been assessed, so he can choose i to maximize expected preference, Eu(w\~ i ). Most results require that the cumulative probability distribution of w\~ 1 and w\~ 2 cross at most once. The results are widely but not universally applicable. Situations are identified where an easy-to-assess, easy-to-analyze preference curve will serve as a proxy for the decision-maker's own preference curve. These situations permit use of any preferences curve from a class having a specified relationship with the decision-maker's curve. For example, in some instances a negative exponential (constant risk aversion) preference function can be used in place of the decision-maker's curve, and in others an expected value analysis will suffice.

Suggested Citation

  • John S. Hammond, III, 1974. "Simplifying the Choice between Uncertain Prospects Where Preference is Nonlinear," Management Science, INFORMS, vol. 20(7), pages 1047-1072, March.
  • Handle: RePEc:inm:ormnsc:v:20:y:1974:i:7:p:1047-1072
    DOI: 10.1287/mnsc.20.7.1047

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    Cited by:

    1. W. Wong & R. Chan, 2008. "Prospect and Markowitz stochastic dominance," Annals of Finance, Springer, vol. 4(1), pages 105-129, January.
    2. Maynard, Leigh J. & Harper, Jayson K. & Hoffman, Lynn D., 1997. "Impact Of Risk Preferences On Crop Rotation Choice," Agricultural and Resource Economics Review, Northeastern Agricultural and Resource Economics Association, vol. 26(1), pages 1-9, April.
    3. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2013. "Risk-averse and Risk-seeking Investor Preferences for Oil Spot and Futures," Documentos de Trabajo del ICAE 2013-31, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Aug 2013.
    4. Anderson, Jock R., 1974. "Risk Efficiency in the Interpretation of Agricultural Production Research," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 42(03), pages 1-54, September.
    5. Lean, H.H. & McAleer, M.J. & Wong, W.-K., 2010. "Investor preferences for oil spot and futures based on mean-variance and stochastic dominance," Econometric Institute Research Papers EI 2010-37, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    6. Ronny Aboudi & Dominique Thon, 1993. "Expected utility and the siegel paradox: A generalization," Journal of Economics, Springer, vol. 57(1), pages 69-93, February.
    7. Chan, Raymond H. & Clark, Ephraim & Wong, Wing-Keung, 2012. "On the Third Order Stochastic Dominance for Risk-Averse and Risk-Seeking Investors," MPRA Paper 42676, University Library of Munich, Germany.
    8. Bruce A. McCarl & David A. Bessler, 1989. "Estimating An Upper Bound On The Pratt Risk A Version Coefficient When The Utility Function Is Unknown," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 33(1), pages 56-63, April.
    9. repec:hal:wpaper:hal-00813199 is not listed on IDEAS
    10. Wong, Wing-Keung, 2007. "Stochastic dominance and mean-variance measures of profit and loss for business planning and investment," European Journal of Operational Research, Elsevier, vol. 182(2), pages 829-843, October.
    11. Elamin H. Elbasha, 2005. "Risk aversion and uncertainty in cost‐effectiveness analysis: the expected‐utility, moment‐generating function approach," Health Economics, John Wiley & Sons, Ltd., vol. 14(5), pages 457-470, May.
    12. Antonella Basso & Paolo Pianca, 1997. "On the relative efficiency of nth order and DARA stochastic dominance rules," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 207-222.
    13. Drynan, Ross G., 1987. "Sufficient Conditions for Dominance of Simply Related Prospects," Review of Marketing and Agricultural Economics, Australian Agricultural and Resource Economics Society, vol. 55(01), pages 1-12, April.

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