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The Likelihood Method for Decision under Uncertainty

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  • Mohammed Abdellaoui

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  • Peter Wakker

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Abstract

This paper introduces the likelihood method for decision under uncertainty. The method allows the quantitative determination of subjective beliefs or decision weights without invoking additional separability conditions, and generalizes the Savage–de Finetti betting method. It is applied to a number of popular models for decision under uncertainty. In each case, preference foundations result from the requirement that no inconsistencies are to be revealed by the version of the likelihood method appropriate for the model considered. A unified treatment of subjective decision weights results for most of the decision models popular today. Savage’s derivation of subjective expected utility can now be generalized and simplified. In addition to the intuitive and empirical contributions of the likelihood method, we provide a number of technical contributions: We generalize Savage’s nonatomiticy condition (“P6â€\x9D) and his assumption of (sigma) algebras of events, while fully maintaining his flexibility regarding the outcome set. Derivations of Choquet expected utility and probabilistic sophistication are generalized and simplified similarly. The likelihood method also reveals a common intuition underlying many other conditions for uncertainty, such as definitions of ambiguity aversion and pessimism. Copyright Springer 2005

Suggested Citation

  • Mohammed Abdellaoui & Peter Wakker, 2005. "The Likelihood Method for Decision under Uncertainty," Theory and Decision, Springer, vol. 58(1), pages 3-76, February.
  • Handle: RePEc:kap:theord:v:58:y:2005:i:1:p:3-76
    DOI: 10.1007/s11238-005-8320-4
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    File URL: http://hdl.handle.net/10.1007/s11238-005-8320-4
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    Citations

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    Cited by:

    1. Hill, Brian, 2010. "An additively separable representation in the Savage framework," Journal of Economic Theory, Elsevier, vol. 145(5), pages 2044-2054, September.
    2. 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.
    3. Craig Webb, 2015. "Piecewise additivity for non-expected utility," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 60(2), pages 371-392, October.
    4. Gijs van de Kuilen & Peter P. Wakker, 2011. "The Midweight Method to Measure Attitudes Toward Risk and Ambiguity," Management Science, INFORMS, vol. 57(3), pages 582-598, March.
    5. Ulrich Schmidt & Horst Zank, 2012. "A genuine foundation for prospect theory," Journal of Risk and Uncertainty, Springer, vol. 45(2), pages 97-113, October.
    6. Kopylov, Igor, 2007. "Subjective probabilities on "small" domains," Journal of Economic Theory, Elsevier, vol. 133(1), pages 236-265, March.
    7. Denis Bouyssou & Thierry Marchant, 2011. "Subjective expected utility without preferences," Working Papers hal-00606939, HAL.

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