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How to deal with partially analyzed acts? A proposal

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Abstract

In some situations, a decision is best represented by an incompletely analyzed act : conditionally to a given event A, the consequences of the decision on sub-events are perfectly known and uncertainty becomes probabilizable, whereas the plausibility of this event itself remains vague and the decision outcome on the complementary event Ac is imprecisely known. In this framework, we study an axiomatic decision model and prove a representation theorem. Resulting decision criteria aggregate partial evaluations consisting in : i) the conditional expected utility associated with the analyzed part of the decision ; and ii) the best and worst consequences of its non-analyzed part. The representation theorem is consistent with a wide variety of decision criteria which allows for expressing various degrees of knowledge on (A, Ac) and various types of attitude towards ambiguity and uncertainty. This diversity is taken into account by specific models already existing in the literature. We take advantage of that fact and propose some particular forms of our model incorporating these models as sub-models and moreover expressing various types of beliefs concerning the relative plausibility of the analyzed and the non-analyzed events ranging from probabilities to complete ignorance that include capacities.

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  • Jean-Yves Jaffray & Meglena Jeleva, 2004. "How to deal with partially analyzed acts? A proposal," Cahiers de la Maison des Sciences Economiques v04098, Université Panthéon-Sorbonne (Paris 1).
  • Handle: RePEc:mse:wpsorb:v04098
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    1. Cohen, Michele & Jaffray, Jean-Yves, 1980. "Rational Behavior under Complete Ignorance," Econometrica, Econometric Society, vol. 48(5), pages 1281-1299, July.
    2. Barbera, S. & Barrett, C. R. & Pattanaik, Prasanta K., 1984. "On some axioms for ranking sets of alternatives," Journal of Economic Theory, Elsevier, vol. 33(2), pages 301-308, August.
    3. Schmeidler, David, 1989. "Subjective Probability and Expected Utility without Additivity," Econometrica, Econometric Society, vol. 57(3), pages 571-587, May.
    4. Saini, Krishan G. & Bates, Philip S., 1984. "A survey of the quantitative approaches to country risk analysis," Journal of Banking & Finance, Elsevier, vol. 8(2), pages 341-356, June.
    5. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
    6. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
    7. Wakker, Peter & Tversky, Amos, 1993. "An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-175, October.
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    Cited by:

    1. Emanuele Borgonovo & Veronica Cappelli & Fabio Maccheroni & Massimo Marinacci, 2016. "Model Uncertainty in Risk Analysis and Decision Theory: A Preliminary Investigation," Working Papers 592, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    2. Michèle Cohen & Alain Chateauneuf & Eric Danan & Thibault Gajdos & Raphaël Giraud & Meglena Jeleva & Fabrice Philippe & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2011. "Tribute to Jean-Yves Jaffray," Theory and Decision, Springer, vol. 71(1), pages 1-10, July.
    3. repec:hal:journl:halshs-00664715 is not listed on IDEAS
    4. Peter Wakker, 2011. "Jaffray’s ideas on ambiguity," Theory and Decision, Springer, vol. 71(1), pages 11-22, July.
    5. Michèle Cohen & Alain Chateauneuf & Eric Danan & Thibault Gajdos & Raphaël Giraud & Meglena Jeleva & Fabrice Philippe & Jean-Marc Tallon & Jean-Christophe Vergnaud, 2011. "Tribute to Jean-Yves Jaffray July 22, 1939 - February 26, 2009," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00664715, HAL.

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    Keywords

    Decision making under uncertainty; partially analyzed decisions.;

    JEL classification:

    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty

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