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How to deal with partially analyzed acts? A proposal

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  • Jean-Yves Jaffray

    ()
    (LIP6 -Université Paris 6)

  • Meglena Jeleva

    ()
    (LEN-C3E et EUREQua)

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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Bibliographic Info

Paper provided by Université Panthéon-Sorbonne (Paris 1) in its series Cahiers de la Maison des Sciences Economiques with number v04098.

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Length: 19 pages
Date of creation: Oct 2004
Date of revision:
Handle: RePEc:mse:wpsorb:v04098

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Keywords: Decision making under uncertainty; partially analyzed decisions.;

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  1. David Schmeidler, 1989. "Subjective Probability and Expected Utility without Additivity," Levine's Working Paper Archive 7662, David K. Levine.
  2. Cohen, Michele & Jaffray, Jean-Yves, 1980. "Rational Behavior under Complete Ignorance," Econometrica, Econometric Society, Econometric Society, vol. 48(5), pages 1281-99, July.
  3. Quiggin, John, 1982. "A theory of anticipated utility," Journal of Economic Behavior & Organization, Elsevier, vol. 3(4), pages 323-343, December.
  4. Gilboa, Itzhak & Schmeidler, David, 1989. "Maxmin expected utility with non-unique prior," Journal of Mathematical Economics, Elsevier, vol. 18(2), pages 141-153, April.
  5. Wakker, Peter & Tversky, Amos, 1993. " An Axiomatization of Cumulative Prospect Theory," Journal of Risk and Uncertainty, Springer, vol. 7(2), pages 147-75, October.
  6. 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.
  7. 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.
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