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About partial probabilistic information

Author

Listed:
  • Alain Chateauneuf

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Caroline Ventura

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

Suppose a decision maker (DM) has partial information about certain events of a σ-algebra A belonging to set ε and assesses their likelihood through a capacity v. When is this information probabilistic, i.e. compatible with a probability ? We consider three notions of compatibility with a probability in increasing degree of preciseness. The weakest requires the existence of a probability P on A such that P(E) ≥ v(E) for all E ∈ ε, we then say that v is a probability minorant. A stronger one is to ask that v be a lower probability, that is the infimum of a family of probabilities on A. The strongest notion of compatibility is for v to be an extendable probability, i.e. there exists a probability P on A which coincides with v on A. We give necessary and sufficient conditions on v in each case and, when ε is finite, we provide effective algorithms that check them in a finite number of steps.

Suggested Citation

  • Alain Chateauneuf & Caroline Ventura, 2009. "About partial probabilistic information," Post-Print halshs-00442859, HAL.
    • Handle: RePEc:hal:journl:halshs-00442859
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00442859
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    Keywords

    extensions of set functions; Partial probabilistic information; exact capacity; core; extensions of set functions.; Information probabiliste partielle; capacité exacte; coeur; extensions de fonctions d'ensembles.;
    All these keywords.

    JEL classification:

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

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