About partial probabilistic information

Alain Chateauneuf and Caroline Ventura ()
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Caroline Ventura: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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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.

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. (search for similar items in EconPapers)
Date: 2009-07
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00442859v1
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Published in 2009

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Working Paper: About partial probabilistic information (2009)
Working Paper: About partial probabilistic information (2009)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00442859

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