Constriction for sets of probabilities

01/13/2023

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by   Michele Caprio, et al.

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Given a set of probability measures 𝒫 representing an agent's knowledge on the elements of a sigma-algebra ℱ, we can compute upper and lower bounds for the probability of any event A∈ℱ of interest. A procedure generating a new assessment of beliefs is said to constrict A if the bounds on the probability of A after the procedure are contained in those before the procedure. It is well documented that (generalized) Bayes' updating does not allow for constriction, for all A∈ℱ <cit.>. In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.