Caprio and Seidenfeld

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Constriction for sets of probabilities

Given a set of probability measures \mathcal{P} representing an agent's knowledge on the elements of a sigma-algebra \mathcal{F}, we can compute upper and lower bounds for the probability of any event A\in\mathcal{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\in\mathcal{F}. In this work, we show that constriction can take place with and without evidence being observed, and we characterize these possibilities.