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arXiv · 2301.05655

Constriction for sets of probabilities

Michele Caprio·Teddy Seidenfeld
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Abstract

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.

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Michele Caprio, Teddy Seidenfeld. 2023-01-13. Constriction for sets of probabilities. https://arxiv.org/abs/2301.05655

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