Constriction for sets of probabilities

2023/01/13 by Michele Caprio, Teddy Seidenfeld, Caprio, Michele +1 · 4 citations
Arts and Humanities · Computer Science · #60A99 #Epistemology, Ethics, and Metaphysics #FOS: Mathematics #Logic, Reasoning, and Knowledge #Primary: 62A01 #Secondary: 60A10 #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2301.05655

openalex publication_date 2023/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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\inF 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\inF. 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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