From conditionalization to imaging through the triviality glass

Abstrakt

This paper presents a unified perspective on a range of probabilistic updating methods ranging from conditionalization to imaging techniques. We focus in particular on an imaging method that we call non-Bayesian, because it changes a prior probability in a belief function, in the sense of Dempster-Shafer theory of evidence. We show the effect of combining that non-Bayesian imaging with the so called pignistic transformation, a method that allows to recover a probability from a belief function. Finally, we leverage the results obtained to present a kind of extension of Lewis’s celebrated triviality result to relate Bayesian and non-Bayesian imaging methods. The main methodological path we will follow is algebraic and, thanks to it, we will employ recently introduced modal algebraic models for conditionals and counterfactuals to shed further light on the Bayesian and the non-Bayesian approaches to imaging.