Gergei Bana (INRIA, Paris): “The subjectivist agent and his model: an attempt to be rigorous about objective chance and Lewis’s Principal Principle”

Abstract: In this talk, we propose a framework for rigorous analysis of objective chance, the Principal Principle, admissible evidence and related notions. We take special care to separate the subjectivist agent and his model of possible worlds that incorporates objective chance. The model along with objective chance are defined mathematically rigorously. We talk about what mathematical objects correspond to statements concerning the setup of a chancy experiment, what to the outcomes, and what historic evidence is.  We show what kind of mathematical object corresponds to the “chance function”. We then use this model to take a new look at the controversial topic of admissible evidence and the so-called “Big Bad Bug” that worried Lewis. In most of the talk we use finite spaces, but at the end we also indicate how to define the Principal Principle rigorously on arbitrary spaces with arbitrary, possibly continuous distributions.