Primitive conditional probabilities, subset relations and comparative regularity

Abstract

Abstract Rational agents seem more confident in any possible event than in an impossible event. But if rational credences are real-valued, then there are some possible events that are assigned 0 credence nonetheless. How do we differentiate these events from impossible events when we order events? De Finetti (1975), Hájek (2012) and Easwaran (2014) suggest that, when ordering events, conditional credences and subset relations are as relevant as unconditional credences. I present a counterexample to all their proposals in this paper. While their proposals order possible and impossible events correctly, they deliver the wrong verdict for disjoint possible events assigned equal positive credence.