Probabilism is the theory that rational degrees of belief have the structure of probabilities; conditionalization is the view that rational individuals update their rational degrees of belief by setting their new degree of belief in a given proposition A to the conditional probability P(A|E) = P(A&E)/P(A) upon learning E and nothing stronger.

In the past two decades, philosophers have proved a variety of so-called accuracy-dominance theorems that support Probabilism.  These theorems state that (given certain assumptions about how to measure the accuracy of beliefs), for any set of beliefs that violates Probabilism, there is an alternative set of beliefs that is guaranteed to be more accurate than the original set of beliefs no matter what.  Therefore, beliefs that violate Probabilism are guaranteed to be less accurate than they might be.  I propose a new way of generalising accuracy-dominance arguments to provide support for Conditionalization.