Bayes Rules in Finite Models

Of the many justifications of Bayesianism, most imply some assumption that is not very compelling, like the differentiability or continuity of some auxiliary function. We show how such assumptions can be replaced by weaker assumptions for finite domains. The new assumptions are a non-informative refinement principle and a concept of information independence. These assumptions are weaker than those used in alternative justifications, which is shown by their inadequacy for infinite domains. They are also more compelling.