An axiomatic characterization of Bayes' Rule

This paper provides an axiomatic characterization of Bayes’ Rule that is widely used for updating beliefs. Bayes’ Rule is viewed as a revision rule. Consider an agent whose belief about a set of states is characterized by a point in a unit simplex of appropriate dimension. Now new information emerges that rules out the possible occurrence of some of the states. The revision rule then assigns new probabilities over the subset of states that is not ruled out. The paper provides a set of axioms that characterizes Bayes’ Rule. The main axiom is Path Independence. A revision rule satisfies Path Independence if the probability distribution over any set of states is unaffected by the order in which new information comes in. D 2004 Elsevier B.V. All rights reserved.