Learn-merge invariance of priors: A characterization of the Dirichlet distributions and processes

Learn-merge invariance is a property of prior distributions (related to postulates introduced by the philosophers W. E. Johnson and R. Carnap) which is defined and discussed within the Bayesian learning model. It is shown that this property in its strong formulation characterizes the Dirichlet distributions and processes. Generalizations towards weaker formulations are outlined.