Probability in many-worlds theories

We consider how to define a natural probability distribution over worlds within a simple class of deterministic many-worlds theories. This can help us understand the typical properties of worlds within such states, and hence explain the empirical success of quantum theory within a many-worlds framework. We give three reasonable axioms which lead to the Born rule in the case of quantum theory, and also yield natural results in other cases, including a many-worlds variant of classical stochastic dynamics.