Three kinds of branching universe (DRAFT- do not cite)

In the light of recent work suggesting that the quantum probability rule can be derived in the Everett interpretation via decision theory, I consider what physical features of quantum mechanics make this possible. I analyse the status of the probabiliy rule in three dierent models of branching universes, each somewhat more complicated than the last, and conclude that only in the last model | in which the branching structure, as in quantum mechanics, emerges in a somewhat imprecise way from the underlying physical reality | is it possible to derive a probability rule, or indeed to behave in any rational way at all.