Quantum probabilities are really credences — statements about the best degree of belief we can assign in conditions of uncertainty — rather than statements about truly stochastic dynamics or frequencies in the limit of an infinite number of outcomes.
Sean Carroll in his blog post about the Born rule in MWI.
If you haven't read the paper talked about in the blog post, you should. It doesn't quite do as much as claimed (fully resolve the problems with Born probabilities in Everett quantum), but it is much more clearly argued than the usual forays into Everett (I suspect its the collaboration between the physicist and the philosopher responsible).
In particular, its the cleanest set of assumptions I've seen that lead to a nice Born rule in an Everett situation (Deutsch/Wallace was all sorts of nonsense).
Another month, another rationality quotes thread. The rules are: