Eliezer, I agree that it looks like you shouldn't be able to get the Born rule a priori, but I don't think you're acknowledging that the same is true of the "equal probability for all worlds" rule. You need some way to translate a third-person physical view into subjective anticipations, and I don't see how this could use anything other than a priori reasoning at some point.

Also -- if I'm unsure whether my utility function says I should care about worlds in proportion to their Born measure or equally independent of their Born measure, and the latter possibility doesn't tell me what to do, then for practical purposes it drops out and I can pretend it's just the former.