...it's still a lot more reliable than deduction from first principles...

I know it's been a while since this comment, but I wanted to comment that sound deduction (ie, logical reasoning) on top of correct premises trumps other forms of evidence, even well-controlled, large-sample experiments. Or put another way, the former renders the latter superfluous. We should not simply take anyone's word for the deduction of course - we have to double-check the premises and understand the deduction step by excruciating step. But once one is satisfied that the premises are correct and the deduction is bullet-proof, one can sleep soundly :)

Nothing trumps sound reasoning. The scientific method itself is a result of reasoning, a point well made by Moldbug here: http://unqualified-reservations.blogspot.sg/2010/06/three-homeworks-for-professor-hanson.html

As an analogy, I find fascinating the MWI vs Collapse debate at LW - Eliezer has concluded MWI wins as an outcome of pure reasoning. No empirical evidence required. It will be (is?) wonderful if (when?) we factorize large numbers quickly and that is evidence of MWI, but as above, it would be (is?) superfluous. If the reasoning offered by Eliezer is coherent (I don't know enough to judge), case closed. Please correct me if I have misunderstood. Thanks

Edit: MWI paragraph added.