A formal proof of the born rule from decision-theoretic assumptions [aka: How to Prove the Born Rule]

I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then prove it formally, and lastly consider a number of proposed ``counter-examples'' to show exactly which premises of the argument they violate. (This is a preliminary version of a chapter to appear --- under the title ``How to prove the Born Rule'' --- in Saunders, Barrett, Kent and Wallace, "Many worlds? Everett, quantum theory and reality", forthcoming from Oxford University Press.).