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.Comment: 36 pages. To appear (under the title "How to prove the Born rule") in
Saunders, Barrett, Kent and Wallace, "Many Worlds? Everett, Quantum Theory,
and Reality" (Oxford University Press