A formal proof of the Born rule from decision-theoretic assumptions

TL;DR

This paper provides a rigorous mathematical proof of the Born rule in Everettian quantum mechanics using decision-theoretic assumptions, clarifying the foundational link between quantum probability and decision theory.

Contribution

It formalizes and rigorously proves the decision-theoretic derivation of the Born rule within the Everett interpretation, addressing previous informal arguments.

Findings

The proof confirms the validity of the Born rule under specified decision-theoretic premises.

Counter-examples are analyzed to show which assumptions they violate.

The approach strengthens the theoretical foundation of quantum probability in many-worlds interpretation.

Abstract

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.