Quantum Probability and Decision Theory, Revisited

TL;DR

This paper revisits the use of decision theory to address probability in the Everett interpretation of quantum mechanics, analyzing Deutsch's approach and proposing alternatives based on Gleason's Theorem.

Contribution

It provides a comprehensive analysis of decision-theoretic solutions to the probability problem in Everettian quantum mechanics, including new perspectives and alternative proofs.

Findings

Decision theory can effectively derive probability in Everettian quantum mechanics.

Alternative approaches based on Gleason's Theorem are viable for understanding quantum probability.

Implications for decision theory from Everettian quantum mechanics are discussed.

Abstract

An extended analysis is given of the program, originally suggested by Deutsch, of solving the probability problem in the Everett interpretation by means of decision theory. Deutsch's own proof is discussed, and alternatives are presented which are based upon different decision theories and upon Gleason's Theorem. It is argued that decision theory gives Everettians most or all of what they need from `probability'. Some consequences of (Everettian) quantum mechanics for decision theory itself are also discussed.