[Paper Review] Everettian Rationality: defending Deutsch's approach to probability in the Everett interpretation

David Wallace|ArXiv.org|Mar 10, 2003

Quantum Mechanics and Applications16 references4 citations

TL;DR

This paper defends David Deutsch's derivation of the Born rule within the Everett (many-worlds) interpretation of quantum mechanics by showing that decision-theoretic assumptions—when applied to branching worlds—naturally yield probabilistic predictions consistent with quantum mechanics. It establishes that rational agents in a many-worlds framework must assign probabilities according to the Born rule, resolving the quantitative probability problem in Everettian quantum theory.

ABSTRACT

An analysis is made of Deutsch's recent claim to have derived the Born rule from decision-theoretic assumptions. It is argued that Deutsch's proof must be understood in the explicit context of the Everett interpretation, and that in this context, it essentially succeeds. Some comments are made about the criticism of Deutsch's proof by Barnum, Caves, Finkelstein, Fuchs, and Schack; it is argued that the flaw which they point out in the proof does not apply if the Everett interpretation is assumed. A longer version of this paper, entitled "Quantum Probability and Decision Theory, Revisted", is also available online.

Motivation & Objective

• To resolve the quantitative probability problem in the Everett interpretation, where all outcomes occur yet probabilities are empirically observed.
• To defend Deutsch's decision-theoretic derivation of the Born rule against criticisms, particularly those based on non-Everettian assumptions.
• To show that the concept of rational decision-making under uncertainty can be consistently applied to quantum branching, even in a deterministic, unitary framework.
• To establish that the Born rule emerges naturally from decision-theoretic axioms when combined with the Everettian ontology of branching worlds.

Proposed method

• Applies decision theory to quantum mechanics under the Everett interpretation, treating branching events as uncertain outcomes for rational agents.
• Uses axioms including Additivity, Dominance, and Measurement Neutrality to derive a value function over quantum payoffs.
• Proves linearity of the value function via sequences of rational approximations, establishing a probability representation theorem.
• Demonstrates non-contextuality of the value function, showing it depends only on outcome probabilities, not on the specific measurement basis.
• Relies on the Everettian framework to justify subjective uncertainty in branching, enabling the application of classical decision theory.
• Reconciles deterministic unitary evolution with probabilistic predictions by grounding probability in rational choice under branching.

Experimental results

Research questions

• RQ1 Can the Born rule be derived from decision-theoretic principles alone within the Everett interpretation?
• RQ2 How can rational agents assign probabilities to branching outcomes when all outcomes occur?
• RQ3 Why should the Born rule, rather than any other probability assignment, be used in decision-making under quantum branching?
• RQ4 What foundational assumptions are necessary to derive probabilities in a many-worlds setting?
• RQ5 How do criticisms of Deutsch's proof fail when the Everett interpretation is properly assumed?

Key findings

• The value function in Deutsch's decision theory is linear, which allows the derivation of a probability measure over outcomes.
• The probability of a branch is given by the Born rule, as shown by the representation theorem: Pr(x) = V(δx), where δx is the payoff function for outcome x.
• The non-contextuality lemma ensures that the value function depends only on the probability of outcomes, not on the specific measurement context.
• Measurement Neutrality is a defensible assumption in the Everett interpretation, linking the value function to real-world decision-making.
• Critics' objections to Deutsch's proof, such as those by Barnum et al., do not apply when the Everett interpretation is assumed, as they rely on non-Everettian assumptions.
• The paper concludes that rational agents in the Everett interpretation must act as if the Born rule governs probabilities, providing a consistent foundation for quantum probability.