Decisions, Decisions, Decisions: Can Savage Salvage Everettian Probability?

TL;DR

This paper critically examines Deutsch, Wallace, and Greaves's attempt to derive quantum probabilities in Everettian quantum mechanics through decision theory, raising objections to their analogy with classical decision-making under uncertainty.

Contribution

The paper provides a critical analysis of the Deutsch-Wallace-Greaves decision-theoretic approach to quantum probabilities, highlighting potential flaws in their analogy with classical decision theory.

Findings

Identifies issues with the decision-theoretic derivation of the Born rule

Questions the applicability of classical decision theory to Everettian quantum mechanics

Suggests alternative perspectives on quantum probability foundations

Abstract

Critics object that the Everett view cannot make sense of quantum probabilities, in one or both of two ways: either it cannot make sense of probability at all, or it cannot explain why probability should be governed by the Born rule. David Deutsch has attempted to meet these objections by appealing to an Everettian version of Savage's rational decision theory. Deutsch argues not only that an analogue of classical decision under uncertainty makes sense in an Everett world; but also that under reasonable assumptions, the betting odds of a rational Everettian agent should be constrained by the Born rule. Deutsch's proposal has been defended and developed by David Wallace, and in a different form by Hilary Greaves. In this paper I offer some objections to the Deutsch-Wallace-Greaves argument, focussing in particular on the supposed analogy with classical decision under uncertainty.