I consider exactly what is involved in a solution to the probability problem of the Everett interpretation, in the light of recent work on applying considerations from decision theory to that problem. I suggest an overall framework for understanding probability in a physical theory, and conclude that this framework, when applied to the Everett interpretation, yields the result that that interpretation satisfactorily solves the measurement problem. Introduction What is probability? 2.1 Objective probability and the Principal Principle 2.2 Three ways of (...) satisfying the functional definition 2.3 Cautious functionalism 2.4 Is the functional definition complete? The Everett interpretation and subjective uncertainty 3.1 Interpreting quantum mechanics 3.2 The need for subjective uncertainty 3.3 Saunders' argument for subjective uncertainty 3.4 Objections to Saunders' argument 3.5 Subjective uncertainty again: arguments from interpretative charity 3.6 Quantum weights and the functional definition of probability Rejecting subjective uncertainty 4.1 The fission program 4.2 Against the fission program Justifying the axioms of decision theory 5.1 The primitive status of the decision-theoretic axioms 5.2 Holistic scepticism 5.3 The role of an explanation of decision theory Conclusion. (shrink)

The decision-theoretic account of probability in the Everett or many-worlds interpretation, advanced by David Deutsch and David Wallace, is shown to be circular. Talk of probability in Everett presumes the existence of a preferred basis to identify measurement outcomes for the probabilities to range over. But the existence of a preferred basis can only be established by the process of decoherence, which is itself probabilistic.

The experimental setup of the self-referential quantum measurement, jovially known as the ‘quantum suicide’ or the ‘quantum Russian roulette’ is analyzed from the point of view of the Principal Principle of David Lewis. It is shown that the apparent violation of this principle – relating objective probabilities and subjective chance – in this type of thought experiment is just an illusion due to the usage of some terms and concepts ill-defined in the quantum context. We conclude that even in the (...) case that Everett’s (or some other ‘no-collapse’) theory is a correct description of reality, we can coherently believe in equating subjective credence with objective chance in quantum-mechanical experiments. This is in agreement with results of the research on personal identity in the quantum context by Parfit and Tappenden. (shrink)

By way of an example, Lewis imagines your being invited to join Schrödinger’s cat in its box for an hour. This box will either fill up with deadly poison fumes or not, depending on whether or not some radioactive atom decays, the probability of decay within an hour being 50%. The invitation is accompanied with some further incentive to comply (Lewis sets it up so there is a significant chance of some pretty bad but not life-threatening punishment if you don’t (...) get in the box). Lewis argues that the many minds theory implies that you should get in the box with the cat, despite this making it 50% likely you will die. (shrink)