What the decision theoretic account explains is why I should expect to see dark regions in a double slit experiment.
So how does it explain that? How can the imperative to maximize your expected utility, require you to "expect to see" photons to arrive in the dark zones less often than they arrive in the light zones, without it also being true that photons actually arrive in the dark zones less often than they arrive in the light zones?
Sorry. I edited my post to make it clearer before I saw yours, so the part you quoted has now disappeared. Anyway, I'm not entirely on board with the Deutsch-Wallace program, so I'm not going to offer a full defense of their view. I do want to make sure it's clear what they claim to be doing.
Consider a simpler case then the two-slit experiment: a Stern-Gerlach experiment on spin-1/2 particles prepared in the superposition sqrt(1/4) |up> + sqrt(3/4) |down>. Ignoring fuzzy world complications for now, the Everettian says that upon measurement of the pa...
The subject has already been raised in this thread, but in a clumsy fashion. So here is a fresh new thread, where we can discuss, calmly and objectively, the pros and cons of the "Oxford" version of the Many Worlds interpretation of quantum mechanics.
This version of MWI is distinguished by two propositions. First, there is no definite number of "worlds" or "branches". They have a fuzzy, vague, approximate, definition-dependent existence. Second, the probability law of quantum mechanics (the Born rule) is to be obtained, not by counting the frequencies of events in the multiverse, but by an analysis of rational behavior in the multiverse. Normally, a prescription for rational behavior is obtained by maximizing expected utility, a quantity which is calculated by averaging "probability x utility" for each possible outcome of an action. In the Oxford school's "decision-theoretic" derivation of the Born rule, we somehow start with a ranking of actions that is deemed rational, then we "divide out" by the utilities, and obtain probabilities that were implicit in the original ranking.
I reject the two propositions. "Worlds" or "branches" can't be vague if they are to correspond to observed reality, because vagueness results from an object being dependent on observer definition, and the local portion of reality does not owe its existence to how we define anything; and the upside-down decision-theoretic derivation, if it ever works, must implicitly smuggle in the premises of probability theory in order to obtain its original rationality ranking.
Some references:
"Decoherence and Ontology: or, How I Learned to Stop Worrying and Love FAPP" by David Wallace. In this paper, Wallace says, for example, that the question "how many branches are there?" "does not... make sense", that the question "how many branches are there in which it is sunny?" is "a question which has no answer", "it is a non-question to ask how many [worlds]", etc.
"Quantum Probability from Decision Theory?" by Barnum et al. This is a rebuttal of the original argument (due to David Deutsch) that the Born rule can be justified by an analysis of multiverse rationality.