I would very much appreciate critical feedback on this comment, as I have no math background.
First, there is no definite number of "worlds" or "branches". They have a fuzzy, vague, approximate, definition-dependent existence.
Some stuff can no longer influence other stuff due to distance and the locality of physics, whereas in the past it could. As time goes on, this is true of more and more things. For each bit of stuff and each other bit, the question of whether they are or are not in range has a definite answer, whether we know it or not. So what is fuzzy?
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.
Historically, this might be true for Wallace or someone else. But one wouldn't say that measure theory is an interpretation of probability, nor that every mathematical equation with pi has to do with/was derived from observing circles (even when in a historical sense, that is how someone figured some equation out, as that has nothing to do with its applications and what it is consistent with).
The math used might be isomorphic to that used to describe rational actors. But if someone is speaking about it in such terms, even if they are right, they must be missing (or not telling me) the higher level, meta, more abstracted truth that describes why both decision theory and quantum mechanics are describable by this math. Is that higher level explained anywhere?
If someone actually believes that they can "make a quantum coinflip come out a different way by redefining [their] utility function," they are wrong about some things, but their using the same mathematical structure to derive the Born identity and describe rational actors isn't thereby too doubtful.
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.