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.
You seem to me to be talking about two different things --
(a) - You argue that worlds must have a definite number, because you argue that everything that exists needs have a definite number
(b)- You say that this cardinality must be all that determines the probability of a world being "observed".
Both of these claims are highly suspect to me.
(a) a fuzzy non-fundamental concept needn't have a definite number, and "world" is such a fuzzy non-fundamental concept
(b) I don't see why the number of how many times something exists must equal how many times something is observed. As I said an instance may exist once but be retrieved many times, while another instance may exist once and retrieved less times.
I don't like it being called "existing more" either -- since that's not how the verb "to exist" is typically used, but "observed more" or "experienced more" are good enough for me.
Those numbers don't have to be equal. They only have to be equal in a "many minds" version of "many worlds", where observations are all that exists anyway. More precisely, in Many Minds, the only branching you care about is the branching of observers, and the only "parts of the whole" that are given existential status, are parts of the wavefunction which correspond to experiences. So you never speak of just having ... (read more)