You can always count how many instances of something exist in a digital computer. The physical state of the computer is made of a definite number of definite states. There is certainly never any need to say that something exists "more than" something else exists, that's just sloppy language. You can count how many times a function is called, you can count the number of instances of a token, you can count the number of copies of a piece of code; at the level of bits, you can even distinguish between instances of an object and pointers to an object, even if they function similarly within a program, because at the level of bits, a genuine instance contains all the bits in the original, whereas a pointer just contains an address where the original may be found. So yes, I do condemn as absurd this talk of "A existing more than B", as if that could mean something other than "there are more copies of A than there are copies of B".
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...
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.