dlthomas comments on A case study in fooling oneself - Less Wrong
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My best understanding of the MWI's take on the Born rule is that the ratio of the number of branches for each outcome to the total number of branches gives you the probability of each outcome. Both numbers must be finite for the division to make sense. If you cannot count branches, you cannot calculate probabilities, reducing the model into just a feel-good narrative (with the Born rule inserted by hand). Refusing to acknowledge this issue is similar to what Mark does in the story.
This is a relevant discussion of the issue.
Is that necessarily true?
If they are infinite, then there should at least be a well-defined way to take a limit (or one of its generalizations), which amounts to nearly the same thing, constructing a sequence of ratios of finite numbers and proving convergence.