Sorry, I did not get your point about the group and subgroups, or at least not its relevance to the question. I would expect that to derive Born probabilities one has to assign measures to different worlds (how else would you express mathematically that “A world with large amplitude is not multiple identical worlds but a single world that is more real.”?) I agree that counting branches is not the only way to do it, just the most obvious one. Unfortunately, none of the ways of assigning “strength” to different branches seems to work any better than this naive one in deriving the Born rule (that is to say, they do not work at all).
Sorry, I did not get your point about the group and subgroups, or at least not its relevance to the question. I would expect that to derive Born probabilities one has to assign measures to different worlds (how else would you express mathematically that “A world with large amplitude is not multiple identical worlds but a single world that is more real.”?) I agree that counting branches is not the only way to do it, just the most obvious one. Unfortunately, none of the ways of assigning “strength” to different branches seems to work any better than this naive one in deriving the Born rule (that is to say, they do not work at all).