Strongly related: the Ebborians
Imagine mapping my brain into two interpenetrating networks. For each brain cell, half of it goes to one map and half to the other. For each connection between cells, half of each connection goes to one map and half to the other. We can call these two mapped out halves Manfred One and Manfred Two. Because neurons are classical, as I think, both of these maps change together. They contain the full pattern of my thoughts. (This situation is even more clear in the Ebborians, who can literally split down the middle.)
So how many people am I? Are Manfred One and Manfred Two both people? Of course, once we have two, why stop there - are there thousands of Manfreds in here, with "me" as only one of them? Put like that it sounds a little overwrought - what's really going on here is the question of what physical system corresponds to "I" in english statements like "I wake up." This may matter.
The impact on anthropic probabilities is somewhat straightforward. With everyday definitions of "I wake up," I wake up just once per day no matter how big my head is. But if the "I" in that sentence is some constant-size physical pattern, then "I wake up" is an event that happens more times if my head is bigger. And so using the variable people-number definition, I expect to wake up with a gigantic head.
The impact on decisions is less big. If I'm in this head with a bunch of other Manfreds, we're all on the same page - it's a non-anthropic problem of coordinated decision-making. For example, if I were to make any monetary bets about my head size, and then donate profits to charity, no matter what definition I'm using, I should bet as if my head size didn't affect anthropic probabilities. So to some extent the real point of this effect is that it is a way anthropic probabilities can be ill-defined. On the other hand, what about preferences that depend directly on person-numbers like how to value people with different head sizes? Or for vegetarians, should we care more about cows than chickens, because each cow is more animals than a chicken is?
According to my common sense, it seems like my body has just one person in it. Why does my common sense think that? I think there are two answers, one unhelpful and one helpful.
The first answer is evolution. Having kids is an action that's independent of what physical system we identify with "I," and so my ancestors never found modeling their bodies as being multiple people useful.
The second answer is causality. Manfred One and Manfred Two are causally distinct from two copies of me in separate bodies but the same input/output. If a difference between the two separated copies arose somehow, (reminiscent of Dennett's factual account) henceforth the two bodies would do and say different things and have different brain states. But if some difference arises between Manfred One and Manfred Two, it is erased by diffusion.
Which is to say, the map that is Manfred One is statically the same pattern as my whole brain, but it's causally different. So is "I" the pattern, or is "I" the causal system?
In this sort of situation I am happy to stick with common sense, and thus when I say me, I think the causal system is referring to the causal system. But I'm not very sure.
Going back to the Ebborians, one interesting thing about that post is the conflict between common sense and common sense - it seems like common sense that each Ebborian is equally much one person, but it also seems like common sense that if you looked at an Ebborian dividing, there doesn't seem to be a moment where the amount of subjective experience should change, and so amount of subjective experience should be proportional to thickness. But as it is said, just because there are two opposing ideas doesn't mean one of them is right.
On the questions of subjective experience raised in that post, I think this mostly gets cleared up by precise description an anthropic narrowness. I'm unsure of the relative sizes of this margin and the proof, but the sketch is to replace a mysterious "subjective experience" that spans copies with individual experiences of people who are using a TDT-like theory to choose so that they individually achieve good outcomes given their existence.