I'm not sure how this solves the measure problem because it's not clear to me how non-equiprobable events are to arise

It's not clear to me either, but then again it's not clear to me in the Everett interpretation. However it works in the Everett interpretation presumably maps nicely back into the MUH. The theory I've proposed suggests that we do a kind of naive count of branches exhibiting unique observer relevant structure, and non-equiprobable outcomes corresponds with the measure of unique branches bearing these outcomes. If we perform a Stern-Gerlach experiment where an electron has 2/3 probability of being measured spin-up, 1/3 spin-down, then we'd expect the full set of all the ways to decompose the quantum state into separate sets of unique decoherent histories with quasiclassical descriptions to be such that the proportion of unique conscious structures of observers seeing spin-up vs spin-down match the expected odds ratio. I'm not sure if my theory commits us to this way of understanding probability, but it's the most obvious thing I can think of.

The origin of interference effects is a mystery in a pure-anthropic-selection based origin of probabilities, if you are looking to derive something like Schrodinger evolution from a deeper theory like MUH.

I think this is what gets explained. Interference effects are what get us quantum weirdness, this is what causes us to think we may be living in an Everettian relative state. The MUH doesn't obviously explain the Hamiltonian, or the Schrodinger equation, and it doesn't (I imagine) easily explain at what level of fine-graining we should expect the physical phenomenology of a branching structure, but it does explain why we'd see this structure at some level.

I would agree, but I don't understand how this is consistent with your structure theory of assigning a single unique consciousness to larger structures that are homomorphic to smaller ones.

This is straightforwardly inconsistent with my theory, I was trying to make sense of your theory on your own terms.

Do you know of a reference where this is accounted for and the usual BB argument still goes through?

Could you put this in other words? I don't think I understand what you're saying, or I'm missing some nuance. It doesn't make sense to me to compare universes to brains, we should be comparing brains to brains. I recognize that the class of BOs who have experiences consistent with being an OO, perhaps have decent reasons to think they OOs, and are currently thinking about the Boltzmann brain problem, is much smaller than the full class of BOs, but we should still expect this restricted class to dominate OOs (in an infinite ergodic universe), because we'd expect Boltzmann brain copies to dominate OO brains for any particular brain, so we'd expect the same for the full class of critical OO consistent brains.

If a cosmic ray or quantum fluctuation can come along and cause really weird memories in OO that are still accompanied by conscious experience, then there are an enormous plurality of BOs that can map onto them

To get a better idea of what I mean, let me refer back to the formalism I introduced in a previous comment. Let's say we're interested in a mental continuity M_a defined by a sequence (B_ak):

M_a := (B_a0, B_a1, ..., B_an)

where the ak's are an enumeration of a set I indexing all of {B_i}. For almost all ordered sequences (B_ak), ak ∈ I, continuity is interrupted. In other words, for almost all (B_ak), M_a ⊕ (B_ak) ∉ {M_J}.

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