The point of the quantum mechanics sequence was the contrast between Rationality and Empiricism. Eliezer argues that the rational response to uncertainty when empirical evidence is absent or equipoise is to assign higher probability to the simpler explanation.

Schoolkids often learn about this with Ptolemy vs Copernicus, I believe. It's a much less confusing example.

I think the subtext: was: even professional physicists don't get it.

fixing the physics is not the solution

Exactly, that's not what this post was about. But I did want to present concrete evidence that the central argument is flawed.

If it doesn't happen in canon, I wouldn't mind collaborating on a QM rationalist fanfic.

I don't think that's very relevant in this context. There are other people who aren't enamored with the section on MWI in the sequences, for reasons including those Mitchell outlines here.

If I understand their thinking correctly, people who believe in MWI think decoherence is responsible for the difference between one copy of a person and their almost-duplicate in another branch. So quantum mechanics turns out to play an absolutely fundamental role in any MWI-based account of consciousness, too; and I certainly have objections to the philosophy of identity that results.

But I've always had multiple problems with MWI, even when judging it just by standards appropriate to mathematical physics. Perhaps the majority of MWI advocacy consists of nothing but rhetoric - adopting the stance that "the wavefunction is all there is, and it doesn't collapse". Many exponents of MWI seem to have trouble understanding that relativity and the Born rule pose specific technical challenges to this assertion, and that they must ultimately present an implementation (of relativity) or derivation (of the Born rule) that is endogenous to the no-collapse framework; otherwise, they don't truly have a physical theory.

I find it remarkable that after years of reading about this stuff, the very first time I have seen even the beginning of a satisfactory approach to relativistic MWI is to be found in an obscure comment on an Internet physics forum (see the section called "Semi-local classical illustration"), dating from earlier this year. To me, that says something about the quality of the discourse about MWI - that the problem of relativity has hardly been posed or tackled. MWI fans may disagree with this, they may think that relativity has been given appropriate attention in the past; but my point is that these criticisms of mine are purely on the level of physics, and are about MWI failing to satisfy the minimal standards that must be met in order to have a theory at all.

So the recipe for recovering probabilities in TI is incoherent.

I agree, more or less. For me, TI is significant as the best-known recent attempt to explain QM with retrocausality. But it has several concrete problems and this is one of them. When I liken the status of retrocausal interpretations to that of many-worlds, I have this in mind too.

Consider a matrix-like world, where the Universe is simulated on a classical computer (classical computers can do everything quantum computers can do, if slower). Would you deny that simulated humans can think and act rationally, only because the simulation does not include quantum mechanics? If not, would sim-EY not be able to write the Simquences (less the QM Sequence) which are identical (modulo QM) to the ones here?

You make a compelling case that the reference to QM in the sequences is at least as arbitrary as the fundamental physics of our universe. I'm not sure that this is quite as compelling and incisive a revelation as you believe it to be, especially to those who take Occam's Razor as seriously as Eliezer advocates. I'd actually say that this weakens your claim and that it would be better to argue, as Tim does, that the points Eliezer is trying to express don't come across nearly as well as they could.

It seems to me like the universe could be simulated on a quantum computer without quantum mechanics in the simulation, or even in a classical computer with quantum mechanics in the simulation (though it'd take a lot longer of course). The information processing itself is the important part, not the means of processing. This doesn't detract from your argument, which I agree with, I just wanted to point that out.

This paper might be of interest to you:

Why Everettians Should Appreciate the Transactional Interpretation

Abstract: The attractive feature of the Everett approach is its admirable spirit of approaching the quantum puzzle with a Zen-like "beginner's mind" in order to try to envision what the pure formalism might be saying about quantum reality, even if that journey leads to a strange place. It is argued that the transactional interpretation of quantum mechanics (TI), appropriately interpreted, shares the same motivation and achieves much more, with far fewer conceptual perplexities, by taking into account heretofore overlooked features of the quantum formalism itself (i.e. advanced states). In particular, TI does not need to talk about brain states, consciousness, or observers (rational or otherwise). In its possibilist variant ("PTI"), it shares the realist virtues of treating state vector branches as genuine dynamical entities, without having to explain how or why all of their associated outcomes actually happen (they don't), how to account for a plenitude of counterpart observers in some coherent notion of trans-temporal identity of the bifurcating observers (observers don't bifurcate in TI), nor how the certainty of all outcomes could be consistent with any coherent theory of probability, let alone the Born probability (the Born probability emerges naturally in TI). In short, TI is precisely the one-world interpretation Kent is looking for in his (2010).

Would John Cramer's transactional interpretation require more complexity (at the level of the fundamental laws, rather than the amount of stuff in the universe) than the many worlds interpretation?

Neither the many-worlds interpretation, nor any retrocausal interpretation, has a canonical, ontologically satisfactory, self-contained definition as a theory. In both cases, you will find people who say that the interpretation is just a way of thinking about quantum mechanics, so the calculational procedure is exactly the same as Copenhagen.

If you dig a little deeper, you can find quantum formalisms which are self-contained algorithmically, and which possess some resemblance to the spirit of the interpretations, such as consistent histories (for many worlds) and two-state-vector formalism (for single-world retrocausality). I can't say that one of these is clearly simpler than the other.

By the way, Eliezer's original argument for simplicity of MWI has the following flaw. The comparison is between Everett and Collapse, and we are told Collapse has two axiomatic forms of dynamics - unitary evolution and collapse - where Everett just has one - unitary evolution. But then we learn that we don't know how to derive the Born rule from unitary evolution alone. So to actually use the "theory", you have to bring back collapse anyway, as a separate part of your calculational algorithm!

Roughly what proportion of the physics community backs it?

Retrocausality is a minority preference compared to many worlds, there's no doubt about that. It could be like 1% versus 20%. If you also counted people who are just interested by it, you should add a few more percent.

Is it ... [various technicalities] ?

It is meant to be relativistically local and that takes care of the majority of those questions. Whether it is non-differentiable or non-deterministic would depend on the details of a proper retrocausal theory. For example, Wheeler-Feynman theory is just classical electrodynamics with waves that converge on a point as well as waves that spread from a point, whereas the two-state-vector formalism is stochastic.

I was saying they were tied for (lack of) clarity three years ago.