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VAuroch comments on Preferences without Existence - Less Wrong
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The point is that this is a derivation for Kolmogorov weighting. These universes are weighted naively; every universe is weighted the same regardless of complexity. From this naive weighting, after you add the nearly-undetectable variations, the Kolmogorov measure falls out naturally.
kokotajlod linked this, which uses the same logic on a more abstract example to demonstrate how the Kolmogorov measure arises. It's significantly better written than my exposition.
Ok, I was completely misunderstanding you.
The claim that we are probably in a complex world makes sense in the naive weighting, but I do not see any motivation to talk about that naive weighting at all, especially since it only seems to make sense in a finite multiverse.
Now I don't understand you. I'll take a stab at guessing your objection and explaining the relevant parts further:
This logical derivation works perfectly well in an infinite universe; it works for all finite description lengths, and that continues in the limit, which is the infinite universe. Every "lawful universe" is the center of a cluster in universe-space, and the size of the cluster is proportional to the simplicity (by the Kolmogorov criterion) of the central universe. This is most easily illustrated in the finite case, but works just as well in the infinite one.
I do implicitly assume that the naive weighting of 'every mathematical object gets exactly one universe' is inherently correct. I don't have any justification for why this should be true, but until I get some I'm happy to treat it as axiomatic.
The conclusion can be summarized as "Assume the naive weighting of universes is true. Then from the inside, the Kolmogorov weighting will appear to be true, and a Bayesian reasoner should treat it as true."
I think I completely understand your position. Thank you for sharing. I agree with it, modulo your axiom that the naive weighting was correct.
All of my objections before were because I did not realize you were using that naive weighting.
I do have two problems with the naive weighting:
First, it has the problem that description length is a man-made construct, and is dependent on your language.
Second, there are predicates we can say about the infinite descriptions which are not measurable, and I am not sure what to do with that.