Every now and then I see a claim that if there were a uniform weighting of mathematical structures in a Tegmark-like 'verse---whatever that would mean even if we ignore the decision theoretic aspects which really can't be ignored but whatever---that would imply we should expect to find ourselves as Boltzmann mind-computations, or in other words thingies with just enough consciousness to be conscious of nonsensical chaos for a brief instant before dissolving back into nothingness. We don't seem to be experiencing nonsensical chaos, therefore the argument concludes that a uniform weighting is inadequate and an Occamian weighting over structures is necessary, leading to something like UDASSA or eventually giving up and sweeping the remaining confusion into a decision theoretic framework like UDT. (Bringing the dreaded "anthropics" into it is probably a red herring like always; we can just talk directly about patterns and groups of structures or correlated structures given some weighting, and presume human minds are structures or groups of structures much like other structures or groups of structures given that weighting.)
I've seen people who seem very certain of the Boltzmann-inducing properties of uniform weightings for various reasons that I am skeptical of, and others who seemed uncertain of this for reason that sound at least superficially reasonable. Has anyone thought about this enough to give slightly more than just an intuitive appeal? I wouldn't be surprised if everyone has left such 'probabilistic' cosmological reasoning for the richer soils of decision theoretically inspired speculation, and if everyone else never ventured into the realms of such madness in the first place.
(Bringing in something, anything, from the foundations of set theory, e.g. the set theoretic multiverse, might be one way to start, but e.g. "most natural numbers look pretty random and we can use something like Goedel numbering for arbitrary mathematical structures" doesn't seem to say much to me by itself, considering that all of those numbers have rich local context that in their region is very predictable and non-random, if you get my metaphor. Or to stretch the metaphor even further, even if 62534772 doesn't "causally" follow 31256 they might still be correlated in the style of Dust Theory, and what meta-level tools are we going to use to talk about the randomness or "size" of those correlations, especially given that 294682462125 could refer to a mathematical structure of some underspecified "size" (e.g. a mathematically "simple" entire multiverse and not a "complex" human brain computation)? In general I don't see how such metaphors can't just be twisted into meaninglessness or assumptions that I don't follow, and I've never seen clear arguments that don't rely on either such metaphors or just flat out intuition.)
Without having looked closely at the rest of your comment yet:
Here I risk a meaningless map/territory distinction, and yet it seems straightforwardly possible that the local universe---the thing we care about most---is perfectly well modeled by a universal prior, whereas the ensemble---say, a stack of universal prior pancakes infinitely high with each pancake having a unique Turing language along the real number line---is more accurately described with something vaguely like a uniform prior. (I have no idea if this is useful, but maybe this is clearer if it wasn't already painfully sickeningly clear: non-technically, you gotsa cylinder Ensemble made up of infinite infinitely thin mini-cylinder Universes (universal priors), where each mini-cylinder (circle!) is tagged with a "language" that is arbitrarily close to the one above or below it ('close' in the sense that the languages of Scheme and Haskell are closer together than The Way Will Newsome Describes The World and Haskell). (As an extremely gratuitous detail I'm imagining the most commonly used strings in each language scribbled along the circumference of each mini-cylinder in exponentially decreasing font size and branching that goes exactly all the way around the circumference. If you zoom out a little bit to examine continuous sets of mini-cylinders, that slightly-less-mini-cylinder too has its own unique language: it's all overlapping. If you zoom out to just see the whole cylinder you get... nothing! Or, well, everything. If your theory can explain everything you have zero knowledge.)
(In decision theory such a scenario really messes with our notions of timeless control---what does it mean, if anything, to be an equivalent or analogous algorithm of a decision algorithm that is located inside a pancake that is in some far-off part of the pancake stack, and thus written in an entirely different language? It's a reframing of the "controlling copies of you in rocks" question but where it feels more like you should be able to timelessly control the algorithm.)
I don't immediately see how your comment argues against this idea, but again I haven't looked at it closely. (Honestly I immediately very much pattern-matched it to "things that really didn't convince me in the past", but I'll try to see if perhaps I've just been missing something obvious.)