Yes, that was the post I read that generated my current line of questioning.
My reply to Viliam_Bur was phrased in terms of probabilities in a single universe, while your post here is in terms of mathematically possible universes. Let me try to rephrase my point to him in many-worlds language. This is not how I originally thought of the question, though, so I may end up a little muddled in translation.
Taking your original example, where half of the Mathematically Possible Universes start with 1, and the other half with 0. It is certainly possible to imagine a hypothetical Actual Multiverse where, nevertheless, there are 5 billion universes with 1, and only 5 universes with 0. Who knows why - maybe there is some overarching multiversal law we are unaware of, or may it's just random. The point is that there is no a priori reason the Multiverse can't be that way. (It may not even be possible to say that the multiverse probably isn't that way without using Solomonoff Induction or Occam's Razor, the very concepts under question.)
If this were the case, and I were somehow universe-hopping, I would over time come to the conclusion that SI was poorly calibrated and stop using it. This, I think, is basically the many-worlds version of my suggestion to Viliam_Bur. As I said to him, I am not arguing for or against SI, I am just asking knowledge people if there is any evidence that the probablities in this universe, or distributions across the multiverse, are actually in proportion to their information-complexities.
Hmm, I think I see what you mean.
Yes, there's no reason for Solomonoff to be well-calibrated in the end, but once we obtain information that most of the universes starting with 0 do not work, that is data against which most of the hypotheses starting with 0 will fail. At this point, brute solomonoff induction will be obviously inefficient, and we should begin using the heuristic of testing almost only hypotheses starting with 1.
In fact, we're already doing this: We know for a fact that we live in the subset of universes where the acceleration between two... (read more)
If it's worth saying, but not worth its own post (even in Discussion), then it goes here.