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Unknowns comments on A Proof of Occam's Razor - Less Wrong
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I don't object to the formal correctness of the proof, but the statement it proves is way too weak. Ideally we'd want something that works for complexity but not flubbity. For any Occamian prior you care to build, I can take the first few hypotheses that comprise 99% of its weight, build a new prior that assigns them a weight of 1e-20 combined, and claim it's just as good as yours by Occamian lights.
If we removed the words "on average" from the formulation of your theorem, we'd have a stronger and more useful statement. Kelly's work shows an approach to proving it not just "on average", but for all possible hypothesis lengths.
ETA: I apologize for not objecting to the formal side of things. I just read the proof once again and failed to understand what it even means by "on average".
I started reading some of Kelly's work, and it isn't trying to prove that the less complex hypothesis is more likely to be true, but that by starting from it you converge on the truth more quickly. I'm sure this is right but it isn't what I was looking for.