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JGWeissman comments on Frequentist Magic vs. Bayesian Magic - Less Wrong
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Yep, the universal prior should be filed under "science fiction". And you know why it's uncomputable? Because for any computable prior I can create a coin-producing machine that will anticipate and thwart the Bayesian's expectations :-)
The frequentist approach is analogous to a minimax strategy in a game: no matter how malicious the universe is, you still get your 90%. Other, non-minimax strategies inevitably take risks to try and exploit stupid opponents. This connection was formalized by Abraham Wald, who was mentioned by Cyan in the two posts that started this whole affair.
Replying to Wei Dai's post, I still don't know which magic is the stronger one or what "stronger" actually means here. In actual statistical practice, choosing good priors clearly requires skills and techniques that aren't part of the naive Bayesian canon. This creates a doubt in my mind that just won't go away.
This is because you constrained the universe to only being able to present with you sequences of one of two possible values, both of which reveal themselves on first inspection 90% of the time.
Let the universe throw at you a machine that, for all you know, can produce any distribution or pattern of coins with any bias. Try to get your guaranteed 90% making predictions on the bias of those coins from a single flip.