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Antisuji comments on A (very) tentative refutation of Pascal's mugging - Less Wrong
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A word of caution - Solomonoff induction applies to things like the laws of physics, not to all hypotheses. Otherwise, if you flipped a coin 100 times, you would expect to see 100 heads much more often than average, and we don't.
If you flip a coin 15 times, this result:
HHHHHHHHHHHHHHH
is far more probable than this:
HTHTTHTHTTTHHTH
That's because some coins are rigged, and it's much easier to rig a coin to conform the first pattern than the second.
This is true, but doesn't explain why we're more surprised when we see the former than the latter.
I don't think this is actually true. If MileyCyrus successfully predicted the exact sequence of coinflips HTHTTHTHTTTHHTH, wouldn't you be more surprised than if it were HHHHHHHHHHHHHHH?
Of course. When I said "we're more surprised" I was referring to the typical person who hasn't read this discussion thread. In the absence of the above prediction, I would be far more surprised to see HHHHHHHHHHHHHHH than HTHTTHTHTTTHHTH. Once the prediction is made, I become extremely surprised if either sequence appears, but somewhat more surprised by HTHTTHTHTTTHHTH.
Oh, I see. In the case of the typical person, the answer is even easier: Lack of understanding of the conjunction rule of probability. HTHTTHTHTTTHHTH feels more representative of a random series of coin flips, so it is intuitively judged as more probable than HHHHHHHHHHHHHHH.