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DanielLC comments on Bayesian Nights (Rationalist Story Time) - Less Wrong
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The Prior replacement doesn't make too much sense, insofar as a moderately large number of monks will have one correct guess by pure chance. The Prior gets to make one guess; the other monks get to make other-monk-quantity of guesses. It doesn't seem terribly rational to replace the Prior due to such random chance.
The monks making bad guesses for self-preservation is also a good point.
It sounds like solomonoff induction. The idea isn't that the one that got the right answer was obviously the best prior. It's that they're the one that matches the new evidence. It's just like how in solomonoff induction, you eliminate all the hypotheses that have been falsified, and leave the ones that just happen to match reality.