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Randaly comments on Bayesian Nights (Rationalist Story Time) - Less Wrong
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This is awesome!
However, you might want to change the idea that the monks guess the traveler's news (i.e. a true/false judgment) to something about probabilities.
I would expect the monks to use some kind of log scoring, and the Prior kills himself if his total score is less than that of any other monk.
As already pointed out, that doesn't mend the perverse incentive that no one wants to be Prior and risk his life constantly. It would make more sense if the worst monk has to kill himself, and the best monk becomes Prior. This is an incentive to be the best and not be the worst.
(And of course, newbies are just 'novices', who aren't subject to the penalties or rewards. They practice until they feel confident they are good enough to compete - and if they aren't, the problem solves itself.)
That is assuming monks value a long life as a simple monk more than a short life as a Prior.
There was a certain invisible university with this problem.