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Houshalter comments on Bayes' Theorem Illustrated (My Way) - Less Wrong
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It would help if you read the links people give you. The situation you've named is essentially that in Pascal's Mugging.
Actually I did. Thats where I got it (after you linked it). And after reading all of that, I still can't find a universal solution to this problem.
Ah. It seemed like you hadn't because rather than use the example there you used a very similar case. I don't know a universal solution either. But it should be clear that the problem exists for non-Bayesians so the dilemma isn't a problem with Bayesianism.