nshepperd comments on Right for the Wrong Reasons - Less Wrong

14 Post author: katydee 24 January 2013 12:02AM

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Comment author: CronoDAS 24 January 2013 02:20:45AM *  0 points [-]

That suggests a question.

If I flip a fair coin, and it comes up heads, what is the probability of that coin flip, which I already made, having instead been tails? (Approximately) 0, because we've already seen that the coin didn't come up tails, or (approximately) 50%, because it's a fair coin and we have no way of knowing the outcome in advance?

Comment author: nshepperd 24 January 2013 03:01:54AM *  1 point [-]

The relevant number for the purpose of judging the "correctness" of predictions is the probability you should have had at the time of the prediction (ie. the epistemically correct prior). Whether the outcome of the coin flip is heads or tails, the correct prior odds are 1:1, because you had no evidence either way.

If royf bets that katydee will win a fencing bout, and in fact they lose fourteen touches in a row, only to win by forfeit, we should update towards suspecting that royf miscounted the evidence, since such a bad athlete should not have much strong evidence predicting their winning. We should believe that the correct prior probability of katydee winning (from royf's point of view) is lower than royf thought it was.