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My favourite probability problem

Posted By: playBunny
Date: Friday, 28 August 2009, at 11:45 p.m.

In Response To: My favourite probability problem (joe freedman)

In that case it's important to know as exactly as possible what chances the Predictor has of getting it right. All we know at the moment is that it's near-certainty, at least well above 99% success rate. I'm happy to use logic when we're talking about a "near-certainty" but if the discrepancy were great enough then a bit of maths would be in order.

When accepting the $1000, how much risk are you taking if the Predictor is correct exactly 50% of the time. 50% of the time there'll be an empty envelope and 50% of the time it will be $M.

How much risk are you taking if the Predictor is correct exactly 99% of the time. 99% of the time there'll be an empty envelope and 1% of the time it will be $M.

But this Predictor is nearly certain to predict your action. Not predicting a hypothetical action but your actual action. That's what it means for it to be a predictor! If the "well above 99% success rate" is not bogus information then you must project your future action back as part of the Predictor's prior knowledge.

And then you act accordingly. You decline the $1000 and have forced the Predictor to give you the $M by virtue of its success rate - which rate is, effectively, your success rate! ;-)

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