Stuart_Armstrong comments on Sleeping Beauty gets counterfactually mugged - Less Wrong

1 Post author: Stuart_Armstrong 26 March 2009 11:44AM

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Tags: newcomb decision theory

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Comment author: jimrandomh 26 March 2009 05:02:20PM *  9 points [-]

The Dutch book odds of being in any of these three situations is the same, 1/3. So the expected return is 1/3(£260-£100-£100) = £20

This is where the mistake happens. You forgot that the expected number of decisions you will have to make is 3/2, so the expected return is1/3(£260-£100-£100)*3/2 = £30, not £20. This agrees with the earlier calculation, as it should, and there's no paradox.

Comment author: Stuart_Armstrong 27 March 2009 02:15:17PM 1 point [-]

This is true, of course; but the paradox comes at the moment when you are asked by Omega. There, you are facing a single decision, not a fraction of a decision, and you don't get to multiply by 3/2.

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