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Coscott comments on The Ultimate Sleeping Beauty Problem - Less Wrong Discussion
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Comments (39)
If you answered 1/2 to the original Sleeping Beauty Problem, the answer to this one should be reasonable to calculate. The probability of exactly n flips is (1/2)^n, so the probability of an even number of flips is (1/2)^2+(1/2)^4+(1/2)^6...=1/3.
If you answered 1/3 to the original Sleeping Beauty Problem, I do not think that there is any sensible answer to this one. I do not however consider this strong evidence that the answer of 1/3 is incorrect for the original problem. This could be an example of evidence for infinite set atheism. Analyzing this problem requires taking as given that the experiment can actually be repeated an arbitrarily large number of times, and we have thus far seen mostly evidence that this is not possible in our universe.
To expand on this: the thought experiment is a problem for SIA precisely in the sense that the St. Petersburg Paradox is a problem for expected utility. I'm not overly freaked out by either thought experiment.
I agree. I am also not very bothered by this paradox. I just thought it was worth pointing out.
To also expand on this: 1/3 is also the answer to the "which odds should I precommit myself to take" question and uses the same math as SIA to yield that result for the original problem. And so it is also undefined which odds one should take in this problem. Precommitting to odds seems less controversial, so we should transplant our indifference to the apparent paradox there to the problem here.