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Misha comments on Yet another Sleeping Beauty - Less Wrong
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Leaving aside the SSA vs. SIA question, which I believe is fundamentally misguided but what do I know, you are incorrect here:
When we make this modification, SIA gives the answer 1/3 (same as without it). SSA gives the answer 1/2 (same as without it). The modification does nothing. In the case of the unlikely observation (which doesn't have to be unlikely, actually -- we can compute the answer in terms of the unknown probability and it cancels out anyway), there is also no difference.
P(HH) = 1/3
P(HT) = 0
P(TH) = 1/3
P(TT) = 1/3
P(H*) = P(HH) + P(HT) = 1/3
Did I make an error? Should all of the probability have been moved to the HH case? If so, why? I understand that SSA essentially just tells you to eliminate the impossible. There is nothing impossible about TT or HH.
If you have another suggestion, I'd like to see it.
Oh, you edited the post (the version I read stated you were using the SIA, and getting the same answer as the SSA). I thought you were saying that with this modification, SIA and SSA gave the same answer, which is false.
I'm not entirely sure what you're saying now, and figuring it out will have to wait until tomorrow. For now, since my objection appears to have been based on a typo, I retract it.
It seems I didn't completely correct my error. Fixed now.
I was saying they gave the same answer. My error was just calling them by the wrong names.