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[epistemic status - I'm new to thinking about anthropics, but I don't see any obvious flaws]
If a tree falls on sleeping beauty famously claims to have dissolved the Sleeping Beauty problem - that SB's correct answer just depended on what the reward structure for her answers, and that her actual credance didn't matter.
Several lesswrongers seem unsatisfied with that answer - understandably, given a longstanding commitment to epistemics and Bayesianism!
I would argue that ata did some key work in answering the problem from a purely epistemic perspective.
Recall the question SB is to be asked upon waking:
Each interview consists of one question, “What is your credence now for the proposition that our coin landed heads?”
And one of the bets ata formulated:
Each interview consists of one question, “What is your credence now for the proposition that our coin landed heads?”, and the answer given will be scored according to a logarithmic scoring rule, with the aggregate result corresponding to the number of utilons (converted to dollars, let’s say) she will be penalized after the experiment.
These questions are actually equivalent! A properly calibrated belief is one that is optimal w.r.t to the logarithmic scoring rule.
ata goes on to show that the answer to that question is 1/3. This result, I think, is actually contingent on the meaning of 'aggregate'. If 'aggregate' just means 'sum over all predictions ever', then ata's math checks out, the thirders are right, and the problem is solved.
However, given the premise of SB - in case of tails, she forgets everything that happened on Monday - you could argue for 'aggregate' meaning 'sum over all predictions she remembers making', in which case the correct answer is one half. Or if we include the log score for predictions that she was told she made, (say because the interviewers wrote it down and told her afterwards), then the answer becomes 1/3 again!
So the SB paradox boils down to what you, as an epistemic rationalist, consider the correct way to aggregate the entropy of predictions!
The 'sum over all predictions' seems best to me (and thus I suppose I lean to the 1/3 answer), but I don't have a definitive reason as to why.
I mean, there's nothing wrong with using the log scoring rule. But since the implied probabilities will change depending on how you aggregate the utilities, it doesn't seem to me that it gets us any closer to a truly objective, consequence-free answer -- 'objective probability' is still meaningless here, it all depends on the bet structure.