JGWeissman comments on Beauty quips, "I'd shut up and multiply!" - Less Wrong
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I'm confused about how that's supposed to have the same relevant features, so the answer to your question is probably "Yes".
Are you suggesting the following?: Flip a coin. Go out and ask a random passerby what the probability is that the coin came up heads.
If so, you've entirely eliminated Beauty's subjective uncertainty about whether she's been woken up once or more than once, which is putatively relevant to subjective probability.
If the coin is tails, you would ask two random passerbies.
Aha. In that case, I'd say it's analogous, but I might just be granting that since the correct answer there is 1/3 as well. Or are there folks that would answer 1/2 to this scenario?
Yes, the answer is 1/3, because I am more likely to be asked if it was tails. But in the original problem, I am not more likely to be asked, I am just asked more often, so there is no analogy.