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Dagon comments on Variations on the Sleeping Beauty - Less Wrong Discussion
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Comments (6)
The first one is straightforward. Yes, you get evidence that not (coin heads && unlucky 50%), so it's definitely 33% heads. Would be the same to an outside observer (replace "you" with "the victim" and simply observe whether the victim is killed or not. The problem with SB isn't the probability, but the multiple indistinguishable observations.
The second one re-adds the memory wipe, making it pretty much sleeping beauty. You have received no information - all paths lead to the same observation (you wake up). So the prior holds: probability is 50/50, but interrogation-instance-weighed opportunities for prediction is 33/66 in favor of tails.
With known days, you do have information if woken on Monday. You know it wasn't heads-tails. On Tuesday, if you remember Monday's wake-up, you know it was heads-heads, and if you don't remember monday, you know it wasn't.
Couples: if partner1 is being interrogated, they know it wasn't heads-partner1kill. This is pretty much the same as problem 1 for each of them. Without communication, their existence is irrelevant.
Clones: no new information - outside prior holds. Same as sleeping beauty.
"Tuesday, if you remember Monday's wake-up" - You have no memory of Monday's interrogation because you are memory wiped.
Memory-wiped in the tails case, but not in the heads-heads case, right? If it's heads-heads, you're woken on Monday and nothing happens on Tuesday, so you presumably remember that you were woken and interrogated yesterday.
You are interrogated on Monday, so what happens on Tuesday is irrelevant to the problem for heads-heads. All that matters is what you say when you are being interogated
Probably doesn't matter how you phrase the handling of Monday night if there's no Tuesday interrogation. If you're interrogated on Tuesday, you know it wasn't heads-heads.