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Notes -
I definitely agree that Groisman did it. I think that Groisman's very slight issue with the pre-filling of the box has apparently left a lot of people unconvinced. They're still publishing papers about it!
So, what I think is useful about my framing is that 1) It doesn't have this issue. Everything is very cleanly just in line with the original Sleeping Beauty setup. Alice is still even making her same bets! 2) I think more important than assigning them to Alice and Bob, my setup with the computer communication is demonstrating that Alice is, herself, retaining knowledge of the different probability spaces. You know this, because you can get her to tell you this (through the computer and her own bets). Even if you just had Alice and Bob doing independent experiments, one could very plausibly still go off the deep end of weird anthropics. By forcing all the conceptual distinctions to be contained within one hypothetical brain, I think you're pretty forced to realize that one brain can, indeed, hold different probabilities for different purposes, rather than "updating" your worldview because they sound similar at first glance or whatever weird timeline causality argument you want to twist your brain into.
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