I like the approach, but I feel you have not given justice to the 1⁄2 position. Some of Nick Bostrom’s work on observer moments is very impressive in this regard; however I’ve been able to show that they imply that Sleeping Beauty can be money pumped.
I would personally take that to show that the 1⁄2 position is just wrong, but it also implies that some who do hold it are not clinging to a position that can be ‘dissolved’ in the way you are saying—they have a position that would result in them taking different odds on the same bets as 1⁄3′s or some 1⁄2′s.
Wei has a UDT approach that is similar to this; I can’t seem to find it, though.
I like the approach, but I feel you have not given justice to the 1⁄2 position. Some of Nick Bostrom’s work on observer moments is very impressive in this regard; however I’ve been able to show that they imply that Sleeping Beauty can be money pumped.
I would personally take that to show that the 1⁄2 position is just wrong, but it also implies that some who do hold it are not clinging to a position that can be ‘dissolved’ in the way you are saying—they have a position that would result in them taking different odds on the same bets as 1⁄3′s or some 1⁄2′s.
Wei has a UDT approach that is similar to this; I can’t seem to find it, though.
This is only true once you have described Beauty’s reward scheme: the whole point of this post is that the probability to use depends on that.