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orthonormal comments on Problematic Problems for TDT - Less Wrong
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The version of CDT that I described explicitly should arrive at the uniformly random solution. You don't have to be able to simulate a program all the way through, just able to prove things about its output.
EDIT: Wait, this is wrong. It won't be able to consistently derive an answer, because of the way it acts given such an answer, and so it will go with whatever its default Nash equilibrium is.
Re: your EDIT. Yes, I've had that sort of reaction a couple of times today!
I'm shifting around between "CDT should pick at random, no CDT should pick Box 1, no CDT should use a logical coin, no CDT should pick it's favourite number in the set {1, 2} with probability 1, and hope that the version in the sim has a different favourite number, no, CDT will just go into a loop or collapse in a heap."
I'm also quite clueless how a TDT is supposed to decide if it's told there's a CDT in the sim... This looks like a pretty evil decision problem in its own right.
Well, the thing is that CDT doesn't completely specify a decision theory. I'm confident now that the specific version of CDT that I described would fail to deduce anything and go with its default, but it's hard to speak for CDTs in general on such a self-referential problem.