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conchis comments on A Request for Open Problems - Less Wrong
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There are a fair number of formal analyses of Newcomb's problem. I particularly like this one:
D.H. Wolpert and G. Benford, What does Newcomb's paradox teach us? (showing that the standard approaches to the paradox encode fundamentally different - and inconsistent - views about the nature of the decision problem, and clearing up a number of other confusions.)