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OrphanWilde comments on Zero-sum conversion: a cute trick for decision problems - Less Wrong
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The helpfulness described here is this: The mathematics are simpler. [Xachariah's response explains why.]
Explanations for decision trees can also be simpler. Newcomblike problems become almost trivial to consider from Omega's perspective, for example, even in the counterfactual mugging case.
I can do all the same mathematics without creating an imaginary enemy. The only thing that is changing here is how I choose to describe the mathematics in question to myself. This evidently allows Manfred to feel comfortable doing specific mathematics that he would not be comfortable doing without describing it in terms of a contrived enemy's perspective.