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paulfchristiano comments on Reflection in Probabilistic Logic - Less Wrong
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Posted an edited version in response to some of these issues. Thanks again for the remarks!
(I feel less strongly about the bidirectional implication than you; as math I can see why you would definitely want it, but in practice I am nearly as happy to eat the epsilon of error.)
My concern is more about "leaving money on the table" so to speak. The result with epsilon error would be satisfying if we knew it was impossible to do better.