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shokwave comments on Counterfactual Calculation and Observational Knowledge - Less Wrong
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Which is the case? What do you do if you're uncertain about which is the case?
Your initial read off your calculator tells you with 99% certainty.
Now Omega comes in and asks you to consider the opposite case. It matters how Omega decided what to say to you. If Omega was always going to contradict your calculator, then what Omega says offers no new information. But if Omega essentially had its own calculator, and was always going to tell you the result even if it didn't contradict yours, then the probabilities become 50%.
True, but I'd like to jump in and say that you can still make a probability estimate with limited information - that's the whole point of having probabilities, after all. If you had unlimited information it wouldn't be much of a probability.