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cousin_it comments on Notes on logical priors from the MIRI workshop - Less Wrong
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If you're proposing to treat Omega's words as just observational evidence that isn't connected to math and could turn out one way or the other with probability 50%, I suppose the existing formalizations of UDT already cover such problems. But how does the agent assign probability 50% to a particular math statement made by Omega? If it's more complicated than "the trillionth digit of pi is even", then the agent needs some sort of logical prior over inconsistent theories to calculate the probabilities, and needs to be smart enough to treat these probabilities updatelessly, which brings us back to the questions asked at the beginning of my post... Or maybe I'm missing something, can you specify your proposal in more detail?
Well, I was thinking more in terms of a logical prior over single statements, see my favorite here.
But yeah I guess I was missing the point of the problem.
Also: suppose Omega comes up to you and says "If 1=0 was true I would have given you billion dollars if and only if you would give me 100 dollars if 1=1 was true. 1=1 is true, so can you spare $100?" Does this sound trustworthy? Frankly not, it feels like there's a principle of explosion problem that insists that Omega would have given you all possible amounts of money at once if 1=0 was true.
A formulation that avoids the principle of explosion is "I used some process that I cannot prove the outcome of to pick a digit of pi. If that digit of pi was odd I would have given you a billion dollars iff [etc]."