The setup is such that muggings and rewards are grouped in pairs, for each coin there is a reward and a mugging, and the decision in the mugging only affects the reward of that same coin. So even if you don’t know where the coin comes from, or whether there are other coins with the same setup, or other coins where you don’t have a calculator, your decision on a mugging for a particular coin doesn’t affect them. If you can manage it, you should pay up only in counterfactuals, situations where you hypothetically observe Omega asserting an incorrect statement.
Recognizing counterfactuals requires that the calculator can be trusted to be more accurate than Omega. If you trust the calculator, the algorithm is that if the calculator disagrees with Omega, you pay up, but if the calculator confirms Omega’s correctness, you refuse to pay (so this confirmation of Omega’s correctness translates into a different decision than just observing Omega’s claim without checking it).
Perhaps in the counterfactual where the logical coin is the opposite of what’s true, the calculator should be assumed to also report the incorrect answer, so that its result will still agree with Omega’s. In this case, the calculator provides no further evidence, there is no point in using it, and you should unconditionally pay up.
Perhaps in the counterfactual where the logical coin is the opposite of what’s true, the calculator should be assumed to also report the incorrect answer, so that its result will still agree with Omega’s. In this case, the calculator provides no further evidence, there is no point in using it, and you should unconditionally pay up.
Yeah, that’s pretty much the assumption made in the post, which goes on to conclude (after a bunch of math) that you should indeed pay up unconditionally. I can’t tell if there’s any disagreement between us...
The setup is such that muggings and rewards are grouped in pairs, for each coin there is a reward and a mugging, and the decision in the mugging only affects the reward of that same coin. So even if you don’t know where the coin comes from, or whether there are other coins with the same setup, or other coins where you don’t have a calculator, your decision on a mugging for a particular coin doesn’t affect them. If you can manage it, you should pay up only in counterfactuals, situations where you hypothetically observe Omega asserting an incorrect statement.
Recognizing counterfactuals requires that the calculator can be trusted to be more accurate than Omega. If you trust the calculator, the algorithm is that if the calculator disagrees with Omega, you pay up, but if the calculator confirms Omega’s correctness, you refuse to pay (so this confirmation of Omega’s correctness translates into a different decision than just observing Omega’s claim without checking it).
Perhaps in the counterfactual where the logical coin is the opposite of what’s true, the calculator should be assumed to also report the incorrect answer, so that its result will still agree with Omega’s. In this case, the calculator provides no further evidence, there is no point in using it, and you should unconditionally pay up.
Yeah, that’s pretty much the assumption made in the post, which goes on to conclude (after a bunch of math) that you should indeed pay up unconditionally. I can’t tell if there’s any disagreement between us...