Suppose I am deciding now whether to one-box or two-box on the problem. That’s a reasonable supposition, because I am deciding now whether to one-box or two-box. There are a couple possibilities for what Omega could be doing:
Omega observes my brain, and predicts what I am going to do accurately.
Omega makes an inaccurate prediction, probabilistically independent from my behavior.
Omega modifies my brain to a being it knows will one-box or will two-box, then makes the corresponding prediction.
If Omega uses predictive methods that aren’t 100% effective, I’ll treat it as combination of case 1 and 2. If Omega uses very powerful mind-influencing technology that isn’t 100% effective, I’ll treat it as a combination of case 2 and 3.
In case 1 , I should decide now to one-box. In case 2, I should decide now to two-box. In case 3, it doesn’t matter what I decide now.
If Omega is 100% accurate, I know for certain I am in case 1 or case 3. So I should definitely one-box. This is true even if case 1 is vanishingly unlikely.
If Omega is even 99.9% accurate, then I am in some combination of case 1, case 2, or case 3. Whether I should decide now to one-box or two-box depends on the relative probability of case 1 and case 2, ignoring case 3. So even if Omega is very accurate, ensuring that the probability of case 2 is small, if the probability of case 1 is even smaller, I should decide now to two-box.
I mean, I am describing a very specific forecasting technique that you can use to make forecasts right now. Perhaps a more precise version is, you observer children in one of two different preschools, and observe which school they are in. You observe that almost 100% of the children in one preschool end up richer than the children in the other preschool. You are then able to forecast that future children observed in preschool A will grow up to be rich, and future children observed in preschool B will grow up to be poor. You then have a child. Should you bring them to preschool A? (Here I don’t mean have them attend the school. They can simply go to the building at whatever time of day the study was conducted, then leave. That is sufficient to make highly accurate predictions, after all!)
I don’t really know what you mean by “the set A of all factors involved”
Suppose I am deciding now whether to one-box or two-box on the problem. That’s a reasonable supposition, because I am deciding now whether to one-box or two-box. There are a couple possibilities for what Omega could be doing:
Omega observes my brain, and predicts what I am going to do accurately.
Omega makes an inaccurate prediction, probabilistically independent from my behavior.
Omega modifies my brain to a being it knows will one-box or will two-box, then makes the corresponding prediction.
If Omega uses predictive methods that aren’t 100% effective, I’ll treat it as combination of case 1 and 2. If Omega uses very powerful mind-influencing technology that isn’t 100% effective, I’ll treat it as a combination of case 2 and 3.
In case 1 , I should decide now to one-box. In case 2, I should decide now to two-box. In case 3, it doesn’t matter what I decide now.
If Omega is 100% accurate, I know for certain I am in case 1 or case 3. So I should definitely one-box. This is true even if case 1 is vanishingly unlikely.
If Omega is even 99.9% accurate, then I am in some combination of case 1, case 2, or case 3. Whether I should decide now to one-box or two-box depends on the relative probability of case 1 and case 2, ignoring case 3. So even if Omega is very accurate, ensuring that the probability of case 2 is small, if the probability of case 1 is even smaller, I should decide now to two-box.
I mean, I am describing a very specific forecasting technique that you can use to make forecasts right now. Perhaps a more precise version is, you observer children in one of two different preschools, and observe which school they are in. You observe that almost 100% of the children in one preschool end up richer than the children in the other preschool. You are then able to forecast that future children observed in preschool A will grow up to be rich, and future children observed in preschool B will grow up to be poor. You then have a child. Should you bring them to preschool A? (Here I don’t mean have them attend the school. They can simply go to the building at whatever time of day the study was conducted, then leave. That is sufficient to make highly accurate predictions, after all!)
I don’t really know what you mean by “the set A of all factors involved”