If Omega didn’t know the outcome of the flip in advance (and is telling the truth), then you should pay if 1/2*U(x+$10,000)+1/2*U(x-100) > U(x).
You could also tell Omega that the bet is riskier than you would have agreed to, but you would have been fine with winning $1,000 if you won, and paying $10 if you lost. (This doesn’t work with anyone other than Omega though—Omega can predict what you’d agree to, and give you $1000 if you win, and ask for $10 if you lose. This would also have to be consistent with you paying the $10 though.)
Good point about risk also being a factor, but just the point in question isn’t how to perform an expected utility calculation, but the justification of it
If Omega didn’t know the outcome of the flip in advance (and is telling the truth), then you should pay if 1/2*U(x+$10,000)+1/2*U(x-100) > U(x).
You could also tell Omega that the bet is riskier than you would have agreed to, but you would have been fine with winning $1,000 if you won, and paying $10 if you lost. (This doesn’t work with anyone other than Omega though—Omega can predict what you’d agree to, and give you $1000 if you win, and ask for $10 if you lose. This would also have to be consistent with you paying the $10 though.)
Good point about risk also being a factor, but just the point in question isn’t how to perform an expected utility calculation, but the justification of it
If I had agreed with Omega about the bet in advance, then I’d pay up. (This covers concerns about risk.)
So, would you pay if the agreement was made, not cleanly ‘in the past’, but time travel was involved?
No. I don’t know the accuracy of the prediction. It’s just that I already know the result of the coin flip.