I think my original post may have been unclear. Sorry about that.
What I meant was not that how accurate omega is impacts what CDC does. What I meant was that the accuracy impacts how much “pick up” you can get from a better theory. So if omega is perfect one boxing get you 1,000,000 vs 1000 from two boxing for an increase of 999,000. If omega is less than perfect, then sometimes the one boxer gets nothing or the two boxer gets 1001000. This brings their average results closer. At some accuracy, P, CDC and the theory which solves the problem and correctly chooses to one box do almost equally well.
Omegas accuracy is related to the information leakage about the choosers decision theory.
What I meant was that the accuracy impacts how much “pick up” you can get from a better theory.
Agreed. Because of the simplicity of Newcomb’s proper, I think this is going to make for an unimpressive graph, though: the rewards are linear in Omega’s accuracy P, so it should just be a simple piecewise function for the clever theory, diverging from the two-boxer at the low accuracy and eventually reaching the increase of $999,000 at P=1.
I think my original post may have been unclear. Sorry about that.
What I meant was not that how accurate omega is impacts what CDC does. What I meant was that the accuracy impacts how much “pick up” you can get from a better theory. So if omega is perfect one boxing get you 1,000,000 vs 1000 from two boxing for an increase of 999,000. If omega is less than perfect, then sometimes the one boxer gets nothing or the two boxer gets 1001000. This brings their average results closer. At some accuracy, P, CDC and the theory which solves the problem and correctly chooses to one box do almost equally well.
Omegas accuracy is related to the information leakage about the choosers decision theory.
Agreed. Because of the simplicity of Newcomb’s proper, I think this is going to make for an unimpressive graph, though: the rewards are linear in Omega’s accuracy P, so it should just be a simple piecewise function for the clever theory, diverging from the two-boxer at the low accuracy and eventually reaching the increase of $999,000 at P=1.