Err, no, I’m not deriving the uselessness of either decision theory here. My point is that only the “pure” Newcomb’s problem—where Omega always predicts correctly and the agent knows it—is well-defined. The “noisy” problem, where Omega is known to sometimes guess wrong, is underspecified. The correct solution (that is whether one-boxing or two-boxing is the utility maximizing move) depends on exactly how and why Omega makes mistakes. Simply saying “probability 0.9 of correct prediction” is insufficient.
But in the “pure” Newcomb’s problem, it seems to me that CDT would actually one-box, reasoning as follows:
Since Omega always predicts correctly, I can assume that it makes its predictions using a full simulation.
Then this situation in which I find myself now (making the decision in Newcomb’s problem) can be either outside or within the simulation. I have no way to know, since it would look the same to me either way.
Therefore I should decide assuming 1⁄2 probability that I am inside Omega’s simulation and 1⁄2 that I am outside.
Err, no, I’m not deriving the uselessness of either decision theory here. My point is that only the “pure” Newcomb’s problem—where Omega always predicts correctly and the agent knows it—is well-defined. The “noisy” problem, where Omega is known to sometimes guess wrong, is underspecified. The correct solution (that is whether one-boxing or two-boxing is the utility maximizing move) depends on exactly how and why Omega makes mistakes. Simply saying “probability 0.9 of correct prediction” is insufficient.
But in the “pure” Newcomb’s problem, it seems to me that CDT would actually one-box, reasoning as follows:
Since Omega always predicts correctly, I can assume that it makes its predictions using a full simulation.
Then this situation in which I find myself now (making the decision in Newcomb’s problem) can be either outside or within the simulation. I have no way to know, since it would look the same to me either way.
Therefore I should decide assuming 1⁄2 probability that I am inside Omega’s simulation and 1⁄2 that I am outside.
So I one-box.