I think I agree, by and large, despite the length of this post.
Whether choice and predictability are mutually exclusive depends on what choice is supposed to mean. The word is not exactly well defined in this context. In some sense, if variable > threshold then A, else B is a choice.
I am not sure where you think I am conflating. As far as I can see, perfect prediction is obviously impossible unless the system in question is deterministic. On the other hand, determinism does not guarantee that perfect prediction is practical or feasible. The computational complexity might be arbitrarily large, even if you have complete knowledge of an algorithm and its input. I can not really see the relevance to my above post.
Finally, I am myself confused as to why you want two different decision theories (CDT and EDT) instead of two different models for the two different problems conflated into the single identifier Newcomb’s paradox. If you assume a perfect predictor, and thus full correlation between prediction and choice, then you have to make sure your model actually reflects that.
Let’s start out with a simple matrix, P/C/1/2 are shorthands for prediction, choice, one-box, two-box.
P1 C1: 1000
P1 C2: 1001
P2 C1: 0
P2 C2: 1
If the value of P is unknown, but independent of C: Dominance principle, C=2, entirely straightforward CDT.
If, however, the value of P is completely correlated with C, then the matrix above is misleading, P and C can not be different and are really only a single variable, which should be wrapped in a single identifier. The matrix you are actually applying CDT to is the following one:
(P&C)1: 1000
(P&C)2: 1
The best choice is (P&C)=1, again by straightforward CDT.
The only failure of CDT is that it gives different, correct solutions to different, problems with a properly defined correlation of prediction and choice. The only advantage of EDT is that it is easier to cheat in this information without noticing it—even when it would be incorrect to do so. It is entirely possible to have a situation where prediction and choice are correlated, but the decision theory is not allowed to know this and must assume that they are uncorrelated. The decision theory should give the wrong answer in this case.
I think I agree, by and large, despite the length of this post.
Whether choice and predictability are mutually exclusive depends on what choice is supposed to mean. The word is not exactly well defined in this context. In some sense, if variable > threshold then A, else B is a choice.
I am not sure where you think I am conflating. As far as I can see, perfect prediction is obviously impossible unless the system in question is deterministic. On the other hand, determinism does not guarantee that perfect prediction is practical or feasible. The computational complexity might be arbitrarily large, even if you have complete knowledge of an algorithm and its input. I can not really see the relevance to my above post.
Finally, I am myself confused as to why you want two different decision theories (CDT and EDT) instead of two different models for the two different problems conflated into the single identifier Newcomb’s paradox. If you assume a perfect predictor, and thus full correlation between prediction and choice, then you have to make sure your model actually reflects that.
Let’s start out with a simple matrix, P/C/1/2 are shorthands for prediction, choice, one-box, two-box.
P1 C1: 1000
P1 C2: 1001
P2 C1: 0
P2 C2: 1
If the value of P is unknown, but independent of C: Dominance principle, C=2, entirely straightforward CDT.
If, however, the value of P is completely correlated with C, then the matrix above is misleading, P and C can not be different and are really only a single variable, which should be wrapped in a single identifier. The matrix you are actually applying CDT to is the following one:
(P&C)1: 1000
(P&C)2: 1
The best choice is (P&C)=1, again by straightforward CDT.
The only failure of CDT is that it gives different, correct solutions to different, problems with a properly defined correlation of prediction and choice. The only advantage of EDT is that it is easier to cheat in this information without noticing it—even when it would be incorrect to do so. It is entirely possible to have a situation where prediction and choice are correlated, but the decision theory is not allowed to know this and must assume that they are uncorrelated. The decision theory should give the wrong answer in this case.
Yes. I was confused, and perhaps added to the confusion.