You’re not talking about Newcomb. In Newcomb, you don’t get any “additional” $1000; these are the only dollars you get, because the $1000000 do magically vanish if you take the “additional” $1000.
CDT, then, isn’t aware of the payoff matrix. It reasons as follows: Either Omega put money in boxes A and B, or only in box B. If Omega put money in both boxes, I’m better off taking both boxes. If Omega put money only in box B, I should also take both boxes instead of only box A. CDT doesn’t deal with the fact that which of these two games it’s playing depends on what it will choose to do in each case.
No, this is false. CDT is the one using the standard payoff matrix, and you are the one refusing to use the standard payoff matrix and substituting your own.
In particular: the money is either already there, or not already there. Once the game has begun, the Predictor is powerless to change things.
The standard payoff matrix for Newcomb is therefore as follows:
Omega predicts you take two boxes, you take two boxes, you get $n>0.
Omega predicts you take two boxes, you take two boxes, you get 0.
Omega predicts you take one box, you take one box, you get $m>n.
Omega predicts you take one box, you take two boxes, you get $m+n>m.
The problem becomes trivial if, as you are doing, you refuse to consider the second and fourth outcomes. However, you are then not playing Newcomb’s Problem.
No, only then am I playing Newcomb. What you’re playing is weak Newcomb, where you assign a probability of x>0 for Omega being wrong, at which point this becomes simple math where CDT will give you the correct result, whatever that may turn out to be.
No, you are assuming that your decision can change what’s in the box, which everybody agrees is wrong: the problem statement is that you cannot change what’s in the million-dollar box.
Also, what you describe as “weak Newcomb” is the standard formulation: Nozick’s original problem stated that the Predictor was “almost always” right. CDT still gives the wrong answer in simple Newcomb, as its decision cannot affect what’s in the box.
Nozick’s original problem stated that the Predictor was “almost always” right.
That’s not the “original problem”, that’s just the fleshed-out introduction to “Newcomb’s Problem and Two Principles of Choice” where he talks about aliens and other stuff that has about as much to do with Newcomb as prisoners have to do with the Prisoner’s Dilemma. Then after outlining some common intuitive answers, he goes on a mathematical tangent and later returns to the question of what one should do in Newcomb with this paragraph:
Now, at last, to return to Newcomb’s example of the predictor. If one believes, for this case, that there is backwards causality, that your choice causes the money to be there or not, that it causes him to have made the prediction that he made, then there is no problem. One takes only what is in the second box. Or if one believes that the way the predictor works is by looking into the future; he, in some sense, sees what you are doing, and hence is no more likely to be wrong about what you do than someone else who is standing there at the time and watching you, and would normally see you, say, open only one box, then there is no problem. You take only what is in the second box. But suppose we establish or take as given that there is no backwards causality, that what you actually decide to do does not affect what he did in the past, that what you actually decide to do is not part of the explanation of why he made the prediction he made. So let us agree that the predictor works as follows: He observes you sometime before you are faced with the choice, examines you with complicated apparatus, etc., and then uses his theory to predict on the basis of this state you were in, what choice you would make later when faced with the choice. Your deciding to do as you do is not part of the explanation of why he makes the prediction he does, though your being in a certain state earlier, is part of the explanation of why he makes the prediction he does, and why you decide as you do.
I believe that one should take what is in both boxes. I fear that the considerations I have adduced thus far will not convince those proponents of taking only what is in the second box. Furthermore I suspect that an adequate solution to this problem will go much deeper than I have yet gone or shall go in this paper. So I want to pose one question. I assume that it is clear that in the vaccine example, the person should not be convinced by the probability argument, and should choose the dominant action. I assume also that it is clear that in the case of the two brothers, the brother should not be convinced by the probability argument offered. The question I should like to put to proponents of taking only what is in the second box in Newcomb’s example (and hence not performing the dominant action) is: what is the difference between Newcomb’s example and the other two examples which make the difference between not following the dominance principle, and following it?
You’re not talking about Newcomb. In Newcomb, you don’t get any “additional” $1000; these are the only dollars you get, because the $1000000 do magically vanish if you take the “additional” $1000.
The payoff matrix for Newcomb is as follows:
You take two boxes, you get $n>0.
You take one box, you get $m>n.
CDT, then, isn’t aware of the payoff matrix. It reasons as follows: Either Omega put money in boxes A and B, or only in box B. If Omega put money in both boxes, I’m better off taking both boxes. If Omega put money only in box B, I should also take both boxes instead of only box A. CDT doesn’t deal with the fact that which of these two games it’s playing depends on what it will choose to do in each case.
No, this is false. CDT is the one using the standard payoff matrix, and you are the one refusing to use the standard payoff matrix and substituting your own.
In particular: the money is either already there, or not already there. Once the game has begun, the Predictor is powerless to change things.
The standard payoff matrix for Newcomb is therefore as follows:
Omega predicts you take two boxes, you take two boxes, you get $n>0.
Omega predicts you take two boxes, you take two boxes, you get 0.
Omega predicts you take one box, you take one box, you get $m>n.
Omega predicts you take one box, you take two boxes, you get $m+n>m.
The problem becomes trivial if, as you are doing, you refuse to consider the second and fourth outcomes. However, you are then not playing Newcomb’s Problem.
No, only then am I playing Newcomb. What you’re playing is weak Newcomb, where you assign a probability of x>0 for Omega being wrong, at which point this becomes simple math where CDT will give you the correct result, whatever that may turn out to be.
No, you are assuming that your decision can change what’s in the box, which everybody agrees is wrong: the problem statement is that you cannot change what’s in the million-dollar box.
Also, what you describe as “weak Newcomb” is the standard formulation: Nozick’s original problem stated that the Predictor was “almost always” right. CDT still gives the wrong answer in simple Newcomb, as its decision cannot affect what’s in the box.
That’s not the “original problem”, that’s just the fleshed-out introduction to “Newcomb’s Problem and Two Principles of Choice” where he talks about aliens and other stuff that has about as much to do with Newcomb as prisoners have to do with the Prisoner’s Dilemma. Then after outlining some common intuitive answers, he goes on a mathematical tangent and later returns to the question of what one should do in Newcomb with this paragraph:
And yes, I think I can agree with him on this.