First, thanks for explaining your down vote and thereby giving me an opportunity to respond.
We say that Omega is a perfect predictor not because it’s so very reasonable for him to be a perfect predictor, but so that people won’t get distracted in those directions.
The problem is that it is not a fair simplification, it disrupts the dilemma in such a way as to render it trivial. If you set the accuracy of the prediction to %100 many of the other specific details of the problem become largely irrelevant. For example you could then put $999,999.99 into box A and it would still be better to one-box.
It’s effectively the same thing as lowering the amount in box A to zero or raising the amount in box B to infinity. And one could break the problem in the other direction by lowering the accuracy of the prediction to %50 or equalizing the amount in both boxes.
We must disagree about what is the heart of the dilemma. How can it be all about whether Omega is wrong with some fractional probability?
It’s because the probability of a correct prediction must be between %50 and %100 or it breaks the structure of the problem in the sense that it makes the answer trivial to work out.
Rather it’s about whether logic (2-boxing seems logical) and winning are at odds.
I suppose it is true that some people have intuitions that persist in leading them astray even when the probability is set to %100. In that sense it may still have some value if it helps to isolate and illuminate these biases.
Or perhaps whether determinism and choice is at odds, if you are operating outside a deterministic world-view. Or perhaps a third thing, but nothing—in this problem—about what kinds of Omega powers are reasonable or possible. Omega is just a device being used to set up the dilemma.
My objection here doesn’t have to do with whether it is reasonable for Omega to possess such powers but with the over-simplification of the dilemma to the point where it is trivial.
I see we really are talking about different Newcomb “problem”s. I took back my down vote. So one of our problems should have another name, or at least a qualifier.
I suppose it is true that some people have intuitions that persist in leading them astray even when the probability is set to %100. In that sense it may still have some value if it helps to isolate and illuminate these biases.
I don’t think Newcomb’s problem (mine) is so trivial. And I wouldn’t call belief in the triangle inequality a bias.
The contents of box 1 = (a>=0)
The contents of box 2 = (b>=0)
2-boxing is the logical deduction that ((a+b)>=a) and ((a+b)>=b).
I do 1-box, and do agree that this decision is a logical deduction. I find it odd though that this deduction works by repressing another logical deduction and don’t think I’ve ever see this before. I would want to argue that any and every logical path should work without contradiction.
I suppose it is true that some people have intuitions that persist in leading them astray even when the probability is set to %100. In that sense it may still have some value if it helps to isolate and illuminate these biases.
My objection here doesn’t have to do with whether it is reasonable for Omega to possess such powers but with the over-simplification of the dilemma to the point where it is trivial.
Perhaps I can clarify: I specifically intended to simplify the dilemma to the point where it was trivial. There are a few reasons for this, but the primary reason is so I can take the trivial example expressed here, tweak it, and see what happens.
This is not intended to be a solution to any other scenario in which Omega is involved. It is intended to make sure that we all agree that this is correct.
I’m finding “correct” to be a loaded term here. It is correct in the sense that your conclusions follow from your premises, but in my view it bears only a superficial resemblance to Newcomb’s problem. Omega is not defined the way you defined it in Newcomb-like problems and the resulting difference is not trivial.
To really get at the core dilemma of Newcomb’s problem in detail one needs to attempt to work out the equilibrium accuracy (that is the level of accuracy required to make one-boxing and two-boxing have equal expected utility) not just arbitrarily set the accuracy to the upper limit where it is easy to work out that one-boxing wins.
I’m finding “correct” to be a loaded term here. It is correct in the sense that your conclusions follow from your premises, but in my view it bears only a superficial resemblance to Newcomb’s problem.
I don’t care about Newcomb’s problem. This post doesn’t care about Newcomb’s problem. The next step in this line of questioning still doesn’t care about Newcomb’s problem.
So, please, forget about Newcomb’s problem. At some point, way down the line, Newcomb’s problem may show up again, but when it does this:
Omega is not defined the way you defined it in Newcomb-like problems and the resulting difference is not trivial.
Will certainly be taken into account. Namely, it is exactly because the difference is not trivial that I went looking for a trivial example.
The reason you find “correct” to be loaded is probably because you are expecting some hidden “Gotcha!” to pop out. There is no gotcha. I am not trying to trick you. I just want an answer to what I thought was a simple question.
First, thanks for explaining your down vote and thereby giving me an opportunity to respond.
The problem is that it is not a fair simplification, it disrupts the dilemma in such a way as to render it trivial. If you set the accuracy of the prediction to %100 many of the other specific details of the problem become largely irrelevant. For example you could then put $999,999.99 into box A and it would still be better to one-box.
It’s effectively the same thing as lowering the amount in box A to zero or raising the amount in box B to infinity. And one could break the problem in the other direction by lowering the accuracy of the prediction to %50 or equalizing the amount in both boxes.
It’s because the probability of a correct prediction must be between %50 and %100 or it breaks the structure of the problem in the sense that it makes the answer trivial to work out.
I suppose it is true that some people have intuitions that persist in leading them astray even when the probability is set to %100. In that sense it may still have some value if it helps to isolate and illuminate these biases.
My objection here doesn’t have to do with whether it is reasonable for Omega to possess such powers but with the over-simplification of the dilemma to the point where it is trivial.
I see we really are talking about different Newcomb “problem”s. I took back my down vote. So one of our problems should have another name, or at least a qualifier.
I don’t think Newcomb’s problem (mine) is so trivial. And I wouldn’t call belief in the triangle inequality a bias.
The contents of box 1 = (a>=0)
The contents of box 2 = (b>=0)
2-boxing is the logical deduction that ((a+b)>=a) and ((a+b)>=b).
I do 1-box, and do agree that this decision is a logical deduction. I find it odd though that this deduction works by repressing another logical deduction and don’t think I’ve ever see this before. I would want to argue that any and every logical path should work without contradiction.
Perhaps I can clarify: I specifically intended to simplify the dilemma to the point where it was trivial. There are a few reasons for this, but the primary reason is so I can take the trivial example expressed here, tweak it, and see what happens.
This is not intended to be a solution to any other scenario in which Omega is involved. It is intended to make sure that we all agree that this is correct.
I’m finding “correct” to be a loaded term here. It is correct in the sense that your conclusions follow from your premises, but in my view it bears only a superficial resemblance to Newcomb’s problem. Omega is not defined the way you defined it in Newcomb-like problems and the resulting difference is not trivial.
To really get at the core dilemma of Newcomb’s problem in detail one needs to attempt to work out the equilibrium accuracy (that is the level of accuracy required to make one-boxing and two-boxing have equal expected utility) not just arbitrarily set the accuracy to the upper limit where it is easy to work out that one-boxing wins.
I don’t care about Newcomb’s problem. This post doesn’t care about Newcomb’s problem. The next step in this line of questioning still doesn’t care about Newcomb’s problem.
So, please, forget about Newcomb’s problem. At some point, way down the line, Newcomb’s problem may show up again, but when it does this:
Will certainly be taken into account. Namely, it is exactly because the difference is not trivial that I went looking for a trivial example.
The reason you find “correct” to be loaded is probably because you are expecting some hidden “Gotcha!” to pop out. There is no gotcha. I am not trying to trick you. I just want an answer to what I thought was a simple question.