Rather high. I noticed that the average LW poster is not very well versed in mathematical logic in general and game theory in particular; for example about 80-90% of the posts in this thread are nonsensical, resulting in a large amount of insane strategies in this tournament where most people didn’t think farther than whether to defect only on the very last or on the two last turns, without doing any frickin’ math.
I understand Newcomb very well. When I posted my original question, I had the hypothesis that people here didn’t understand CDT. It turned out that they understood CDT, but not the distinction between actual Newcomb (Omega) and weak Newcomb (empirical evidence), and didn’t realize that the first problem couldn’t exist in causal space, a.k.a reality, and that the second problem is simple calculus based on priors, and if people disagree on whether to one-box or two-box in weak Newcomb, that is a result of different priors, and not of different algorithms.
The claim that actual Newcomb or something suitably close cannot exist in reality is very strong. I wonder how you propose to think about research by Haynes et al. (pdf), which suggests that yes/no decisions may be predicted from brain states as long as 7-10 seconds before the decision is made and with accuracy ranging from 54% to 59% depending on the brain region used (assuming I’m reading their Supplementary Figure 6 correctly). In Newcomb’s problem, the predictor doesn’t need to do much better than chance in order for two-boxing to have lower expectation than one-boxing; in particular, the accuracy obtained by Haynes et al. is good enough.
So … do you really mean to say that it is impossible that the sort of predictions Haynes et al. make could be done in real time in advance of the choice that a person makes in a Newcomb problem?
Huh? It’s not as if my current brain state was influenced by a decision I’m going to make in ten seconds; it’s the decision I make right now that is influenced by my brain state from 10 seconds ago.
So I don’t see your point; a good friend of mine could make a far more accurate prediction than 60%. Hell, you could.
Then let me just re-iterate, I don’t see what about Newcomb you think is impossible.
The Newcomb set-up is just the following:
Predictor tells you that you are going to play a game in which you pick one box or two. Predictor tells you the payouts for those choices under two scenarios: (1) that Predictor predicts you will choose one box and (2) that Predictor predicts you will choose two boxes. Predictor also tells you its success rate (or you are allowed to learn this empirically). Predictor then looks at something about you (behavior, brain states, writings, whatever) and predicts whether you will take one box or two boxes. After the prediction is made and the payouts determined, you make your decision.
Indeed, your decision now does not affect your brain states in the past. Nor does your decision now affect Predictor’s prediction, though your past brain states might depending on how the scenario is realized. And that’s kind of the whole point. What you decide now doesn’t affect the payouts. So, for CDT, you should take both boxes.
Notice, though, that the problem is not pressing unless the expected value of choosing one box is greater than the expected value of choosing two boxes. That is, the problem is not pressing if Predictor’s accuracy is too low.
Now, you have been claiming that Newcomb is impossible. But in your comment here, you seem to be saying that it is really easy to set up. So, I don’t know what you are trying to say cannot exist.
Predictor tells you that you are going to play a game in which you pick one box or two. Predictor tells you the payouts for those choices under two scenarios: (1) that Predictor predicts you will choose one box and (2) that Predictor predicts you will choose two boxes. Predictor also tells you its success rate (or you are allowed to learn this empirically). Predictor then looks at something about you (behavior, brain states, writings, whatever) and predicts whether you will take one box or two boxes. After the prediction is made and the payouts determined, you make your decision.
I prefer the formulation in which Predictor first looks at something about you (without you knowing), makes its prediction and sets the boxes, then presents you with the boxes and tells you the rules of the game (and ideally, you have never heard of it before). Your setting allows you to sidestep the thorny issues peculiar to Newcomb if you have strong enough pre-commitment faculties.
Both ways of setting it up allow pre-commitment solutions. The fact that one might not have thought about such solutions in time to implement them is not relevant to the question of which decision theory one ought to implement.
Why do you think it matters whether you have heard of the game before or whether you know that Predictor (Omega … whatever) is looking?
I admit that your way of setting it up makes a Haynes-style realization of the problem unlikely. But so what? My way of setting it up is still a Newcomb problem. It has every bit of logical / decision theoretical force as your way of setting it up. The point of the problem is to test decision theories. CDT (without pre-commitment) is going to take two boxes on your set-up and also on mine. And that should be enough to say that Newcomb problems are possible. (Nomologically possible, not just metaphysically possible or logically possible.)
What I meant was simply this: if I am told of the rules first, before the prediction is made, and I am capable of precommitment (by which I mean binding my future self to do in the future what I choose for it now) then I can win with CDT. I can reason “if I commit to one-box, Omega will predict I will one-box, so the money will be there”, which is a kind of reasoning CDT allows. I thought the whole point of Newcombe is to give an example where CDT loses and we are forced to use a more sophisticated theory.
I am puzzled by you saying “Both ways of setting it up allow pre-commitment solutions.” If I have never heard of the problem before being presented with the boxes, then how can I precommit?
I confess I thought this was obvious, so the fact that both you and Dave jumped on my statement makes me suspect we have some miscommunication, or that I have some “unknown unknown” misconception on these issues.
I agree that if I know the rules, I can reason “if I commit to one-box, Omega will predict I will one-box, so the money will be there”, and if I don’t know the rules, I can’t reason that way (since I can’t know the relationship between one-boxing and money).
It seems to me that if I don’t know the rules, I can similarly reason “if I commit to doing whatever I can do that gets me the most money, then Omega will predict that I will do whatever I can do that gets me the most money. If Omega sets up the rules such that I believe doing X gets me the most money, and I can do X, then Omega will predict that I will do X, and will act accordingly. In the standard formulation, unpredictably two-boxing gets me the most money, but because Omega is a superior predictor I can’t unpredictably two-box. Predictably one-boxing gets me the second-most money. Because of my precommitment, Omega will predict that upon being informed of the rules I will one-box, and the money will be there. ”
Now, I’m no kind of decision theory expert, so maybe there’s something about CDT that precludes reasoning in this way. So much the worse for CDT if so, since this seems like an entirely straightforward way to reason.
Incidentally, I don’t agree to the connotations of “jumped on.”
Checking the definition, it seems that “jump on” is more negative that I thought it was. I just meant both of you disagreed in similar way and fairly quickly; I didn’t feel reprimanded or attacked.
I do not understand at all the reasoning that follows “if I don’t know the rules”. If you are presented with the two boxes out of the blue and explained the rules then for the first time, there is no commitment to make (you have to decide in the moment) and the prediction has been made before, not after.
The best time to plant a tree is twenty years ago. The second-best time is now.
Similarly, the best time to commit to always doing whatever gets me the most utility in any given situation is at birth, but there’s no reason I shouldn’t commit to it now. I certainly don’t have to wait until someone presents me with two boxes.
Sure, I can and should commit to doing “whatever gets me the most utility”, but this is general and vague. And the detailed reasoning that follows in your parent comment is something I cannot do now if I have no conception of the problem. (In case it is not clear, I am assuming in my version that before being presented with the boxes and explained the rules, I am an innocent person who has never thought of the possibility of my choices being predicted, etc.)
Consider the proposition C: “Given a choice between A1 and A2, if the expected value of A1 exceeds the expected value of A2, I will perform A1.”
If I am too innocent to commit to C, then OK, maybe I’m unable to deal with Newcombe-like problems. But if I can commit to C, then… well, suppose I’ve done so.
Now Omega comes along, and for reasons of its own, it decides it’s going to offer me two boxes, with some cash in them, and the instructions: one-box for N1, or two-box for N2, where N1 > N2. Further, it’s going to put either N1 or N1+N2 in the boxes, depending on what it predicts I will do.
So, first, it must put money in the boxes. Which means, first, it must predict whether I’ll one-box or two-box, given those instructions.
Are we good so far?
Assuming we are: so OK, what is Omega’s prediction?
It seems to me that Omega will predict that I will, hypothetically, reason as follows: ”There are four theoretical possibilities. In order of profit, they are: 1: unpredictably two-box (nets me N1 + N2) 2: predictably one-box (nets me N1) 3: predictably two-box (nets me N2) 4: unpredictably one-box (nets me N2)
So clearly I ought to pick 1, if I can. But can I? Probably not, since Omega is a very good predictor. If I try to pick 1, I will likely end up with 3. Which means the expected value of picking 1 is less than the expected value of picking 2. So I should pick 2, if I can. But can I? Probably, since Omega is a very good predictor. If I try to pick 2, I will likely end up with 2. So I will pick 2.”
And, upon predicting that I will pick 2, Omega will put N1 + N2 in the boxes.
At this point, I have not yet been approached, am innocent, and have no conception of the problem.
Now, Omega approaches me, and what do you know: it was right! That is in fact how I reason once I’m introduced to the problem. So I one-box.
At this point, I would make more money if I two-box, but I am incapable of doing so… I’m not the sort of system that two-boxes. (If I had been, I most likely wouldn’t have reached this point.)
If there’s a flaw in this model, I would appreciate having it pointed out to me.
I agree with what Dave says in his comment, which is basically that you could have a very generic pre-commitment strategy.
But suppose you couldn’t come up with a very generic pre-commitment strategy or that it is really implausible that you could come up with a pre-commitment solution at all before hearing the rules of the game. Would that mean that there are no pre-commitment solutions? No. You’ve already identified a pre-commitment solution. We only seem to disagree about how important it is that the reasoner be able to discover a pre-commitment solution quickly enough to implement it.
What I am saying is that the logic of the problem does not depend on the reasoning capacity of the agent involved. Good reasoning is good reasoning whether the agent can carry it out or not.
If I have a “strong enough” precommitment to do whatever gets me the most money, and Predictor privately sets the payoffs for (1box, 2box) such that 1box > 2box, then Predictor can predict that upon being told the payoffs, I will 1box, and Predictor will therefore set the boxes as for the 1box scenario. Conversely, if Predictor privately sets the payoffs such that 2boxing gets me the most money, then Predictor can predict that upon being told the payoffs I’ll 2box.
So what thorny issues does this delayed specification of the rules prevent me from sidestepping?
Rather high. I noticed that the average LW poster is not very well versed in mathematical logic in general and game theory in particular; for example about 80-90% of the posts in this thread are nonsensical, resulting in a large amount of insane strategies in this tournament where most people didn’t think farther than whether to defect only on the very last or on the two last turns, without doing any frickin’ math.
I understand Newcomb very well. When I posted my original question, I had the hypothesis that people here didn’t understand CDT. It turned out that they understood CDT, but not the distinction between actual Newcomb (Omega) and weak Newcomb (empirical evidence), and didn’t realize that the first problem couldn’t exist in causal space, a.k.a reality, and that the second problem is simple calculus based on priors, and if people disagree on whether to one-box or two-box in weak Newcomb, that is a result of different priors, and not of different algorithms.
The claim that actual Newcomb or something suitably close cannot exist in reality is very strong. I wonder how you propose to think about research by Haynes et al. (pdf), which suggests that yes/no decisions may be predicted from brain states as long as 7-10 seconds before the decision is made and with accuracy ranging from 54% to 59% depending on the brain region used (assuming I’m reading their Supplementary Figure 6 correctly). In Newcomb’s problem, the predictor doesn’t need to do much better than chance in order for two-boxing to have lower expectation than one-boxing; in particular, the accuracy obtained by Haynes et al. is good enough.
So … do you really mean to say that it is impossible that the sort of predictions Haynes et al. make could be done in real time in advance of the choice that a person makes in a Newcomb problem?
Huh? It’s not as if my current brain state was influenced by a decision I’m going to make in ten seconds; it’s the decision I make right now that is influenced by my brain state from 10 seconds ago.
So I don’t see your point; a good friend of mine could make a far more accurate prediction than 60%. Hell, you could.
Then let me just re-iterate, I don’t see what about Newcomb you think is impossible.
The Newcomb set-up is just the following:
Predictor tells you that you are going to play a game in which you pick one box or two. Predictor tells you the payouts for those choices under two scenarios: (1) that Predictor predicts you will choose one box and (2) that Predictor predicts you will choose two boxes. Predictor also tells you its success rate (or you are allowed to learn this empirically). Predictor then looks at something about you (behavior, brain states, writings, whatever) and predicts whether you will take one box or two boxes. After the prediction is made and the payouts determined, you make your decision.
Indeed, your decision now does not affect your brain states in the past. Nor does your decision now affect Predictor’s prediction, though your past brain states might depending on how the scenario is realized. And that’s kind of the whole point. What you decide now doesn’t affect the payouts. So, for CDT, you should take both boxes.
Notice, though, that the problem is not pressing unless the expected value of choosing one box is greater than the expected value of choosing two boxes. That is, the problem is not pressing if Predictor’s accuracy is too low.
Now, you have been claiming that Newcomb is impossible. But in your comment here, you seem to be saying that it is really easy to set up. So, I don’t know what you are trying to say cannot exist.
I prefer the formulation in which Predictor first looks at something about you (without you knowing), makes its prediction and sets the boxes, then presents you with the boxes and tells you the rules of the game (and ideally, you have never heard of it before). Your setting allows you to sidestep the thorny issues peculiar to Newcomb if you have strong enough pre-commitment faculties.
Both ways of setting it up allow pre-commitment solutions. The fact that one might not have thought about such solutions in time to implement them is not relevant to the question of which decision theory one ought to implement.
Why do you think it matters whether you have heard of the game before or whether you know that Predictor (Omega … whatever) is looking?
I admit that your way of setting it up makes a Haynes-style realization of the problem unlikely. But so what? My way of setting it up is still a Newcomb problem. It has every bit of logical / decision theoretical force as your way of setting it up. The point of the problem is to test decision theories. CDT (without pre-commitment) is going to take two boxes on your set-up and also on mine. And that should be enough to say that Newcomb problems are possible. (Nomologically possible, not just metaphysically possible or logically possible.)
What I meant was simply this: if I am told of the rules first, before the prediction is made, and I am capable of precommitment (by which I mean binding my future self to do in the future what I choose for it now) then I can win with CDT. I can reason “if I commit to one-box, Omega will predict I will one-box, so the money will be there”, which is a kind of reasoning CDT allows. I thought the whole point of Newcombe is to give an example where CDT loses and we are forced to use a more sophisticated theory.
I am puzzled by you saying “Both ways of setting it up allow pre-commitment solutions.” If I have never heard of the problem before being presented with the boxes, then how can I precommit?
I confess I thought this was obvious, so the fact that both you and Dave jumped on my statement makes me suspect we have some miscommunication, or that I have some “unknown unknown” misconception on these issues.
I agree that if I know the rules, I can reason “if I commit to one-box, Omega will predict I will one-box, so the money will be there”, and if I don’t know the rules, I can’t reason that way (since I can’t know the relationship between one-boxing and money).
It seems to me that if I don’t know the rules, I can similarly reason “if I commit to doing whatever I can do that gets me the most money, then Omega will predict that I will do whatever I can do that gets me the most money. If Omega sets up the rules such that I believe doing X gets me the most money, and I can do X, then Omega will predict that I will do X, and will act accordingly. In the standard formulation, unpredictably two-boxing gets me the most money, but because Omega is a superior predictor I can’t unpredictably two-box. Predictably one-boxing gets me the second-most money. Because of my precommitment, Omega will predict that upon being informed of the rules I will one-box, and the money will be there. ”
Now, I’m no kind of decision theory expert, so maybe there’s something about CDT that precludes reasoning in this way. So much the worse for CDT if so, since this seems like an entirely straightforward way to reason.
Incidentally, I don’t agree to the connotations of “jumped on.”
Checking the definition, it seems that “jump on” is more negative that I thought it was. I just meant both of you disagreed in similar way and fairly quickly; I didn’t feel reprimanded or attacked.
I do not understand at all the reasoning that follows “if I don’t know the rules”. If you are presented with the two boxes out of the blue and explained the rules then for the first time, there is no commitment to make (you have to decide in the moment) and the prediction has been made before, not after.
The best time to plant a tree is twenty years ago. The second-best time is now.
Similarly, the best time to commit to always doing whatever gets me the most utility in any given situation is at birth, but there’s no reason I shouldn’t commit to it now. I certainly don’t have to wait until someone presents me with two boxes.
Sure, I can and should commit to doing “whatever gets me the most utility”, but this is general and vague. And the detailed reasoning that follows in your parent comment is something I cannot do now if I have no conception of the problem. (In case it is not clear, I am assuming in my version that before being presented with the boxes and explained the rules, I am an innocent person who has never thought of the possibility of my choices being predicted, etc.)
Consider the proposition C: “Given a choice between A1 and A2, if the expected value of A1 exceeds the expected value of A2, I will perform A1.”
If I am too innocent to commit to C, then OK, maybe I’m unable to deal with Newcombe-like problems.
But if I can commit to C, then… well, suppose I’ve done so.
Now Omega comes along, and for reasons of its own, it decides it’s going to offer me two boxes, with some cash in them, and the instructions: one-box for N1, or two-box for N2, where N1 > N2. Further, it’s going to put either N1 or N1+N2 in the boxes, depending on what it predicts I will do.
So, first, it must put money in the boxes.
Which means, first, it must predict whether I’ll one-box or two-box, given those instructions.
Are we good so far?
Assuming we are: so OK, what is Omega’s prediction?
It seems to me that Omega will predict that I will, hypothetically, reason as follows:
”There are four theoretical possibilities. In order of profit, they are:
1: unpredictably two-box (nets me N1 + N2)
2: predictably one-box (nets me N1)
3: predictably two-box (nets me N2)
4: unpredictably one-box (nets me N2)
So clearly I ought to pick 1, if I can.
But can I?
Probably not, since Omega is a very good predictor. If I try to pick 1, I will likely end up with 3. Which means the expected value of picking 1 is less than the expected value of picking 2.
So I should pick 2, if I can.
But can I?
Probably, since Omega is a very good predictor. If I try to pick 2, I will likely end up with 2.
So I will pick 2.”
And, upon predicting that I will pick 2, Omega will put N1 + N2 in the boxes.
At this point, I have not yet been approached, am innocent, and have no conception of the problem.
Now, Omega approaches me, and what do you know: it was right! That is in fact how I reason once I’m introduced to the problem. So I one-box.
At this point, I would make more money if I two-box, but I am incapable of doing so… I’m not the sort of system that two-boxes. (If I had been, I most likely wouldn’t have reached this point.)
If there’s a flaw in this model, I would appreciate having it pointed out to me.
I agree with what Dave says in his comment, which is basically that you could have a very generic pre-commitment strategy.
But suppose you couldn’t come up with a very generic pre-commitment strategy or that it is really implausible that you could come up with a pre-commitment solution at all before hearing the rules of the game. Would that mean that there are no pre-commitment solutions? No. You’ve already identified a pre-commitment solution. We only seem to disagree about how important it is that the reasoner be able to discover a pre-commitment solution quickly enough to implement it.
What I am saying is that the logic of the problem does not depend on the reasoning capacity of the agent involved. Good reasoning is good reasoning whether the agent can carry it out or not.
Also, sorry if I jumped too hard.
Can you expand on the difference here?
If I have a “strong enough” precommitment to do whatever gets me the most money, and Predictor privately sets the payoffs for (1box, 2box) such that 1box > 2box, then Predictor can predict that upon being told the payoffs, I will 1box, and Predictor will therefore set the boxes as for the 1box scenario. Conversely, if Predictor privately sets the payoffs such that 2boxing gets me the most money, then Predictor can predict that upon being told the payoffs I’ll 2box.
So what thorny issues does this delayed specification of the rules prevent me from sidestepping?
See my response to Jonathan.