I was reading the Stanford Encyclopedia's entry on Causal Decision Theory after reading this, since I am trying to understand why anyone would argue for taking both boxes. It just seems silly to conclude that taking two boxes is the dominant strategy, given that it has a 0% chance of it yielding $M + $T and a 100% chance of yielding $T. If a strategy has a 0% chance of yielding a higher value than the opposing strategy, then that strategy is not dominant. Saying, "but if a person took two boxes when the computer predicted one box, they would be better off" is irrelevant since that would entail a contradiction, since the problem assumed that this scenario is infeasible. I also don't see how this destroys decision theory, since you only have two choices, get $M or get $T. The other "possibilities," have a 0% chance of occurring. What is the debate really about, then? Is it something to do with how the word "possibility" is being used (e.g., can there be logically possibly outcomes with 0% probabilities?)? Does the fact that the computer "merely predicts" instead of causes create skepticism of the one box option? Of course, this is an unrealistic problem, since maybe perfect prediction is not actually possible without causation, but if the problem is unrealistic, then what is the issue with the rational choice being unrealistic?
I agree with you about the perfect predictor case, but the standard problem assumes that the predictor is very reliable but not perfect. In that case, $0 and $M+K are possibilities, just unlikely.
I have the same critique, then. You only care about expected value, so the dominant strategy is just whatever maximizes expected value. Actually, the strategy that always produces the highest expected value is the definition of a dominant strategy, at least in game theory, but maybe I am preaching to the choir here.
This must be what Peter van Inwagen feels like, since I do not understand what the two box position is. This is what the Stanford Encyclopedia entry says about what the supposed dilemma is,
"Because the outcome of two-boxing is better by $T than the outcome of one-boxing given each prediction, two-boxing dominates one-boxing. Two-boxing is the rational choice according to the principle of dominance."
But this is simply false. I mean, the statement is true if the probabilities of each outcome were equal, but in the problem, they are radically different (e.g., the probability of receiving both the million and the thousand dollars is super low). This just seems like Game Theory 101 to me.
You should write something or schedule a debate with Yudkowsky on FDT. I don’t think it holds up well for the reasons Wolfgang points out but I’d be interested in what you have to say.
Nice! I'm also a one-boxer, but it seems to me that two-boxers should pre-commit to one-boxing. If they do so, then that pre-commitment gurantees that the box will contain a million, and relieves them of the freedom to two-box, therefore allowing them to one-box rationally (by their lights) and win. Pre-commitment allows them to accept that their decision can have a causal effect on the outcome.
When the issue of pre-commitment is made, as I understand it, we are relaxing those conditions. Pre-commitment arises in a variation of the question where you know about the experiment before the prediction is locked in.
Yes, two-boxers would grant that if they can causally influence future predictions by now convincing themselves of one-boxing, then that is the rational strategy even at the cost of them later being compelled to one-box.
So that's a different problem with, unsurprisingly, a different solution!
I wonder how useful it is to debate what is the "correct" decision theory to use here, given that the Newcomb situation is practically impossible and quite possibly self-contradictory. Both sides tend to present their (very strong) arguments, without showing what the flaws are in the other side's arguments. And if you can prove that 1-boxing gives the best result, and can also prove that 2-boxing gives the best result, then your premises must be flawed.
You can prove that two-boxing gives the "best result" only relative to decision-theoretic values that I very much do not share. If I care about maximizing the amount of money that I have, then the best I can do is act such that I'm more likely to have more money. If two-boxers care about something else, then that's their prerogative; as I say in the post, I don't suppose that there must be some common ground between us.
I think both sides are trying to maximise money. 1-boxers think they do that by 1-boxing, 2-boxers think they do that by 2-boxing. Some seem to think that since their strategy maximises money, the other side must not be trying to maximise money. But this seems obviously invalid.
I suppose that I'm just thinking of any attempt to maximize money as acting such that you expect to have the most money. Accordingly, if some decision rule labels the "rational action" as one where you expect to have less money, then that's a decision rule concerned with something apart from having the most money. And everyone agrees that you expect to have more money if you one-box than if you two-box.
I was reading the Stanford Encyclopedia's entry on Causal Decision Theory after reading this, since I am trying to understand why anyone would argue for taking both boxes. It just seems silly to conclude that taking two boxes is the dominant strategy, given that it has a 0% chance of it yielding $M + $T and a 100% chance of yielding $T. If a strategy has a 0% chance of yielding a higher value than the opposing strategy, then that strategy is not dominant. Saying, "but if a person took two boxes when the computer predicted one box, they would be better off" is irrelevant since that would entail a contradiction, since the problem assumed that this scenario is infeasible. I also don't see how this destroys decision theory, since you only have two choices, get $M or get $T. The other "possibilities," have a 0% chance of occurring. What is the debate really about, then? Is it something to do with how the word "possibility" is being used (e.g., can there be logically possibly outcomes with 0% probabilities?)? Does the fact that the computer "merely predicts" instead of causes create skepticism of the one box option? Of course, this is an unrealistic problem, since maybe perfect prediction is not actually possible without causation, but if the problem is unrealistic, then what is the issue with the rational choice being unrealistic?
I agree with you about the perfect predictor case, but the standard problem assumes that the predictor is very reliable but not perfect. In that case, $0 and $M+K are possibilities, just unlikely.
I have the same critique, then. You only care about expected value, so the dominant strategy is just whatever maximizes expected value. Actually, the strategy that always produces the highest expected value is the definition of a dominant strategy, at least in game theory, but maybe I am preaching to the choir here.
This must be what Peter van Inwagen feels like, since I do not understand what the two box position is. This is what the Stanford Encyclopedia entry says about what the supposed dilemma is,
"Because the outcome of two-boxing is better by $T than the outcome of one-boxing given each prediction, two-boxing dominates one-boxing. Two-boxing is the rational choice according to the principle of dominance."
But this is simply false. I mean, the statement is true if the probabilities of each outcome were equal, but in the problem, they are radically different (e.g., the probability of receiving both the million and the thousand dollars is super low). This just seems like Game Theory 101 to me.
You should write something or schedule a debate with Yudkowsky on FDT. I don’t think it holds up well for the reasons Wolfgang points out but I’d be interested in what you have to say.
Nice! I'm also a one-boxer, but it seems to me that two-boxers should pre-commit to one-boxing. If they do so, then that pre-commitment gurantees that the box will contain a million, and relieves them of the freedom to two-box, therefore allowing them to one-box rationally (by their lights) and win. Pre-commitment allows them to accept that their decision can have a causal effect on the outcome.
You can't pre-commit to a choice, because the prediction was made before you found out what the choices are.
When the issue of pre-commitment is made, as I understand it, we are relaxing those conditions. Pre-commitment arises in a variation of the question where you know about the experiment before the prediction is locked in.
Yes, two-boxers would grant that if they can causally influence future predictions by now convincing themselves of one-boxing, then that is the rational strategy even at the cost of them later being compelled to one-box.
So that's a different problem with, unsurprisingly, a different solution!
I wonder how useful it is to debate what is the "correct" decision theory to use here, given that the Newcomb situation is practically impossible and quite possibly self-contradictory. Both sides tend to present their (very strong) arguments, without showing what the flaws are in the other side's arguments. And if you can prove that 1-boxing gives the best result, and can also prove that 2-boxing gives the best result, then your premises must be flawed.
You can prove that two-boxing gives the "best result" only relative to decision-theoretic values that I very much do not share. If I care about maximizing the amount of money that I have, then the best I can do is act such that I'm more likely to have more money. If two-boxers care about something else, then that's their prerogative; as I say in the post, I don't suppose that there must be some common ground between us.
I think both sides are trying to maximise money. 1-boxers think they do that by 1-boxing, 2-boxers think they do that by 2-boxing. Some seem to think that since their strategy maximises money, the other side must not be trying to maximise money. But this seems obviously invalid.
I suppose that I'm just thinking of any attempt to maximize money as acting such that you expect to have the most money. Accordingly, if some decision rule labels the "rational action" as one where you expect to have less money, then that's a decision rule concerned with something apart from having the most money. And everyone agrees that you expect to have more money if you one-box than if you two-box.