Well, if you know advance that Omega is more likely to do this than it is to impose a dilemma where it will fill both boxes only if you two-box, then I’d agree that this is an appropriate solution.
I think that if in advance you have a flat probability distribution for what sort of Omega scenarios might occur (Omega is just as likely to fill both boxes only if you would two-box in the first scenario as it is to fill both boxes only if you would one-box,) then this solution doesn’t make sense.
In the transparent Newcomb’s problem, when both boxes are filled, does it benefit you to be the the sort of person who would one-box? No, because you get less money that way. If Omega is more likely to impose the transparent Newcomb’s problem than its inversion, then prior to Omega foisting the problem on you, it does benefit you to be the sort of person who would one-box (and you can’t change what sort of person you are mid-problem.)
If Omega only presents transparent Newcomb’s problems of the first sort, where the box containing more money is filled only if the person presented with the boxes would one-box, then situations where a person is presented with two transparent boxes of money and picks both will never arise. People who would one-box in the transparent Newcomb’s problem come out ahead.
If Omega is equally likely to present transparent Newcomb’s problems of the first sort, or inversions where Omega fills both boxes only for people it predicts would two-box in problems of the first sort, then two-boxers come out ahead, because they’re equally likely to get the contents of the box with more money, but always get the box with less money, while the one-boxers never do.
You can always contrive scenarios to reward or punish any particular decision theory. The Transparent Newcomb’s Problem rewards agents which one-box in the Transparent Newcomb’s Problem over agents which two-box, but unless this sort of problem is more likely to arise than ones which reward agents which two-box in Transparent Newcomb’s Problem over ones that one-box, that isn’t an an argument favoring decision theories which say you should one-box in Transparent Newcomb’s.
If you keep a flat probability distribution of what Omega would do to you prior to actually being put into a dilemma, expected-utility-maximizing still favors one-boxing in the opaque version of the dilemma (because based on the information available to you, you have to assign different probabilities to the opaque box containing money depending on whether you one-box or two-box,) but not one-boxing in the transparent version.
You can always contrive scenarios to reward or punish any particular decision theory. The Transparent Newcomb’s Problem rewards agents which one-box in the Transparent Newcomb’s Problem over agents which two-box, but unless this sort of problem is more likely to arise than ones which reward agents which two-box in Transparent Newcomb’s Problem over ones that one-box, that isn’t an an argument favoring decision theories which say you should one-box in Transparent Newcomb’s.
No, Transparent Newcomb’s, Newcomb’s and Prisoner’s Dilemma with full mutual knowledge don’t care what the decision algorithm is. They reward agents that take one box and mutually cooperate for no other reason than they decide to make the decision that benefits them.
You have presented a fully general argument for making bad choices. It can be used to reject “look both ways before crossing a road” just as well as it can be used to reject “get a million dollars by taking one box”. It should be applied to neither.
It’s not a fully general counterargument, it demands that you weigh the probabilities of potential outcomes.
If you look both ways at a crosswalk, you could be hit by a falling object that you would have avoided if you hadn’t paused in that location. Does that justify not looking both ways at a crosswalk? No, because the probability of something bad happening to you if you don’t look both ways at the crosswalk is higher than if you do.
You can always come up with absurd hypotheticals which would punish the behavior that would normally be rational in a particular situation. This doesn’t justify being paralyzed with indecision, the probabilities of the absurd hypotheticals materializing are miniscule. But the possibilities of absurd hypotheticals will tend to balance out other absurd hypotheticals.
Transparent Newcomb’s Problem is a problem that rewards agents which one-box in Transparent Newcomb’s Problem, via Omega predicting whether the agent one-boxes in Transparent Newcomb’s Problem and filling the boxes accordingly. Inverted Transparent Newcomb’s Problem is one that rewards agents that two-box in Transparent Newcomb’s Problem via Omega predicting whether the agent two-boxes in Transparent Newcomb’s Problem, and filling the boxes accordingly.
If one type of situation is more likely than the other, you adjust your expected utilities accordingly, just as you adjust your expected utility of looking both ways before you cross the street because you’re less likely to suffer an accident if you do than if you don’t.
Transparent Newcomb’s Problem is a problem that rewards agents which one-box in Transparent Newcomb’s Problem
Yes.
Inverted Transparent Newcomb’s Problem is one that rewards agents that two-box in Transparent Newcomb’s Problem via Omega predicting whether the agent two-boxes in Transparent Newcomb’s Problem, and filling the boxes accordingly.
That isn’t an ‘inversion’ but instead an entirely different problem in which agents are rewarded for things external to the problem.
There’s no reason an agent you interact with in a decision problem can’t respond to how it judges you would react to different decision problems.
Suppose Andy and Sandy are bitter rivals, and each wants the other to be socially isolated. Andy declares that he will only cooperate in Prisoner’s Dilemma type problems with people he predicts would cooperate with him, but not Sandy, while Sandy declares that she will only cooperate in Prisoner’s Dilemma type problems with people she predicts would cooperate with her, but not Andy. Both are highly reliable predictors of other people’s cooperation patterns.
If you end up in a Prisoner’s Dilemma type problem with Andy, it benefits you to be the sort of person who would cooperate with Andy, but not Sandy, and vice versa if you end up in a Prisoner’s Dilemma type problem with Sandy. If you might end up in a Prisoner’s Dilemma type problem with either of them, you have higher expected utility if you pick one in advance to cooperate with, because both would defect against an opportunist willing to cooperate with whichever one they ended up in a Prisoner’s Dilemma with first.
That isn’t an ‘inversion’ but instead an entirely different problem in which agents are rewarded for things external to the problem.
If you want to call it that, you may, but I don’t see that it makes a difference. If ending up in Transparent Newcomb’s Problem is no more likely than ending up in an entirely different problem which punishes agents for one-boxing in Transparent Newcomb’s Problem, then I don’t see that it’s advantageous to one-box in Transparent Newcomb’s Problem. You can draw a line between problems determined by factors external to the problem, and problems determined only by factors internal to the problem, but I don’t think this is a helpful distinction to apply here. What matters is which problems are more likely to occur and their utility payoffs.
In any case, I would honestly rather not continue this discussion with you, at least if TheOtherDave is still interested in continuing the discussion. I don’t have very high expectations of productivity from a discussion with someone who has such low expectations of my own reasoning as to repeatedly and erroneously declare that I’m calling up a fully general counterargument which could just as well be used to argue against looking both ways at a crosswalk. If possible, I would much rather discuss this with someone who’s prepared to operate under the presumption that I’m willing and able to be reasonable.
(I haven’t followed the discussion, so might be missing the point.)
If ending up in Transparent Newcomb’s Problem is no more likely than ending up in an entirely different problem which punishes agents for one-boxing in Transparent Newcomb’s Problem, then I don’t see that it’s advantageous to one-box in Transparent Newcomb’s Problem.
If you are actually in problem A, it’s advantageous to be solving problem A, even if there is another problem B in which you could have much more likely ended up. You are in problem A by stipulation. At the point where you’ve landed in the hypothetical of solving problem A, discussing problem B is a wrong thing to do, it interferes with trying to understand problem A. The difficulty of telling problem A from problem B is a separate issue that’s usually ruled out by hypothesis. We might discuss this issue, but that would be a problem C that shouldn’t be confused with problems A and B, where by hypothesis you know that you are dealing with problems A and B. Don’t fight the hypothetical.
In the case of Transparent Newcomb’s though, if you’re actually in the problem, then you can already see either that both boxes contain money, or that one of them doesn’t. If Omega only fills the second box, which contains more money, if you would one-box, then by the time you find yourself in the problem, whether you would one-box or two-box in Transparent Newcomb’s has already had its payoff.
If I would two-box in a situation where I see two transparent boxes which both contain money, that ensures that I won’t find myself in a situation where Omega lets me pick whether to one-box or two-box, but only fills both boxes if I would one-box. On the other hand, A person who one-boxes in that situation could not find themself in a situation where they can pick one or both of two filled boxes, where Omega would only fill both boxes if they would two-box in the original scenario.
So it seems to me that if I follow the principle of solving whatever situation I’m in according to maximum expected utility, then unless the Transparent Newcomb’s Problem is more probable, I will become the sort of person who can’t end up in Transparent Newcomb’s problems with a chance to one-box for large amounts of money, but can end up in the inverted situation which rewards two-boxing, for more money. I don’t have the choice of being the sort of person who gets rewarded by both scenarios, just as I don’t have the choice of being someone who both Andy and Sandy will cooperate with.
I agree that a one-boxer comes out ahead in Transparent Newcomb’s, but I don’t think it follows that I should one-box in Transparent Newcomb’s, because I don’t think having a decision theory which results in better payouts in this particular decision theory problem results in higher utility in general. I think that I “should” be a person who one-boxes in Transparent Newcomb’s in the same sense that I “should” be someone who doesn’t type between 10:00-11:00 on a Sunday if I happen to be in a world where Omega has, unbeknownst to anyone, arranged to rob me if I do. In both cases I’ve lucked into payouts due to a decision process which I couldn’t reasonably have expected to improve my utility.
I agree that a one-boxer comes out ahead in Transparent Newcomb’s, but I don’t think it follows that I should one-box in Transparent Newcomb’s, because I don’t think having a decision theory which results in better payouts in this particular decision theory problem results in higher utility in general.
We are not discussing what to do “in general”, or the algorithms of a general “I” that should or shouldn’t have the property of behaving a certain way in certain problems, we are discussing what should be done in this particular problem, where we might as well assume that there is no other possible problem, and all utility in the world only comes from this one instance of this problem. The focus is on this problem only, and no role is played by the uncertainty about which problem we are solving, or by the possibility that there might be other problems. If you additionally want to avoid logical impossibility introduced by some of the possible decisions, permit a very low probability that either of the relevant outcomes can occur anyway.
If you allow yourself to consider alternative situations, or other applications of the same decision algorithm, you are solving a different problem, a problem that involves tradeoffs between these situations. You need to be clear on which problem you are considering, whether it’s a single isolated problem, as is usual for thought experiments, or a bigger problem. If it’s a bigger problem, that needs to be prominently stipulated somewhere, or people will assume that it’s otherwise and you’ll talk past each other.
It seems as if you currently believe that the correct solution for isolated Transparent Newcomb’s is one-boxing, but the correct solution in the context of the possibility of other problems is two-boxing. Is it so? (You seem to understand “I’m in Transparent Newcomb’s problem” incorrectly, which further motivates fighting the hypothetical, suggesting that for the general player that has other problems on its plate two-boxing is better, which is not so, but it’s a separate issue, so let’s settle the problem statement first.)
It seems as if you currently believe that the correct solution for isolated Transparent Newcomb’s is one-boxing, but the correct solution in the context of the possibility of other problems is two-boxing. Is it so?
Yes.
I don’t think that the most advantageous solution for isolated Transparent Newcomb’s is likely to be a very useful question though.
I don’t think it’s possible to have a general case decision theory which gets the best possible results for every situation (see the Andy and Sandy example, where getting good results for one prisoner’s dilemma necessitates getting bad results from the other, so any decision theory wins in at most one of the two.)
That being the case, I don’t think that a goal of winning in Transparent Newcomb’s Problem is a very meaningful one for a decision theory. The way I see it, it seems like focusing on coming out ahead in Sandy prisoner’s dilemmas, while disregarding the relative likelihoods of ending up in a dilemma with Andy or Sandy, and assuming that if you ended up in an Andy prisoner dilemma you could use the same decision process to come out ahead in that too.
If possible, I would much rather discuss this with someone who’s prepared to operate under the presumption that I’m willing and able to be reasonable.
Don’t confuse an intuition aid that failed to help you with a personal insult. Apart from making you feel bad it’ll ensure you miss the point. Hopefully Vladimir’s explanation will be more successful.
I didn’t take it as a personal insult, I took it as a mistaken interpretation of my own argument which would have been very unlikely to come from someone who expected me to have reasoned through my position competently and was making a serious effort to understand it. So while it was not a personal insult, it was certainly insulting.
I may be failing to understand your position, and rejecting it only due to a misunderstanding, but from where I stand, your assertion makes it appear tremendously unlikely that you understand mine.
If you think that my argument generalizes to justifying any bad decision, including cases like not looking both ways when I cross the street, when I say otherwise, it would help if you would explain why you think it generalizes in this way in spite of the reasons I’ve given for believing otherwise, rather than simply repeating the assertion without acknowledging them, otherwise it looks like you’re either not making much effort to comprehend my position, or don’t care much about explaining yours, and are only interested in contradicting someone you think is wrong.
Edit: I would prefer you not respond to this comment, and in any case I don’t intend to respond to a response, because I don’t expect this conversation to be productive, and I hate going to bed wondering how I’m going to continue tomorrow what I expect to be a fruitless conversation.
Well, if you know advance that Omega is more likely to do this than it is to impose a dilemma where it will fill both boxes only if you two-box, then I’d agree that this is an appropriate solution.
I think that if in advance you have a flat probability distribution for what sort of Omega scenarios might occur (Omega is just as likely to fill both boxes only if you would two-box in the first scenario as it is to fill both boxes only if you would one-box,) then this solution doesn’t make sense.
In the transparent Newcomb’s problem, when both boxes are filled, does it benefit you to be the the sort of person who would one-box? No, because you get less money that way. If Omega is more likely to impose the transparent Newcomb’s problem than its inversion, then prior to Omega foisting the problem on you, it does benefit you to be the sort of person who would one-box (and you can’t change what sort of person you are mid-problem.)
If Omega only presents transparent Newcomb’s problems of the first sort, where the box containing more money is filled only if the person presented with the boxes would one-box, then situations where a person is presented with two transparent boxes of money and picks both will never arise. People who would one-box in the transparent Newcomb’s problem come out ahead.
If Omega is equally likely to present transparent Newcomb’s problems of the first sort, or inversions where Omega fills both boxes only for people it predicts would two-box in problems of the first sort, then two-boxers come out ahead, because they’re equally likely to get the contents of the box with more money, but always get the box with less money, while the one-boxers never do.
You can always contrive scenarios to reward or punish any particular decision theory. The Transparent Newcomb’s Problem rewards agents which one-box in the Transparent Newcomb’s Problem over agents which two-box, but unless this sort of problem is more likely to arise than ones which reward agents which two-box in Transparent Newcomb’s Problem over ones that one-box, that isn’t an an argument favoring decision theories which say you should one-box in Transparent Newcomb’s.
If you keep a flat probability distribution of what Omega would do to you prior to actually being put into a dilemma, expected-utility-maximizing still favors one-boxing in the opaque version of the dilemma (because based on the information available to you, you have to assign different probabilities to the opaque box containing money depending on whether you one-box or two-box,) but not one-boxing in the transparent version.
No, Transparent Newcomb’s, Newcomb’s and Prisoner’s Dilemma with full mutual knowledge don’t care what the decision algorithm is. They reward agents that take one box and mutually cooperate for no other reason than they decide to make the decision that benefits them.
You have presented a fully general argument for making bad choices. It can be used to reject “look both ways before crossing a road” just as well as it can be used to reject “get a million dollars by taking one box”. It should be applied to neither.
It’s not a fully general counterargument, it demands that you weigh the probabilities of potential outcomes.
If you look both ways at a crosswalk, you could be hit by a falling object that you would have avoided if you hadn’t paused in that location. Does that justify not looking both ways at a crosswalk? No, because the probability of something bad happening to you if you don’t look both ways at the crosswalk is higher than if you do.
You can always come up with absurd hypotheticals which would punish the behavior that would normally be rational in a particular situation. This doesn’t justify being paralyzed with indecision, the probabilities of the absurd hypotheticals materializing are miniscule. But the possibilities of absurd hypotheticals will tend to balance out other absurd hypotheticals.
Transparent Newcomb’s Problem is a problem that rewards agents which one-box in Transparent Newcomb’s Problem, via Omega predicting whether the agent one-boxes in Transparent Newcomb’s Problem and filling the boxes accordingly. Inverted Transparent Newcomb’s Problem is one that rewards agents that two-box in Transparent Newcomb’s Problem via Omega predicting whether the agent two-boxes in Transparent Newcomb’s Problem, and filling the boxes accordingly.
If one type of situation is more likely than the other, you adjust your expected utilities accordingly, just as you adjust your expected utility of looking both ways before you cross the street because you’re less likely to suffer an accident if you do than if you don’t.
Yes.
That isn’t an ‘inversion’ but instead an entirely different problem in which agents are rewarded for things external to the problem.
There’s no reason an agent you interact with in a decision problem can’t respond to how it judges you would react to different decision problems.
Suppose Andy and Sandy are bitter rivals, and each wants the other to be socially isolated. Andy declares that he will only cooperate in Prisoner’s Dilemma type problems with people he predicts would cooperate with him, but not Sandy, while Sandy declares that she will only cooperate in Prisoner’s Dilemma type problems with people she predicts would cooperate with her, but not Andy. Both are highly reliable predictors of other people’s cooperation patterns.
If you end up in a Prisoner’s Dilemma type problem with Andy, it benefits you to be the sort of person who would cooperate with Andy, but not Sandy, and vice versa if you end up in a Prisoner’s Dilemma type problem with Sandy. If you might end up in a Prisoner’s Dilemma type problem with either of them, you have higher expected utility if you pick one in advance to cooperate with, because both would defect against an opportunist willing to cooperate with whichever one they ended up in a Prisoner’s Dilemma with first.
If you want to call it that, you may, but I don’t see that it makes a difference. If ending up in Transparent Newcomb’s Problem is no more likely than ending up in an entirely different problem which punishes agents for one-boxing in Transparent Newcomb’s Problem, then I don’t see that it’s advantageous to one-box in Transparent Newcomb’s Problem. You can draw a line between problems determined by factors external to the problem, and problems determined only by factors internal to the problem, but I don’t think this is a helpful distinction to apply here. What matters is which problems are more likely to occur and their utility payoffs.
In any case, I would honestly rather not continue this discussion with you, at least if TheOtherDave is still interested in continuing the discussion. I don’t have very high expectations of productivity from a discussion with someone who has such low expectations of my own reasoning as to repeatedly and erroneously declare that I’m calling up a fully general counterargument which could just as well be used to argue against looking both ways at a crosswalk. If possible, I would much rather discuss this with someone who’s prepared to operate under the presumption that I’m willing and able to be reasonable.
(I haven’t followed the discussion, so might be missing the point.)
If you are actually in problem A, it’s advantageous to be solving problem A, even if there is another problem B in which you could have much more likely ended up. You are in problem A by stipulation. At the point where you’ve landed in the hypothetical of solving problem A, discussing problem B is a wrong thing to do, it interferes with trying to understand problem A. The difficulty of telling problem A from problem B is a separate issue that’s usually ruled out by hypothesis. We might discuss this issue, but that would be a problem C that shouldn’t be confused with problems A and B, where by hypothesis you know that you are dealing with problems A and B. Don’t fight the hypothetical.
In the case of Transparent Newcomb’s though, if you’re actually in the problem, then you can already see either that both boxes contain money, or that one of them doesn’t. If Omega only fills the second box, which contains more money, if you would one-box, then by the time you find yourself in the problem, whether you would one-box or two-box in Transparent Newcomb’s has already had its payoff.
If I would two-box in a situation where I see two transparent boxes which both contain money, that ensures that I won’t find myself in a situation where Omega lets me pick whether to one-box or two-box, but only fills both boxes if I would one-box. On the other hand, A person who one-boxes in that situation could not find themself in a situation where they can pick one or both of two filled boxes, where Omega would only fill both boxes if they would two-box in the original scenario.
So it seems to me that if I follow the principle of solving whatever situation I’m in according to maximum expected utility, then unless the Transparent Newcomb’s Problem is more probable, I will become the sort of person who can’t end up in Transparent Newcomb’s problems with a chance to one-box for large amounts of money, but can end up in the inverted situation which rewards two-boxing, for more money. I don’t have the choice of being the sort of person who gets rewarded by both scenarios, just as I don’t have the choice of being someone who both Andy and Sandy will cooperate with.
I agree that a one-boxer comes out ahead in Transparent Newcomb’s, but I don’t think it follows that I should one-box in Transparent Newcomb’s, because I don’t think having a decision theory which results in better payouts in this particular decision theory problem results in higher utility in general. I think that I “should” be a person who one-boxes in Transparent Newcomb’s in the same sense that I “should” be someone who doesn’t type between 10:00-11:00 on a Sunday if I happen to be in a world where Omega has, unbeknownst to anyone, arranged to rob me if I do. In both cases I’ve lucked into payouts due to a decision process which I couldn’t reasonably have expected to improve my utility.
We are not discussing what to do “in general”, or the algorithms of a general “I” that should or shouldn’t have the property of behaving a certain way in certain problems, we are discussing what should be done in this particular problem, where we might as well assume that there is no other possible problem, and all utility in the world only comes from this one instance of this problem. The focus is on this problem only, and no role is played by the uncertainty about which problem we are solving, or by the possibility that there might be other problems. If you additionally want to avoid logical impossibility introduced by some of the possible decisions, permit a very low probability that either of the relevant outcomes can occur anyway.
If you allow yourself to consider alternative situations, or other applications of the same decision algorithm, you are solving a different problem, a problem that involves tradeoffs between these situations. You need to be clear on which problem you are considering, whether it’s a single isolated problem, as is usual for thought experiments, or a bigger problem. If it’s a bigger problem, that needs to be prominently stipulated somewhere, or people will assume that it’s otherwise and you’ll talk past each other.
It seems as if you currently believe that the correct solution for isolated Transparent Newcomb’s is one-boxing, but the correct solution in the context of the possibility of other problems is two-boxing. Is it so? (You seem to understand “I’m in Transparent Newcomb’s problem” incorrectly, which further motivates fighting the hypothetical, suggesting that for the general player that has other problems on its plate two-boxing is better, which is not so, but it’s a separate issue, so let’s settle the problem statement first.)
Yes.
I don’t think that the most advantageous solution for isolated Transparent Newcomb’s is likely to be a very useful question though.
I don’t think it’s possible to have a general case decision theory which gets the best possible results for every situation (see the Andy and Sandy example, where getting good results for one prisoner’s dilemma necessitates getting bad results from the other, so any decision theory wins in at most one of the two.)
That being the case, I don’t think that a goal of winning in Transparent Newcomb’s Problem is a very meaningful one for a decision theory. The way I see it, it seems like focusing on coming out ahead in Sandy prisoner’s dilemmas, while disregarding the relative likelihoods of ending up in a dilemma with Andy or Sandy, and assuming that if you ended up in an Andy prisoner dilemma you could use the same decision process to come out ahead in that too.
Don’t confuse an intuition aid that failed to help you with a personal insult. Apart from making you feel bad it’ll ensure you miss the point. Hopefully Vladimir’s explanation will be more successful.
I didn’t take it as a personal insult, I took it as a mistaken interpretation of my own argument which would have been very unlikely to come from someone who expected me to have reasoned through my position competently and was making a serious effort to understand it. So while it was not a personal insult, it was certainly insulting.
I may be failing to understand your position, and rejecting it only due to a misunderstanding, but from where I stand, your assertion makes it appear tremendously unlikely that you understand mine.
If you think that my argument generalizes to justifying any bad decision, including cases like not looking both ways when I cross the street, when I say otherwise, it would help if you would explain why you think it generalizes in this way in spite of the reasons I’ve given for believing otherwise, rather than simply repeating the assertion without acknowledging them, otherwise it looks like you’re either not making much effort to comprehend my position, or don’t care much about explaining yours, and are only interested in contradicting someone you think is wrong.
Edit: I would prefer you not respond to this comment, and in any case I don’t intend to respond to a response, because I don’t expect this conversation to be productive, and I hate going to bed wondering how I’m going to continue tomorrow what I expect to be a fruitless conversation.