Thanks for a great post Adam, I’m looking forward to the rest of the series.
This might be missing the point, but I just can’t get past it. How does a rational agent come to believe that the being they’re facing is “an unquestionably honest, all knowing agent with perfect powers of prediction”?
I have the suspicion that a lot of the bizarreness of this problem comes out of transporting our agent into an epistemologically unattainable state.
Is there a way to phrase a problem of this type in a way that does not require such a state?
There’s a fellow named James Omega who (with the funding of certain powerful philosophy departments), travels around the country offering random individuals the chance to participate in Newcomb’s problem, with James as Omega. Rather than scanning your brain with his magic powers, he spends a day observing you in your daily life, and uses this info to make his decision. Here’s the catch: he’s done this 300 times, and never once mis-predicted. He’s gone up against philosophers and lay-people, people that knew they were being observed and people that didn’t, but it makes no difference: he just has an intuition that good. When it comes time to do the experiment, it’s set up in such a way that you can be totally sure (and other very prestigous parties have verified) that the amounts in the box do not change after your decision.
So when you’re selected, what do you do? Nothing quite supernatural is going on, we just have the James fellow with an amazing track record, and you with no particular reason to believe that you’ll be his first failure. Even if he is just human, isn’t it rational to assume the ridiculously likely thing (301/302 chance according to Laplace’s Law) that he’ll guess you correctly? Even if we adjust for the possibility of error, the payoff matrix is still so lopsided that it seems crazy to two-box.
See if that helps, and of course everyone else is free to offer improvements if I’ve missed something. You know, help get this Least Convenient Possible World going.
Now I want to read a series of stories starring James Omega in miscellaneous interesting situations. The kind of ability implied by accuracy at Newcomb’s Dilemma would seem to imply capability in other situations as well. (If nothing else, he would kill at rock-paper-scissors.)
How does a rational agent come to believe that the being they’re facing is “an unquestionably honest, all knowing agent with perfect powers of prediction”?
Let’s make things clearer by asking the meta-question: is the predictor’s implementation, and the process by which we learn of it, relevant to the problem? Let’s unpack “relevant”: should the answer to Newcomb’s Problem depend on these extraneous details about the predictor? And let’s unpack “should”: if decision theory A tells you to one-box in approximately-Newcomb-like scenarios without requiring further information, and decision theory B says the problem is “underspecified” and the answer is “unstable” and you can’t pin it down without learning more about the real-world situation… which decision theory do you like more?
Of course, that’s assuming that by newcomb-like scenarios you only include those were one-boxing is actually statistically correlated with greater wealth once all other factors are canceled out.
If Decision Theory A’s definition of newcomb-like included a scenario where the person was doing well enough to make one-boxing appear to be the winning move, but was actually basing her decisions on hair-colour, then I would be more tempted by Decision Theory B.
Newcomb’s Problem still holds in much more realistic situations. So say someone who knows you really, really well comes up to you and makes the same offer. Imagine you don’t mind taking their money and you reckon they know you well enough that they’re 80% likely to be correct in their bet. One boxing is still the right decision because you have the following gain from one boxing:
(.8 x 1 000 000) + (.2 x 0) = 800 000
and for two boxing:
(.8 x 1000) + (.2 x 1 001 000) = 800+ 200 200 = 201 000
But Causal Decision Theory will still undertake the same reasoning because your decision still doesn’t have a causal influence on whether the boxes are in state 1 or 2. So Causal Decision Theory will still two box.
So Newcomb’s Problem still holds in more realistic situations.
Is that the sort of thing you were looking for or have I missed the point?
Even if you don’t believe such a situation can exist, you can make inferences for how you should act in such a case, base on how you should act in realistic cases.
Like AdamBell said, you can consider a more realistic scenario where someone simply has a good chance of guessing what you do.
Then take it a step further: write your decision theory as a function of how accurate the guesser is. Presumably, for the “high but not 100%” accuracy cases, you’ll want to one-box. So, in order to have a decision theory that doesn’t have some sort of discontinuity, you will have to set it so that it would imply that on a 100% guesser-accuracy case, you should one-box as well.
In short, it’s another case of Belief in the Implied Invisible, or implied optimal, as is the case here. While you may not be in a position to test claim X directly, it falls out as an implication of the best theories, which are directly testable.
(I should probably write an article justifying the importance of Newcomb’s problem and why it has real implications for our lives—there are many other ways it’s important, such as in predicting the output of a process.)
If you want a way of phrasing this problem which involves the agent being in an attainable state, this may be of some small interest, Alexandros. A few years back I wrote an article discussing a situation with some similiarities with the one in Newcomb’s problem and with an attainable-state agent. While the article doesn’t prove anything really profound in philosophy, it might give a useful context. It is here: http://www.paul-almond.com/GameTheoryWithYourself.htm.
SilasBarta, yes. I decided to change to this username as it is more obvious who I am. I generally use my real name in online discussions of this type: I have it on my website anyway. I don’t envisage using the PaulUK name again.
Is there a way to phrase a problem of this type in a way that does not require such a state?
There is, and it is useful to look at such phrasings to allay those suspicions. However once we have looked at the issue enough to separate practical implications of imperfect knowledge from the core problem the simple version becomes more useful. It turns out that the trickiest part becomes unavoidable once we clear out the distractions!
When I was getting my head around the subject I made them up myself. I considered what the problem would look like if I took out the ‘absolute confidence’ stuff. For example—forget Omega, replace him with Patrick Jane. Say Jane has played this game 1,000 times before with other people and only got it wrong (and/or lied) 7 times.
I assume you can at least consider TV show entertainment level counterfactuals for the purpose of solving these problems. Analysing the behavior of fictional characters in TV shows is a legitimate use for decision theory.
Asking folks to hypothetically accept the unbelievable does not, IMHO, “clear out distractions”.
That would have made things difficult in high school science. Most example problems do exactly that. I distinctly remember considering planes and pulleys that were frictionless.* The only difference here is that the problem is harder (on our intuitions, if nothing else.)
* Did anyone else find it amusing when asked to consider frictionless ropes that were clearly fastened to the 200 kg weights with knots?
Thanks for a great post Adam, I’m looking forward to the rest of the series.
This might be missing the point, but I just can’t get past it. How does a rational agent come to believe that the being they’re facing is “an unquestionably honest, all knowing agent with perfect powers of prediction”?
I have the suspicion that a lot of the bizarreness of this problem comes out of transporting our agent into an epistemologically unattainable state.
Is there a way to phrase a problem of this type in a way that does not require such a state?
It’s not perfect, per se, but try this:
There’s a fellow named James Omega who (with the funding of certain powerful philosophy departments), travels around the country offering random individuals the chance to participate in Newcomb’s problem, with James as Omega. Rather than scanning your brain with his magic powers, he spends a day observing you in your daily life, and uses this info to make his decision. Here’s the catch: he’s done this 300 times, and never once mis-predicted. He’s gone up against philosophers and lay-people, people that knew they were being observed and people that didn’t, but it makes no difference: he just has an intuition that good. When it comes time to do the experiment, it’s set up in such a way that you can be totally sure (and other very prestigous parties have verified) that the amounts in the box do not change after your decision.
So when you’re selected, what do you do? Nothing quite supernatural is going on, we just have the James fellow with an amazing track record, and you with no particular reason to believe that you’ll be his first failure. Even if he is just human, isn’t it rational to assume the ridiculously likely thing (301/302 chance according to Laplace’s Law) that he’ll guess you correctly? Even if we adjust for the possibility of error, the payoff matrix is still so lopsided that it seems crazy to two-box.
See if that helps, and of course everyone else is free to offer improvements if I’ve missed something. You know, help get this Least Convenient Possible World going.
Now I want to read a series of stories starring James Omega in miscellaneous interesting situations. The kind of ability implied by accuracy at Newcomb’s Dilemma would seem to imply capability in other situations as well. (If nothing else, he would kill at rock-paper-scissors.)
Let’s make things clearer by asking the meta-question: is the predictor’s implementation, and the process by which we learn of it, relevant to the problem? Let’s unpack “relevant”: should the answer to Newcomb’s Problem depend on these extraneous details about the predictor? And let’s unpack “should”: if decision theory A tells you to one-box in approximately-Newcomb-like scenarios without requiring further information, and decision theory B says the problem is “underspecified” and the answer is “unstable” and you can’t pin it down without learning more about the real-world situation… which decision theory do you like more?
Decision theory A is by far preferable to me.
Of course, that’s assuming that by newcomb-like scenarios you only include those were one-boxing is actually statistically correlated with greater wealth once all other factors are canceled out.
If Decision Theory A’s definition of newcomb-like included a scenario where the person was doing well enough to make one-boxing appear to be the winning move, but was actually basing her decisions on hair-colour, then I would be more tempted by Decision Theory B.
IOW: whichever one wins for me :p
Newcomb’s Problem still holds in much more realistic situations. So say someone who knows you really, really well comes up to you and makes the same offer. Imagine you don’t mind taking their money and you reckon they know you well enough that they’re 80% likely to be correct in their bet. One boxing is still the right decision because you have the following gain from one boxing:
(.8 x 1 000 000) + (.2 x 0) = 800 000
and for two boxing:
(.8 x 1000) + (.2 x 1 001 000) = 800+ 200 200 = 201 000
But Causal Decision Theory will still undertake the same reasoning because your decision still doesn’t have a causal influence on whether the boxes are in state 1 or 2. So Causal Decision Theory will still two box.
So Newcomb’s Problem still holds in more realistic situations.
Is that the sort of thing you were looking for or have I missed the point?
Even if you don’t believe such a situation can exist, you can make inferences for how you should act in such a case, base on how you should act in realistic cases.
Like AdamBell said, you can consider a more realistic scenario where someone simply has a good chance of guessing what you do.
Then take it a step further: write your decision theory as a function of how accurate the guesser is. Presumably, for the “high but not 100%” accuracy cases, you’ll want to one-box. So, in order to have a decision theory that doesn’t have some sort of discontinuity, you will have to set it so that it would imply that on a 100% guesser-accuracy case, you should one-box as well.
In short, it’s another case of Belief in the Implied Invisible, or implied optimal, as is the case here. While you may not be in a position to test claim X directly, it falls out as an implication of the best theories, which are directly testable.
(I should probably write an article justifying the importance of Newcomb’s problem and why it has real implications for our lives—there are many other ways it’s important, such as in predicting the output of a process.)
If you want a way of phrasing this problem which involves the agent being in an attainable state, this may be of some small interest, Alexandros. A few years back I wrote an article discussing a situation with some similiarities with the one in Newcomb’s problem and with an attainable-state agent. While the article doesn’t prove anything really profound in philosophy, it might give a useful context. It is here: http://www.paul-almond.com/GameTheoryWithYourself.htm.
I believe you used to post here as PaulUK, and joined in for this discussion of your website’s articles.
SilasBarta, yes. I decided to change to this username as it is more obvious who I am. I generally use my real name in online discussions of this type: I have it on my website anyway. I don’t envisage using the PaulUK name again.
Others have given good answers; here’s another.
There is, and it is useful to look at such phrasings to allay those suspicions. However once we have looked at the issue enough to separate practical implications of imperfect knowledge from the core problem the simple version becomes more useful. It turns out that the trickiest part becomes unavoidable once we clear out the distractions!
And where, pray tell, might I look?
Asking folks to hypothetically accept the unbelievable does not, IMHO, “clear out distractions”.
When I was getting my head around the subject I made them up myself. I considered what the problem would look like if I took out the ‘absolute confidence’ stuff. For example—forget Omega, replace him with Patrick Jane. Say Jane has played this game 1,000 times before with other people and only got it wrong (and/or lied) 7 times.
I assume you can at least consider TV show entertainment level counterfactuals for the purpose of solving these problems. Analysing the behavior of fictional characters in TV shows is a legitimate use for decision theory.
That would have made things difficult in high school science. Most example problems do exactly that. I distinctly remember considering planes and pulleys that were frictionless.* The only difference here is that the problem is harder (on our intuitions, if nothing else.)
* Did anyone else find it amusing when asked to consider frictionless ropes that were clearly fastened to the 200 kg weights with knots?