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underling comments on Open Thread: February 2010 - Less Wrong
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Right, but exactly this information seems to the 2-boxer to point to 2-boxing! If the game is rigged against you, so what? Take both boxes. You cannot lose, and there's a small chance the conman erred.
Mhm. I'm still far from convinced. Is this my fault? Am I at all right in assuming that 1-boxing is heavily favored in this community? And that this is a minority belief among experts?
Perhaps it will make sense if you view the argument as more of a reason to be the kind of person who one-boxes, rather than an argument to one-box per se.
That's too cryptic for me. Where's the connection to your first comment?
As i said in reply to byrnema, I don't dispute that wanting to be the kind of person who 1-boxes in iterated games or in advance is rational, but one-shot? I don't see it. What's the rationale behind it?
You have the information that in Newcomblike problems, it is better to (already) be inclined to predictably one-box, because the game is "rigged". So, if you (now) become predictably and generally inclined to one-box, you can win at Newcomblike problems if you encounter them in the future. Even if you only ever run into one.
Of course, Omega is imaginary, so it's entirely a thought experiment, but it's interesting anyway!
Agree completely.
But the crucial difference is: in the one-shot case, the box is already filled or not.
Yes. But it was filled, or not, based on a prediction about what you would do. We are not such tricksy creatures that we can unpredictably change our minds at the last minute and two-box without Omega anticipating this, so the best way to make sure the one box has the goodies in it is to plan to actually take only that box.
I agree. I would add that situations can and do arise in real life where the other fellow can predict your behavior better than you can predict it yourself.
For example, suppose that your wife announces she is going on a health kick. She is joining a gym; she will go 4 or 5 times a week; she will eat healthy; and she plans to get back into the shape she was in 10 years ago. You might ask her what she thinks her probability of success is, and she might honestly tell you she thinks there is a 60 or 70% chance her health kick will succeed.
On the other hand, you, her husband know her pretty well and know that she has a hard time sticking to diets and such. You estimate her probability of success at no more than 10%.
Whose probability estimate is better? I would guess it's the husband's.
Well, in the Newcomb experiment, the AI is like the husband who knows you better than you know yourself. Trying to outguess and/or surprise such an entity is a huge uphill battle. So, even if you don't believe in backwards-causality, you should probably choose as if backwards causality exists.
JMHO
I do not anticipate ever becoming someone's husband.
Well, it's just a hypothetical. If you like, you can switch the roles of wife and husband. Or substitute domestic partners, or anything you like :)
Neither do I. That would be stupid. Why would anyone ever want to become anyone's husband?
Maybe your wife-to-be is a wealthy heiress?
If we rule out backwards causation, then why on earth should this be true???
Imagine a simple but related scenario that involves no backwards causation:
You're a 12 year old kid, and you know your mom doesn't want you to play with your new Splogomax unless an adult is with you. Your mom leaves you alone for an hour to run to the store, telling you she'll punish you if you play with the Splogomax, and that, whether there's any evidence of it when she returns, she knows you well enough to know if you're going to play with it, although she'll refrain from passing judgement until she has just gotten back from the store.
Assuming you fear punishment more than you enjoy playing with your Splogomax, do you decide to play or not?
Edit: now I feel stupid. There's a much simpler way to get my point across. Just imagine Omega doesn't fill any box until after you've picked up one or two boxes and walked away, but that he doesn't look at your choice when filling the boxes.
So what is your point? That no backwards causation is involved is assumed in both cases. If this scenario is for dialectic purposes, it fails: It is equally clear, if not clearer, that my actual choice has no effect on the content of the boxes.
For what it's worth, let me reply with my own story:
Omega puts the two boxes in front of you, and says the usual. Just as you’re about to pick, I come along, grab both boxes, and run. I do this every time Omega confronts someone with his boxes, and I always do as good as a two-boxer and better than a one-boxer. You have the same choice as me: Just two-box. Why won’t you?
If Omega fills the boxes according to its prediction of the choice of the person being offered the boxes and not the person who ends up with the boxes, then the above statement where your argument breaks down.
The one-shot game still has all of the information for the money in the boxes. If you walked in and picked both boxes you wouldn't be surprised by the result. If you walked in and picked one box you wouldn't be surprised by the result. Picking one box nets more money, so pick one box.
I deny that 1-boxing nets more money - ceteris paribus.
Then you're simply disagreeing with the problem statement. If you 1-box, you get $1M. If you 2-box, you get $1k. If you 2-box because you're considering the impossible possible worlds where you get $1.001M or $0, you still get $1k.
At this point, I no longer think you're adding anything new to the discussion.
I never said I could add anything new to the discussion. The problem is: judging by the comments so far, nobody here can, either. And since most experts outside this community agree on 2-boxing (ore am I wrong about this?), my original question stands.
Ceteris ain't paribus. That's the whole point.
What helps me when I get stuck in this loop (the loop isn't incorrect exactly, it's just non-productive) is to meditate on how the problem assumes that, for all my complexity, I'm still a deterministic machine. Omega can read my source code and know what I'm going to pick. If I end up picking both boxes, he knew that before I did, and I'll end up with less money. If I can convince myself -- somehow -- to pick just the one box, then Omega will have seen that coming too and will reward me with the bonus. So the question becomes, can your source code output the decision to one-box?
The answer in humans is 'yes' -- any human can learn to output 1-box -- but it depends sensitively upon how much time the human has to think about it, to what extent they've been exposed to the problem before, and what arguments they've heard. Given all these parameters, Omega can deduce what they will decide.
These factors have come together (time + exposure to the right arguments, etc.) on Less Wrong so that people who hang out at Less Wrong have been conditioned to 1-box. (And are thus conditioned to win in this dilemma.)
I agree with everything you say in this comment, and still find 2-boxing rational. The reason still seems to be: you can consistently win without being rational.
By rational, I think you mean logical. (We tend to define 'rational' as 'winning' around here.*)
... and -- given a certain set of assumptions -- it is absolutely logical that (a) Omega has already made his prediction, (b) the stuff is already in the boxes, (c) you can only maximize your payoff by choosing both boxes. (This is what I meant by this line of reasoning isn't incorrect, it's just unproductive in finding the solution to this dilemma.)
But consider what other logical assumptions have already snuck into the logic above. We're not familiar with outcomes that depend upon our decision algorithm, we're not used to optimizing over this action. The productive direction to think along is this one: unlike a typical situation, the content of the boxes depends upon your algorithm that outputs the choice, only indirectly on your choice.
You're halfway to the solution of this problem if you can see both ways of thinking about the problem as reasonable. You'll feel some frustration that you can alternate between them -- like flip-flopping between different interpretations of an optical illusion -- and they're contradictory. Then the second half of the solution is to notice that you can choose which way to think about the problem as a willful choice -- make the choice that results in the win. That is the rational (and logical) thing to do.
Let me know if you don't agree with the part where you're supposed to see both ways of thinking about the problem as reasonable.
* But the distinction doesn't really matter because we haven't found any cases where rational and logical aren't the same thing.
May I suggest again that defining rational as winning may be the problem?
My point of view is that the winning thing to do here and the logical thing to do are the same.
If you want to understand my point of view or if you want me to understand your point of view, you need to tell me where you think logical and winning diverge. Then I tell you why I think they don't, etc.
You've mentioned 'backwards causality' which isn't assumed in our one-box solution to Newcomb. How comfortable are you with the assumption of determinism? (If you're not, how do you reconcile that Omega is a perfect predictor?)
Only to rule it out as a solution. No problem here.
In general, very. Concerning Newcomb, I don't think it's essential, and as far as I recall, it isn't mentioned in the orginal problem.
I'll try again: I think you can show with simple counterexamples that winning is neither necessary nor sufficient for being logical (your term for my rational, if I understand you correctly).
Here we go: it's not necessary, because you can be unlucky. Your strategy might be best, but you might lose as soon as luck is involved. It's not sufficient, because you can be lucky. You can win a game even if you're not perfectly rational.
1-boxing seems a variant of the second case, instead of (bad) luck the game is rigged.
Around here, "rational" is taken to include in its definition "not losing predictably". Could you explain what you mean by the term?
(2nd reply)
I'm beginning to come around to your point of view. Omega rewards you for being illogical.
.... It's just logical to allow him to do so.
This is why I find it incomprehensible that anyone can really be mystified by the one-boxer's position. I want to say "Look, I've got a million dollars! You've got a thousand dollars! And you have to admit that you could have seen this coming all along. Now tell me who had the right decision procedure?"