For any interested, below is a link to Huw Price’s (wonderful) paper. As far as I can tell, it’s distinct from the line I’ve been pushing here, but there are some interesting parallels.

http://www.usyd.edu.au/time/price/preprints/chewcomb.pdf

Anyway, it’s been fun!

Hmm, sounds like we’re back to square one. I have nothing new to add at the moment.

Holding the predictor’s prediction constant, what is the situation in which one-boxing is better than, and preferable to, two-boxing? Or, alternatively, why should we not hold the predictor’s prediction constant?

Perhaps you think the second premise in my last argument begs the question? If so, I disagree, but I see how it appears that way. I suppose it should say something like: When the decision to one-box or two-box does not affect the predictor’s prediction, two-boxing dominates, and when choice A dominates choice B, then choice A is better than choice B…

6:01 am? Wow! I guess you’re still on London time!

Warren, I agree with many of the points you make, but the conclusion you appear to draw from your first paragraph argument in the comment above (“But two-boxing is *always* better”) seems blatantly false. There is clearly a situation in which one-boxing is better than, and preferable to, two-boxing. I’d repeat the same things I said in my longest comment above (June 13/12:21am).

And, given its second premise, who are you hoping to convince with that last argument?? : )

Is it? I encounter the Newcomb Paradox. The predictor has already made his prediction. If he’s predicted that I’ll one-box, then I’ll be better off if I two-box. If he’s predicted that I’ll two-box, then I’ll be better off if I two-box. Either way, I’ll be better off if I two-box. Yet, you say that it’s obvious that people who one-box do better. But two-boxing is *always* better. What’s going on?

In your simulation, people who one-box do better than people who two-box because their “one-boxing” or “two-boxing” nature has an effect on the predictor’s prediction. (That’s just the way it works in your model.) But, in the Newcomb Paradox, the player’s choice does not affect the predictor’s prediction. The predictor’s prediction has already been made. All that’s left is to choose a box or two.

That’s the difference between the questions I distinguished above. It’s also the difference between our answers to the Newcomb question. You say that people who one-box are better off than people who two-box. I agree (sorta). But that’s only true because their “one-boxing” nature affects the predictor’s prediction: “being a one-boxer” means both “being likely to one-box” and “making it likely that the predictor will predict that you’ll one-box”. However, in the Newcomb scenario, one can’t influence the predictor. “One-boxing” simply means “choosing one box”; it has no effect on the predictor’s prediction. (The difference between “being the sort of…” and “two-boxing” should now be clear.)

It’s better to “one-box” than “two-box” when the decision to do one or the other affects the predictor’s prediction. It’s better to “two-box” than “one-box” when the decision to do one or the other does *not* affect the predictor’s prediction. In the Newcomb scenario, the choice does not affect the predictor’s prediction. Therefore, it’s better to two-box.

Does that clarify things?

But if you say that there is a difference between, e.g. “adopting a strategy of one-boxing 99.9% of the time” and “one-boxing,” I have to ask what the difference actually is. Do you mean to say that in a particular instance, if you get “lucky” (not sure that’s the word) enough to two-box under your mixed strategy, it’s better to two-box? I suppose that’s true, but it doesn’t seem especially relevant.

Unless of course you’re saying only that it is “better” in some abstract sense to two-box, but the rational agent would not actually *do* this—at least not 99.9% of the time—because he has adopted the appropriate mixed strategy. Then “better” is divorced from its meaning of “preferable to a rational agent.” In such a case, I don’t even know what the word “better” is intended to mean.

Honestly, I don’t get it. It’s so obvious that people who one-box do better. Therefore you should be a person who one-boxes. Therefore you should one-box. The only way to get around this would be to deny all these “meta-rational” arguments and adopt some simplistic, algorithmic account of rationality. Of course, that would make you about as obstinate as Buridan’s ass.

You question the possibility of simultaneously holding that it is better to be the sort of person who one-boxes AND that it is better to two-box. Can one hold both views simultaneously? The answer depends on what one means when one says that it is “better to be the sort of person who one-boxes.” I didn’t give a clear sense of what I meant by this. I’ll do so now.

In my previous post, when I distinguished between questions regarding (1) what sort of person to be and (2) what to do, I was responding to your game-theoretic simulation of the Newcomb Paradox. So, when I introduced the distinction, I had in mind an interpretation of (1) that corresponds to your game-theoretic approach. That is, I understood “being the sort of person who one-boxes” as “being one who chooses one box X percent of the time (where X is a sufficiently large number)”. Call this the Game-Theoretic (GI) interpretation (or perhaps it would be better to call it the “Mixed-Strategy” interpretation).

This interpretation is consistent with your game-theoretic simulation, but it in no way conflicts with the claim that it is better to two-box. There is nothing paradoxical in simultaneously holding the following two views: (1) it is better to act in accordance with a mixed-strategy that involves choosing one box X percent of the time (and two-boxes (1-X) percent of the time) than to act in accordance with a mixed-strategy that involves choosing one box Y percent of the time (and two-boxes (1-Y) percent of the time), where X>Y, and (2) once the predictor has made his prediction, it is always better to choose two boxes than one. In other words, there’s nothing paradoxical in agreeing with the outcome of your game-theoretic simulation and still holding that it is better to two-box.

You think there is something paradoxical in holding these two views. Specifically, you say that it is “like holding that it’s better to be a doctor than a lawyer, but it’s better to practice law than medicine.” What is wrong with holding these two views? Simplifying a bit, we can say that “to be a doctor” simply IS “to practice medicine” and “to be a lawyer” simply IS “to practice law”. So, to hold that it is better to be a doctor than a lawyer simply IS to hold that it is better to practice medicine than to practice law. But this clearly contradicts the claim that it is better to practice law than to practice medicine. Therefore one can’t consistently hold both views.

The problem, however, is that the same relationship that exists between “being a doctor/lawyer” and “practicing medicine/law” does not exist between “being the sort of person who one-boxes/two-boxes” and “one-boxing/two-boxing” on the GI interpretation. According to the GI interpretation, it is simply not the case that “being the sort of person who one-boxes” simply IS “one-boxing”. Rather, as we have already seen, “being the sort of person who one-boxes” simply means “being one who chooses one box X percent of the time (where X is a sufficiently large number)”. On this interpretation, there is no contradiction between “being the sort of person who one-boxes” and “two-boxing”. Thus, I deny your claim that holding the two views “would be like holding that it’s better to be a doctor than a lawyer, but it’s better to practice law than medicine.”

Of course, there’s an obvious response open to you. You could simply claim that the GI interpretation is the wrong interpretation of what it is to be “the sort of person who one-boxes”. You could present an alternative interpretation in which “being the sort of person who one-boxes/two-boxes” and “one-boxing/two-boxing” bear the same relationship as in the doctor/lawyer example. Call this the Doctor/Lawyer (DL) interpretation. On such a view, I grant that it would be contradictory to hold both that one should be the sort of person who one-boxes and that one should two-box.

But there is a problem with this strategy: your game-theoretic defense of one-boxing does not apply to it. As I said earlier, your game-theoretic simulation provides support for the view that it is better to be the sort of person who one-boxes than the sort of person who two-boxes. However, that is only true on the GI interpretation of what it is to be the sort of person who one-boxes/two-boxes. Your game theoretic defense of one-boxing says nothing about the DL interpretation. (And, I might add, if you think GI is the wrong interpretation, one might ask why you presented your game-theoretic simulation at all.)

So, you face a dilemma. If you choose the GI interpretation, then you can offer your game-theoretic simulation as a defense of “being the sort of person who one-boxes”. However, because, on this interpretation, “being the sort of person who one-boxes” and “two-boxing” are perfectly compatible, this argument provides no defense of the rationality of one-boxing. You can plug the gap in your argument (the gap between “being the sort of person…” and “choosing to…”) by shifting to the DL interpretation. However, in doing so, you will be forced to forfeit the very defense of “being the sort of person who one-boxes” on which your argument relies. Your argument only appears to succeed because you shift from GI to DL without noticing.

I’d still two-box. No, wait! I’d one-box (“Nudge nudge. Wink wink. Know what I mean? Say no more…know what I mean?)

You may be right that the ideal strategy would be to present an *image* of a one-boxing character but in fact be a two-boxer, but if we assume that the predictor is highly accurate this is difficult if not impossible. I’d still one-box.