The Amateur Philosopher

So, at first, I was really excited by the argument I’m going to make in this post, and I still think it’s kind of fun. But all it really is is yet another argument for two-boxing. And there are kazillions of arguments for two-boxing out there. At any rate, here’s one more, presented for your delectation.

Newcomb’s Paradox

What’s two-boxing? It’s a particular belief about the correct way to play a game in a puzzle of decision theory called Newcomb’s Paradox. In Newcomb’s Paradox, you’re faced with a game set up by a character we shall call The Predictor. For simplicity’s sake, let’s suppose that The Predictor is a perfect predictor of your behavior–he’s always been able to predict exactly what you’re going to do, well in advance of when you do it. If that seems implausible to you, I’ll note here that you can make Newcomb’s Paradox work as long as The Predictor has any demonstrated skill at figuring out what you’re going to do–as long as his predictions are any better than pure random chance–but let’s stick with a perfect Predictor for now, because it makes the math easier.

The Predictor has set up a pair of closed boxes, called Box A and Box B. He gives you a choice: You can open Box A alone and keep whatever’s inside it, or you can open both boxes and keep whatever’s inside them. But–and here’s the trick–The Predictor has predicted what you’re going to do, and has filled the boxes accordingly:

• If The Predictor predicts you’re going to open only Box A, he has put $1,000,000 in Box A, and $100 in Box B.
• If the Predictor predicts you’re going to open both boxes, he has put nothing in Box A, and $100 in Box B.

So, what should you do? Should you open just both boxes, or just Box A?

If you’re a two-boxer, you think the rational thing to do is to open both boxes. In all likelihood, you’re convinced by an argument like the following: There’s $100 in box B. So whatever the predictor put in Box A, I’m going to get $100 more picking both boxes than if I just picked box A. Why leave $100 on the table? The rational choice is to pick both boxes.

If you’re a one-boxer, you think that the rational thing to do is to open just Box A. You’re probably convinced by an argument like the following: Look, people who open just box A come away from this situation with $1,000,000. Every time. And people who open both boxes come away with $100. Every time. What group do I want to be a part of? The millionaires, of course. So I should open just Box A. The rational choice is just to pick box A.

My Argument

Like, I believe, the vast majority of philosophers today, I’m a two-boxer. But I’ve got what I think is a kind of novel argument, not directly against one-boxing, but against the argument form that one-boxers find more appealing. (For the technically inclined, this is an argument against the thesis that the choice with the highest expected value is always the rational choice.)

The argument uses a variant of Newcomb’s paradox, where The Predictor is replaced by someone who I’ll call The Sage. The Sage is exactly as good at predicting your behavior as is The Predictor, but she has one further ability: She has solved all the problems in decision theory. She knows, given any Newcomb-like situation, what the rational decision is.

The Sage, like the Predictor, has set up a pair of boxes, and she gives you the same choices as the Predictor did. But she’s filled them using the following rules:

• If she has predicted that you’re going to make the irrational choice, she’s put $1,000,000 in Box A and $100 in Box B.
• If she has predicted that you’re going to make the rational choice, she has put nothing in Box A and $100 in Box B.

Now, suppose you’re a one-boxer. Then, if the standard one-boxing argument appeals to you, the same argument with “make the irrational choice” substituted for “pick Box A” should appeal to you just as well:

Look, people who make the irrational choice come away from this situation with $1,000,000. Every time. And people who make the rational choice come away with $100. Every time. What group do I want to be a part of? The millionaires, of course. So I should make the irrational choice. The rational choice is the irrational choice.

Unless I’m missing something, that’s a contradiction. So I don’t think the argument for one-boxing is very convincing.

Edit 12/19:  The more I think about this argument, the less I’m sure about it. I have a feeling that there might be a Liar-sentence-type problem with the way I’ve set up the Sage’s game: The mapping of choices to money depends on what the rational choice is, but what the rational choice is (presumably) depends on the mapping of choices to money. If that’s true, it may be possible that there simply is no game of the sort I’ve suggested. Thoughts?