I’m interested to hear more about your position on one-boxing. If your predictor is known to rely primarily on public proclamations, then why not proclaim yourself to be a one-boxer, but secretly plan to be a two-boxer all the while?
(Of course, if this works, he isn’t a very good predictor. But why wouldn’t it work?)

Regarding Newcomb’s cafeteria — it’s true that if the predictor relies on past actions in the game to predict future actions, then one-boxing is a useful signal. The game becomes like a repeated prisoner’s dilemma, with the predictor playing the tit-for-tat strategy. And, as you say, there would then be good causalist reasons for one-boxing.

But the tit-for-tat predictor would be easy to fool every so often. All you’d have to do is one-box a few times in a row, and two-box the last time. The predictor would mess up. I guess I have been assuming that the predictor keeps his 99% accuracy rating regardless of what strategem you apply to mess him up. So I don’t think your past one-boxing or two-boxing can play a significant role in the predictor’s decisions, even if the meals are packaged every morning. Which means that a causalist has no incentive to be a one-boxer here.

Basically there are two alternatives: Either all the meals are prepackaged far in advance, or they’re newly packaged every day. Suppose they’re newly packaged every day. Then it makes sense to one-box every day as a signal to the predictor that you’re going to one-box the next day. Causal decision theorists should have no problem with that.

The other alternative is that the meals are prepackaged far in advance. But can we really conceive of this world? I find it possible to imagine a world in which a predictor can judge a single choice very accurately, but I’m not sure how a predictor could judge thousands of choices accurately enough to set the problem up. That requires knowing exactly when the two-boxer falls off the wagon; or for that matter exactly when someone may crave a snack. And I’m not sure that we can really draw any moral from a situation that requires a predictor of such uncanny accuracy.

I wanted to mention the example that illustrates why one boxing makes sense to me. (It can be applied to Kenny’s other examples too.)

Imagine you are in a world where, three times a day, you go to a cafeteria to get food. Your food is served in two Newcomb boxes. The opaque box is empty or it contains a decent meal. The transparent box contains a small snack, like an apple or a cookie. There is no other source of food in this world — and let’s say it’s for some reason impossible to beg, borrow, or steal food from other people.

You try the game a few times, and 99% of the time when you take one box, you get a meal; 99% of the time when you take both boxes, you get a snack. You know that if you don’t eat an average of between 1-2 meals a day, you will eventually starve.

Now, how many real-life two-boxers would slowly starve to death over the course of a month, all the while saying that they were making rational decisions? I don’t think many would. If they give in and become one boxers, does that mean they are weak or not very smart? I don’t think that’s right either.

We have a deeply ingrained notion that causality is a crucial component of reasoned actions, because in real life it always is. I must throw the spear in order to impale the deer. I must go to the bank in order to get cash from the ATM. And so on. But Newcomb situations never happen in real life. In a hypothetical “Newcomb world” where causal reasoning frequently doesn’t work (i.e. leads to people starving), I think people would have a very different notion of what constitutes a reasoned action. And it seems to me that it’s only fair to judge Newcomb’s paradox as would an inhabitant of a “Newcomb world.”

Wondering how the predictor anticipates people’s choices, you just can’t forget that what’s done is done and not worry about yielding to a last-minute temptation to take BOTH. To combat that worry you should commit yourself to taking ONE. So instead of wondering how the predictor does it, you should recall what Muhammad Ali said prior to facing the seemingly invincible heavyweight champion Sonny Liston: “If Cassius Clay says a rooster can lay an egg, don’t ask how – grease that skillet!”

In the standard Newcomb problem the person taking the boxes is given the choice after the predictor has decided whether or not to put the million dollars in the box. It does seem like the biggest payout comes from somehow forming the intention now (before the chooser has been presented with a Newcomb problem choice) to be a one-boxer no matter what when presented with the choice in the future. The rationale for this is that the predictor will predict this and therefore put the million dollars in the box, hence the chooser will be better of than if they had formed the intention to take both boxes and the predictor had predicted this. But once the choice is given (i.e. the million dollars is now either present or absent in the box) the chooser should switch, ignore all their previous intentions, and take both boxes. Doing this makes them one thousand dollars better off than taking just the one box.

Of course if the predictor is good at their job they will have predicted that the chooser will switch; but no matter how adamant the chooser was when forming their intentions (specifically the intention that if they were presented with a Newcomb problem choice in the future that they would take one box), it still remains that the rational thing to do once they are presented with the choice is to switch. As Lewis puts it in ‘Why Ain’cha Rich?’, the irrational are richly pre-rewarded.

http://bjps.oxfordjournals.org/cgi/content/abstract/45/4/1001

“PRISONER’S DILEMMA AND RESOLUTE CHOICE” IN “PARADOXES OF RATIONALITY AND COOPERATION”, CAMPBELL, RICHMOND (ED), 94-104.

http://www.ubcpress.ca/search/title_book.asp?BookID=1614

“The Rationality of Being Guided by Rules” in The Oxford Handbook of Rationality, Mele, Alfred R (ed), 222-239.

http://www.oxfordscholarship.com/oso/private/content/philosophy/9780195145397/p058.html#acprof-0195145399-chapter-12

Also, his book “Rationality and Dynamic Choice” might be worth looking at in this connection.