Missives from a fly bottle
barang dot sg
Last revised 18 October 2017
Newcomb’s problem


This was written in 2009 although I’ve known about this “one-boxing” solution for quite a while. Wittgenstein once said that you can tell that an itch is gone if you no longer find yourself returning to scratch it. This solution did it for me. My target is essentially the epigraph by David Lewis at the start of the essay. Lewis was a famous “two-boxer” and these words of his encapsulate everything that is wrong with two-box reasoning, in my opinion.

Other Sites

Thinking inside the boxes: Newcomb’s problem still flummoxes the great philosophers (2002), by Jim Holt.
www.slate.com

Newcomb’s paradox: an argument for irrationality (2010), by Julia Galef.
rationallyspeaking.blogspot.com

Theology throwdown: Newcomb’s paradox (2010), by Jethro Flench.
www.thesmogblog.com
9. The modified predictor

Imagine that the predictor actually wants to offer you a choice between a thousand dollars and a million but plans to do it in such an unusual way that you may end up questioning whether the choice has really been offered to you.

The issue for the predictor is not whether you will choose the million over the thousand, for if you believed you had that choice, you presumably would.

The issue rather is whether you will believe, owing to the unusual way in which the choice is offered to you, that the choice really has been offered to you. This is what interests the predictor and what we may assume he is good at predicting.

He lays down two boxes A and B and informs you that one of these two situations obtains without saying which one:
A contains $1,000 and B contains a frog.
A contains a frog and B contains $1,000,000.
As before, you have a choice between taking box A and taking box B. If he predicted you would take A, the first situation obtains, whereas if he predicted you would take B, the second one does. He claims thereby to be offering you a choice between a thousand dollars and a million, only in a slightly unusual way.

Now this frog thing is just for drama, to indicate the cases where the contents of a box “don’t matter” in the sense previously explained. We should really replace the first frog with nothing and the second frog with $1,001,000, otherwise (as will soon become clear) the predictor cannot reasonably predict the behaviour of someone who rejects that the choice in question has been laid before him. (The point of the replacements is to ensure that box A is always more valuable than box B.)

Note that the contents of the boxes are now in line with the previous Newcomb situation.

Having thus replaced the frogs, we can see that, in order to predict whether you will take box A or box B, the predictor simply has to predict whether you will accept or reject his contention that he has offered you a choice between a thousand and a million.

For if you accept that this is a perfectly legitimate (though unusual) way of offering that choice, you will simply choose the million by taking box B. You won’t be fooled by the presence of the irrelevant items occupying the frog positions, be they frogs, old newspapers or even large amounts of money.

In contrast, if you reject that any such choice has been bestowed upon you in this perverse state of affairs, then your attitude is presumably that, in choosing between taking box A and taking box B, you are choosing between the actual contents of the boxes, whatever they may be. As such, noticing that box A is always more valuable than box B, you will undoubtedly take box A.

Indeed the question of whether you should take box A or box B just boils down to the question of whether someone can bestow upon you a choice between a thousand and a million in this unusual way. In the situation described, and assuming the predictor can anticipate your answer, do you really have the choice in question? I believe the answer is yes and so you should take box B.

Those who reject this answer and favour taking box A will presumably also reject that you had a choice between gifts A and B in the birthday case above. Their view would be that, having secured gift A alone, my secretary deprived you of a choice between A and B, notwithstanding that she knew you would never choose B.

I have already explained why I think this view is incorrect. In fact, I think it is rather perverse. In fact, it is as perverse as the view that foreknowledge of choice rules out freedom of choice.