Missives from a fly bottle
barang dot sg
Last revised 31 August 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
3. Why you should take both boxes

The answer is that the case for taking both boxes is so simple and strong as to knock one over completely.

Thus, notwithstanding the predictor’s powers (which may be granted), remember that his prediction has already been made and cannot now be changed.

Correspondingly, the contents of box B have already been settled and cannot now change. The contents of box B are fixed and unalterable, as it were.

Obviously then, whatever those contents may be, you will get $1,000 more if you take both boxes. For taking just box B merely gets you the contents of box B (whatever they may be) whereas taking both boxes gets you those same contents plus an extra thousand dollars.

Consider this table, which depicts all possibilities:

B contains nothingB contains a million
Take just B$0$1,000,000
Take both$1,000$1,001,000

It shows that, whether box B contains nothing or a million dollars, you do better by taking both boxes – one thousand dollars better, either way.

In a sense, this should be perfectly obvious. Clearly, as the boxes stand before you, there is more money in both boxes than in box B alone. This seems impossible to deny! Are there not more sheep on both islands of New Zealand than on the South Island alone? If your sole aim is money, you must surely take both boxes.

Once this sinks in, it becomes hard to accept that taking both boxes (“two-boxing”) can be the wrong decision. How can it be the wrong decision if it gets you a thousand dollars more?

Well-known two-boxers moved by these simple considerations include the philosophers J. M. Fischer and David Lewis, not to mention Robert Nozick himself.

Indeed, two-boxing is widely regarded as the “default” correct decision, in the sense that if it’s the wrong decision, a really good explanation would have to be given of this. As such, many people regard it as the “safe” answer to adopt, e.g., in a textbook discussion of Newcomb’s problem. (Braver souls hold that two-boxing is obviously the correct decision and laugh off any suggestion of a “paradox”.)

In practice, you will also meet many people who start off as one-boxers but end up as firmly-converted two-boxers “upon seeing the light,” but you will rarely meet someone who has moved the other way.

Indeed, taking just box B can come to seem indefensible once one fully absorbs the case for taking both boxes and there are many striking ways to illustrate this.

Consider a variant of the problem involving just one box. You may simply take the box and keep its contents or else clap your hands three times before doing so. (Your two choices.) The predictor has left a million dollars in the box if he predicted you would clap your hands, otherwise he has left a mere thousand in it.

Should you clap your hands before taking the box?

A one-boxer would, whereas a two-boxer would consider this absurd. After all, whatever the powers of the predictor, the contents of the box are not going to change just because one claps one’s hands three times (or any number of times).

Moreover, one-boxers fully concur on this last point, which makes two-boxers shake their heads further in disbelief.