The Newcomb Problem

by Kevin J. Lin

A being, who you believe to have superior predictive powers, makes you an offer. Before you are two boxes, identical in appearance. Within one box, let us call it 'Box A', there is either one million dollars or nothing. Within the other box, 'Box B', there is definitely one thousand dollars.

The being, whom in deference to tradition we will call the Newcomb Being, will allow you to either take both boxes, or just Box A.

Twenty-four hours ago, the Newcomb being made a prediction about what you would choose. At this point, it placed the money in the boxes. If the Newcomb Being predicted that you would take both boxes, it left nothing for you in Box A and the $1000 in Box B. If the Newcomb Being predicted that you would only take Box A, it would leave the million dollars in it, as well as the thousand dollars in Box B. If the being predicts you will base your choice on a random event (like flipping a coin), it will leave Box A empty.

Now you have grounds to believe that in such matters, the Newcomb Being has a success rate on predictions of about 90%.

Depending upon you choice and the being's anticipation of your choice, you could walk away with $1,000,000, $1,001,000, $1000, or nothing. If you choose both boxes, the least you could receive is $1000 and the most would be $1,001,000. This seems to be the decision which would maximize your return, while minimizing risk.

On the other hand, if you pick both boxes, chances are that the Being would have predicted this and left you nothing in Box A. Giving up an almost certain one million for a certain one thousand seems awfully foolish.

Working out the expected return, based on the Being's 90% success rate, you come up with following decision matrix:

You Choose	Box A Contains:	Box B Contains:	Expected Value
Only A	.9 x $1,000,000	$1000	$900,000
Both Boxes	.1 x $1,000,000	$1000	$101,000

It seems like choosing only Box A gives you a lot higher expected return on average, even if there is the risk of nothing. But there you stand, before the boxes, and the Being has already placed the money. There either is or is not $1,000,000 in Box A. There certainly is $1000 in Box B. Nothing you could do at this point will change what is in the boxes. Why shouldn't you just take both to be on the safe side?

The being awaits your response. What do you do?

Since it was originally posed by William Newcomb, The Newcomb Problem has generated a great deal of commentary in philosophic circles on both sides. In fact, this problem is an oft-used example in the free will debate.

See the Solution