Wednesday, April 15, 2009

Newcomb's paradox

Wikipedia article
Some website's article.
There are two boxes, labelled A and B . You face a choice between taking just box B or both boxes.
Box A contains 1000$ . If Predictor had predicted that you'll take just the box B, box B contains 1000000$. Else if Predictor has predicted that you'll take both boxes, box B contains nothing.
A million people played this game, and Predictor was never wrong.
Will you take just the box B or will you take both boxes?
(I'm "one-boxer")

I think this paradox is not weird enough and needs to be made weirder. Imagine that boxes are made of glass. In such case, would you still choose one box? Why does it make difference when even with opaque boxes you know that taking both boxes always gives you 1000$ more?
(There is why it makes difference, actually: you could pre-decide to pick box B if it empty, and pick both if B is not empty, making predictor certainly wrong)
Also, what happens if its 50$ vs 100$ ? 99$ vs 100$ ? 0.01$ vs 100$ ?


  1. This doesn't sound...exactly right. I think there's an option to pick box A and get the 1000 guaranteed no matter what. Otherwise it wouldn't make much sense. Who would be so greedy as to pick both boxes, trying to get an extra 1000 when they already have the one million?

  2. Given recent advances in neuroscience, which enable a machine to detect your decision to (say) push a button with your left hand (as opposed to your right hand) a fraction of a second before you are aware of having made the decision, the intriguing possibility arises of actually carrying out Newcomb's dilemma in the lab.

    That is, we have a clock that counts down to zero. At the moment the clock shows zero, you have t seconds to decide whether to push Button 1 or Button 2, corresponding to the two choices of Newcomb's problem. At time zero, the machine puts money (or not) into the opaque box according to its prediction of your decision. (If you press both buttons, or neither button, by the time t seconds elapse, then you get nothing.) The value of t is chosen to be small enough so that the machine can reliably predict your choice, but large enough so that you have the subjective impression that you are making your decision after the clock reaches zero.

    This experiment ought to be feasible with current technology, but I haven't heard of anyone actually performing it.