### Musings on Newcomb’s Paradox

So, I’ve been thinking about Newcomb’s Paradox lately.

I think part of the issue is it conflates a couple issues, and it might be useful to consider them separately. So, think on these paradoxes:

**Determinism vs. Nondeterminism**

Consider a superhuman predictor and a fair coin. The predictor predicts what the coin will show, then you flip it. The predictor is [nearly] always right.

**Removal of free will**

A computer has been programmed to maximize its expected score as a player in the Newcomb scenario, given that the predictor has a copy of the program to analyze, run in simulation or on another computer, etc. How will it play?

My take on Newcomb’s paradox? It reduces to the question of whether free will makes our choices inherently unpredictable, and the paradox is thorny because free will isn’t well defined enough to provide a clear answer.

If we have no free will, it’s just the computer scenario. If we assume free willed actions are inherently unpredictable, then the existence of a predictor contradicts that assumption, just like it contradicts the assumption that the outcome of a fair coin flip cannot be predicted.

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

afterthe clock reaches zero.This experiment ought to be feasible with current technology, but I haven’t heard of anyone actually performing it.

Comment by Timothy Chow — 18-Sep-2009 @ 14:29