bigideas

A while ago we talked about Newcomb’s Paradox down the pub. In the end I came up with this slightly lengthy response to it, which I think defuses the paradox, although it has a slightly odd characteristic.

My argument is that the only way to rationally play the game is probabilistically — you choose box B only with probability p, determined by the success rate of the predictor and how much you stand to lose if you’re wrong. I argue that NP is reducible to a pair of sorites paradoxes. Starting with one paradox and ending up with two might not sound like progress, but there’s a huge body of work on the sorites (including an unpublished effort of mine), and there are various different ways you can defuse it.

The odd characteristic is that the proposed “rational” strategy doesn’t pay off as well (ie you don’t win as much over multiple plays) as either of the traditional strategies — always choosing Box B because you believe in some sort of predestination or time travel, or always choosing both boxes because you believe in free will. To put it another way, it isn’t as good as holding a “faith position” and being right. It does beat holding such a position and being wrong, and it sort of simulates the idea of tentatively holding such a position, but modulating it depending on how things pan out. This seems to me to be very typical of rationalist strategies in general.