An extremely reliable predictor of human behavior places two boxes -- a clear one and a black one -- on the table. He's going to give you the choice between taking (1) just the black one, or (2) both of them. But he's already predicted which choice you'll take. And if he predicted that you'll take just the black one, then he put a million dollars under it. If he predicted that you'll take both of them, then he put nothing under it. Either way, he also puts $1000 under the clear one. Which choice do you take?I, who am a two-boxer, reason like this, which seems perfectly obvious to me: no matter what he's predicted, I'm better off, by $1000, taking both. That's because there either is a million dollars or there is not a million dollars in the black box, which means there is a total of either $1000 or $1,001,000 on the table, and I don't get to pick which. So I should take all of the money on the table. Allan, who is a one-boxer, offers this argument for one-boxism (Matt, who is also a one-boxer, has not told us why he is, but maybe it's for a reason like this):
P1: There is a strong probabilistic connection between taking one box and getting a million dollars (i.e. 99% of people who take one box get a million dollars). P2: There is a strong probabilistic connection between taking two boxes and getting a thousand dollars (i.e. 99% of people who take two boxes get a thousand dollars). C: I should take one box (if I want more money).Even if the premises are correct, I think that the argument is invalid. Once the predictor has done his predicting, Allan just doesn't have any say in the matter of whether he gets that million. The "strong probabilistic connection" is not causal. I think that the underlying structure of the probabilistic connection actually looks like this:
- There is a strong probabilistic connection between taking one box and being the kind of person who takes one box.
- There is a strong probabilistic connection between being the kind of person who takes one box and being predicted by the predictor to take one box.
- There is a (perfectly) strong probabilistic connection between being predicted by the predictor to take one box and getting more money.