Social Science Statistics Blog

I don't see how this story in particular forces us to countenance the notion of "reverse" causality unless we accept that some people have a time machine in their back yard (kindly introduce me to them). Please elaborate.

One argument that is often made in response to Newcomb's paradox is that one should just choose box "B". After all, the predictor is always right so everyone who selected just "B" received the million dollars. But, the "predictor's" decision is fixed at the time you arrive to make your decision. Therefore, arguments that suggest you should choose just box B imply that your action in the future is causing the event in the past. Usually, we believe for event "X" to cause event "Y" that "X" must occur before "Y".

Apologies for not being more explicit. Does that remedy the question?

Nah, I still don't get how this compells us to accept the existence of reverse causality in the Real World. The Predictor predicts at time 1. We decide at time 2. No reversal of time necessary, as long as we countenance the possibility of perfect foresight (which, actually, I don't for all practical intents and purposes, though it is fun to play around with in the abstract). - - - The reason, I think, we care about Newcomb's paradox is because some authors have - mistakenly - have used a weaker version of the story to argue for reverse causality. For example, my expectations about my future educational achievement may cause my educational investment in the present, which in turn influence my actual achievement in the future. Is this reverse causality? Hardly. Expectations at time 1 influence investment at time 2 influence achievement at time 3. No time machines involved. (Check out Heckman 2005 for the strongest arguments to date about joint or simultaneous causation - though still nothing that would really compell us to accept "reverse" causation if "reverse" is understood to mean "against the flow of time").

There was a good discussion of this at Andrew Gelman's blog, a while ago... including comments from Radford Neal.

I go back and forth on this one. If we are to assume that backwards causality is impossible, and that the predictor isn't just lucky, then the situation is essentially this. There's some state of a person, or disjunction of states, S, which is such that it's incredibly likely that somebody who has it will be a one-boxer and somebody who doesn't will be a two-boxer. Either I was in S when the predictor predicted or not; of course I do not know this. If I was in S, and take one box, I get the million. If I was in S and take both boxes, I get a little more than a million, plus the satisfaction of proving the predictor wrong. If I wasn't in S and take one box, I get nothing apart from the pyrrhic satisfaction of proving the predictor wrong. If I wasn't in S and take both boxes, at least I come away with something. It looks like two boxes is the way to go. Of course, if I take one box, it probably turns out I was in S, but I can't make myself have been in S by taking one box. That's already been settled.

Perhaps one should believe in backwards causation, so that one does not end up thinking one's self out of a million bucks.