It's nearly the weekend, and I need to give my colleagues something to keep their brains working while they're away from their desk. So...
It's been a week since you encountered Newcomb's Predictor. You, being a classic two-boxer personality, opted to take both boxes, and although mildly disappointed to find you won only £10,000, you felt satisfied in your choice. One cannot always win such games.
However, as you are walking home one day you find yourself before the Predictor once more. He explains how he's had a cunning idea. This time round, he's either made a prediction and filled the boxes appropriately, or he hasn't gone to the effort and will wait till you announce your choice and then surreptitiously fill the boxes as necessary. The Predictor does these options with equal frequency.
As you contemplate this, you receive a tap on the shoulder. You turn round to find yourself faced with yet another Being, who introduces himself as the Meta-Predictor. He can not only predict your actions, but he also has a great track record of predicting the actions of the Predictor. The Meta-Predictor tells you this:
"You will either choose A and B, and the Predictor will fill the boxes after the fact, or you will opt to take only box B, and the Predictor has already made his decision and the boxes already contain the right amount of money."
Puzzled, you contemplate matters a little further...
Now, if you were previously a one-boxer in this situation, nothing's really changed dramatically for you. You make your choice, take one box and walk off (almost certainly) completely loaded.
If you're a two-boxer however, you might have a problem. Maybe your actions really will affect the box contents. If you were going to take two boxes, you may find your choice will have a causal effect on the future. In that case, you should take one box, as the Predictor will then fill it with loads of money. If you're going to take one box though, it seems likely that the Predictor hasn't made his move, and nothing you do will affect the contents, so maybe you should take two boxes after all?
This one is due to Nick Bostrom.
Personally I think there might be an internal inconsistency here - are the statements about the frequencies with which the Predictor takes each path correct? Perhaps they're globally correct, but not right for this particular case where the Meta-Predictor makes his statement (he's perhaps screwed with the probabilities in a manner not entirely unlike Monty Hall). If not, perhaps the Meta-Predictor's statement changes things and there is already in effect a decision made which the Predictor is inexorably constrained to follow - in a sense the fact the boxes aren't already filled doesn't matter, as the fact he will choose to fill the boxes later is already laid out.
It's an interesting twist, but I think the really puzzling stuff still lies in the conventional Newcomb situation.
Edd -
thanks, good to know you're thinking of us. Maybe I'll discuss it with whoever sits next to me on the plane, and spread the joy. In the meantime, I'll be smug in the knowing that I'm _clearly_ sitting on the right side of the fence here!