I came across this cool thing: Newcomb's paradox

Quote: person is playing a game operated by the Predictor, an entity somehow presented as being exceptionally skilled at predicting people's actions. The exact nature of the Predictor varies between retellings of the paradox. Some assume that the character always has a reputation for being completely infallible and incapable of error. The Predictor can be presented as a psychic, as a superintelligent alien, as a deity, etc. However, the original discussion by Nozick says only that the Predictor's predictions are "almost certainly" correct, and also specifies that "what you actually decide to do is not part of the explanation of why he made the prediction he made". With this original version of the problem, some of the discussion below is inapplicable. The player of the game is presented with two opaque boxes, labeled A and B. The player is permitted to take the contents of both boxes, or just of box B. (The option of taking only box A is ignored, for reasons soon to be obvious.) Box A contains $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain $1,000,000. By the time the game begins, and the player is called upon to choose which boxes to take, the prediction has already been made, and the contents of box B have already been determined. That is, box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, the player is aware of all the rules of the game, including the two possible contents of box B, the fact that its contents are based on the Predictor's prediction, and knowledge of the Predictor's infallibility. The only information withheld from the player is what prediction the Predictor made, and thus what the contents of box B are.

So, would you choose one box or both boxes? Note that BTW when you're presented with the choice, boxes are already containing or not containing the money, so at that moment you lose nothing from choosing both... but if you do choose both, and if it has been predicted, you get just the 1000 rather than 1000 000 or 1001000.

From the conditions given in the problem definition, as I see it, the right choice is obviously to take just the box B and 1 000 000$ it will contain (almost always, or always, as stated in the problem definition).

Then you've made one of the possible arguments.

The other argument goes as follows: The Predictor has *already made* a choice. That cannot change. The contents of the boxes are the contents of the boxes. If box B contains the million, you get it whether you take both boxes or you only take B, because it contains what it contains. Similarly if it doesn't, it doesn't. Either way, by taking both boxes you come out $1,000 ahead.

I would tell everyone on the internet that I only plan to take box B, but then I would actually take both boxes.

Statistically speaking, taking only B is the best option.

The predictor is Almost Always right. Say that's 99% of the time.

Then you have (taking only B) 99% chance of $1000000 and 1% chance of $0. Average: $990000.
The other option (taking A and B) is 99% chance of $1000 and only 1% chance of $1001000. Average: only $11000.

So yeah, if gambling worked like that it'd be VERY easy to make money.

Quote: Original post by Zahlman
Then you've made one of the possible arguments.

The other argument goes as follows: The Predictor has *already made* a choice. That cannot change. The contents of the boxes are the contents of the boxes. If box B contains the million, you get it whether you take both boxes or you only take B, because it contains what it contains. Similarly if it doesn't, it doesn't. Either way, by taking both boxes you come out $1,000 ahead.

Yeah, I looked it up after I made up my choice.

I an fully aware of maximizing expected pay-offs and all that but I don't really see it apply here. It is given that it will guess correctly what you will decide. The paradoxical nature of it predicting your move is out of the question here.

The question is: If the conditions given are true what decision is right? There is no possibility of the predictor making a choice different to yours. The paradoxical nature of that claim itself is not under question here.

Anyway, that is my view, and since its one of two views commonly taken, the arguments presented above have no doubt already been presented many times. :)

As I consider myself a somewhat rational person, I would not base my decision on the assumption that a Predictor existed and could predict my choice. Taking both boxes would thus be the rational choice, as I would get either 1,000 (if the prediction was correct) or 1,000,000 (if it was not). You can't trick me into taking only box b, by telling me that someone is a psychic.

I'd tell the Predictor to construct the set of all sets that don't contain themselves, and then I'd steal both boxes and leave through the backdoor.

Quote: As I consider myself a somewhat rational person, I would not base my decision on the assumption that a Predictor existed and could predict my choice.

In this particular case, the Predictor doesn't need to be precogniscent. If I was the Predictor, I would just ask myself "if the person knows I am always right, which box will he choose?" and then I'd "predict" that box.

You take both boxes, receiving $1001000. Then you cut the Predictor in for his 50% of the extra thousand.