The alien has apparently predicted you'll take one or both. It doesn't allow you to walk away.

That's where the "paradox" lies. How can the alien's prediction not allow you to walk away? Obviously, choosing only B is a valid "decision path," as is taking B and then A. So if you look in B, and there isn't a million dollars, as a human being with normal faculties, how is it that you are forced to also take box A (and so validate the aliens apparent prediction that you would take both)? The alien just left the boxes there; he no longer has any "influence." Under a typical understanding of human psychology, a person clearly would not also take box A, once having found box B empty, thereby invalidating the alien's prediction. Likewise, a person clearly would also take box A, once he has already gotten the million dollars from box B.

Indeed, as you say, if we grant that the alien is correct, we will somehow "magically" be forced not to take box A once we've found a million dollars, or be forced to to take it once we've found B empty, but that dramatically violates common understanding of human behavior. That's why it seems very plausible that such a prediction is not actually compatible with the universe we live in.

As an addendum: The idea that, from your perspective, your present actions have an impact on what happened in the past (what was already placed in the boxes) is merely weird, but seemingly without contradiction. The apparent contradiction (and thus "paradox") arises only when you consider what SamLowry suggests, that you can know the content of the alien's prediction (by opening just box B before you actually choose whether to open box A. But this suggests either that something weird would happen that restricts your choice anyway, or that the notion of such a prediction in our universe was contradictory to begin with.

How can the alien's prediction not allow you to walk away? [/quote]
I thought it was an axiom in the original post:

The alien says that you are free to take either just box B or to take both boxes.[/quote]

Even without it as an axiom, I might instead say that the alien makes no claims about the contents of box B if the human doesn't follow the "rules".

The alien just left the boxes there; he no longer has any "influence."[/quote]
I am not denying that. What I am saying is that assuming the alien can predict a human's decisions, and if he tells the truth about "his side" of the bargain, then there is no way to get $1,000,000 + $100. Any human that thinks they can will find box B empty. A human that leaves A untouched, but opens B will get $1,000,000.

By "forced", I mean following the rules of the game the alien presented the human. You can only get $1,000,000 by agreeing, not just now but in perpetuity, to not open box A. The alien has already predicted that you will not do so to get the $1,000,000.

If you turn around and open box A after getting the million, then the alien cannot predict human decisions. Which I believe is consistent with my explanation as I've based my reasoning on the assumption that it can make these predictions.

Even without it as an axiom, I might instead say that the alien makes no claims about the contents of box B if the human doesn't follow the "rules".

In that case, it's as I said originally: weird, but without contradiction, and so definitely not a paradox. It's just an example of the present "influencing" the past; it seems counter-intuitive from our perspective, but in a deterministic universe (in which such predictions can be made) it's really no more absurd than the present "influencing" the future. If the universe is deterministic, time is just another spatial dimension; the idea of "cause" is as more an artifact of human perception as it is a real thing.

On a more concrete note it is indeed possible for the future to "influence" the past, but the catch is that you can't verify that this has occurred until after the future happens, and so it doesn't yield any method for gaining information about the future.

There's no turning the tables on the alien, and either walking away, destroying the boxes or even opening A after finding B empty, since the OP doesn't state any of these options.

I also don't get that a rational human would take both boxes, for a guaranteed gain. The alien is assumed to be perfectly rational and with 99.99% certainty predict your choice. If you open B only, then the alien predicted that and thus put in $1M. To take A and B would be stupid, as you're only guaranteed $100 which doesn't get you anywhere.

I also don't get that a rational human would take both boxes, for a guaranteed gain. The alien is assumed to be perfectly rational and with 99.99% certainty predict your choice. If you open B only, then the alien predicted that and thus put in $1M. To take A and B would be stupid, as you're only guaranteed $100 which doesn't get you anywhere.

To play devil's advocate, some would say that a rational human would know that whatever is in the boxes is "already" there, and so their choice can't really effect the contents of the boxes once the alien has already left. Thus, by not taking both boxes, all you are doing is throwing away $100.

Personally, I'd ask the alien what my choice will be and, if he answers, save myself the time and effort of guessing what he thinks I'll choose.

[quote name='Don Carnage' timestamp='1301181404' post='4790816']
I also don't get that a rational human would take both boxes, for a guaranteed gain. The alien is assumed to be perfectly rational and with 99.99% certainty predict your choice. If you open B only, then the alien predicted that and thus put in $1M. To take A and B would be stupid, as you're only guaranteed $100 which doesn't get you anywhere.

To play devil's advocate, some would say that a rational human would know that whatever is in the boxes is "already" there, and so their choice can't really effect the contents of the boxes once the alien has already left. Thus, by not taking both boxes, all you are doing is throwing away $100.
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But if you open both boxes, the alien would have predicted that, and you only get $100. Getting $1000100 can't happen or the alien was deceiving you. If you open B only, you get $1M, or the alien is deceiving. There's nothing compelling you to open the other box, since you know whats in it. By your argument, you could never get anything but $100, so the alien is lying again. What kind of alien is this anyway, seems like an intergalactic con artist. Like where did he get the money in the first place - selling off human embryos or something? I say take those boxes of fake money and fly into a black hole you extraterrestial scum!

Maybe suggest to the alien to give say 9 other people the same choice, so you could have 20 boxes with the rewards split out. If enough people then opens B to find it empty, the confidence in the aliens' prediction would decline, thus making A+B the more rational choice.

To play devil's advocate, some would say that a rational human would know that whatever is in the boxes is "already" there, and so their choice can't really effect the contents of the boxes once the alien has already left.
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I'm thinking about it as a tree. The options where you might get $1,000,100 have been pre-pruned by the alien. You don't have a choice. If you pick up B, and it has $1,000,000, you've been committed to a path which forgoes the $100. If you pick up B, and it is empty, you are clearly on a path where you next pick up A.

Thus, by not taking both boxes, all you are doing is throwing away $100.
[/quote]
To simplify, assuming the alien can predict and is not lying, then your strategy nets you $100 and mine nets me $1,000,000. I may walk away from $100 but I think I could live with that. On the other hand, by committing to taking both boxes as the only logical choice I see you as walking away from $999,900.

I see this as essentially a one player prisoner's dilemma; therefore I see defection as being the sub-rational decision. Co-operating with the rules seems the obvious conclusion to me, again assuming we trust the alien.

You are presented with three boxes, and told that one box contains $100. The other two contain nothing. You are allowed to put your hand on one box, and then the presenter will take one of the other boxes away. The box that the presenter removes is guaranteed (and shown) to be an empty box. Then you are given a choice: You may stick with the box under your hand, and get whatever's inside, or switch to the other box. Which do you choose?

There is a rational choice to be made, but many people guess. Is rationality why you answered as you did?

I know I've heard this explained before, but I can't remember the reason. Isn't it something like the box you put your hand in has a 33% chance of having the item, but after he takes away the other box the remaining box has a 50% chance of containing the item so you should choose that one?