You beat me to it. It’s the only way the premises hold. The only guy who ever sees $1M1K there is the guy who would pick only one box, regardless. The 2-box strategists wrongly claim that this guy’s strategy is wrong, but in doing so, they’re merely challenging the hypothesis.
Of course, it’s quite possibly that the hypothesis is logically inconsistent from the get-go. If it is, then of course anything can follow: from a contridiction you can prove anything. So the question is this: is the ability to predict the future a logical fallacy a-prior? I don’t think this thought experiment is the best one to illustrate that issue, though admittedly it raises it.
I can predict that the sun will rise tomorrow with the same success rate that the Predictor can pick a one or two boxer. Is it a logical fallacy to say that I am able to predict a thing with such certainty?
All the hypo does is up the stakes. The Predictor is so good at human psychological analysis that he can pick what you will choose at the moment of truth. It’s only a variant in degrees, not a contradiction or a paradox.
Really? You walk on stage, see both boxes filled, and you still tell yourself “I’m free to, five seconds from now, pick either one box or both boxes”?
Well, in that case, why aren’t you taking both?
Your answer: “If I was taking both, the money wouldn’t be there!” Then the decision has already been made, in the future, and you know what you’re going to do based on information from the future.
So you say, “Fine, dammit, but I’ll pick box B anyway, because that’s what will give me the highest payout, even if it doesn’t make any sense”. Now logic no longer works as a method for finding the highest payout.
Fourth option: You give up, grab both boxes, and make off with the full amount. Then the prediction was just wrong, which fights the hypo.
Still same problem, same paradox, only now you’re acting as both contestant and predictor rolled into one.
No, that is clearly not a logical fallacy. We can predict lots of shit with near 100% accuracy. That’s part of the reason why this problem is such a pain in the ass.
The problem seems to apply to a particular sort of prediction. Either predictions regarding entities with free will, or predictions that can interfere causally with their outcomes, or both, or something slightly different.
No. The decision was made because it was in my personality and make up to understand the nature and the problem and refrain from taking the second box. If I didn’t, the money wouldn’t be there.
It may be that the box is always empty because of such human frailties. If the box isn’t empty, it’s because I will follow through with only picking B.
Of course logic works. How is it illogical to understand the constraints of the problem and choose the higher payout? It’s just that in our universe nobody can read another person like this, so it’s not a consideration.
Bingo. But, it’s a problem, not a refutation. That is, I sure don’t know whether these kinds of predictions involve a logical fallacy. My suspicion is we could construct some that are.
This particular case is a gray area, where it’s really not clear whether the initial conditions are inherently contradictory, or whether the two-boxers are just plain logically wrong. But I suspect it has to be one of these two cases. (I’m not restricting the problem to this world, where prediction might be impossible, but to some theoretically valid worlds where it is. There might be no free will in such a world.)
The problem that the two-boxers are facing is that game theory would suggest that two-boxing is a dominant strategy. What they don’t seem to be factoring in is the nature of the predictor, which alters the game theory equation to the point that one boxing is the dominant strategy.
For those who just can’t accept a perfect predictor, lack of free will, etc; treat it as I suggested a while back : the game is rigged. they’re cheating. There’s a trap door under Box B that takes the money away if you pick both boxes.
OK, you walk on stage, see $1000 in box A and a million in box B. You tell yourself that there is a trap door under box B. Which is fine. Except for the tiny detail that there actually isn’t one.
Heck, I’ll put the money in two cardboard boxes, take them to your house and put them on your living room floor (makes for interesting TV). In terms of game theory, sure, you can act like there’s a trap door, but it would be delusional.
I know. I’m setting up an analogous situation to try and ease the anxiety of the two-box people who are freaking out. And if this situation happened in real life, I would assume that there was cheating, since I don’t believe in reverse causality.
The two box people are seeing a game theory grid : four squares outlining the possible choices for both participants. The guesser gets “One Box” or “Two Box”, and the predictor gets “One Box” or “Two Box”. You fill in the squares with the money that the guesser gets based on the combination of choices. And game theory says two-boxing is the dominant strategy.
But you’ve set up the grid wrong. One, the predictor isn’t trying to maximize his utility, so game theory is questionable to begin with, but more fundamentally, the predictor is always right. So the grid would be a single column with two rows for the guesser. If the guesser takes one box, he gets a million. Two boxes, he gets $1000. The dominant strategy if you accept the hypothetical is one-boxing.
Well, a trap door’s a little more plausible than a magic man who tells the future, but whatever floats your boat, sparky. The two situations are equivalent in terms of outcome. I’m just trying to help.
I apologize. In my head, my post didn’t sound as inexplicably dickish as it came out.
Yeah, the trap door is a good illustration of why one-boxing is the dominant strategy.
My point was that, even so, the two-boxer strategy seems to make sense, and one-boxing has an element of absurdity to it. But then again, I don’t really want to relieve the anxiety of the two-boxers, or the one-boxers for that matter. I like watching all of them squirm.
