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Post by BlueDolphin on Apr 13, 2007 15:02:39 GMT -5
Let's say you have a room with two boxes inside. Box A has $1000 in it. Box B contains either $0 or $1,000,000. When walking into the room, you may pick both boxes or just box B. Then you can open the boxes outside and keep the money.
Whether B contains a million depends on the Predictor. The Predictor is a hyper accurate entity that can predict what a person does in the room. He has predicited accurately the choices of people before you at a rate that is currently 100%.
If he predicts that you take both boxes, he will put $0 in the box before you enter. If he predicts you take B alone, he will put $1,000,000 inside.
All his actions are done before you enter the room. Once you are inside, he cannot alter the contents of the boxes.
Which is the most rational choice?
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Post by Paveltc on Apr 13, 2007 15:41:12 GMT -5
well, if you can take both boxes why not take them both? You get the 1,000 either way, or am I misunderstanding something?
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Post by BlueDolphin on Apr 13, 2007 15:49:05 GMT -5
But what about the Predictor's actions? Would he have predicited this and left you nothing?
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Post by Random on Apr 13, 2007 16:01:54 GMT -5
anyone going into it who intended to only take the B box would just take both once they were in, and get both amounts of money, unless the predictor would factor that in, and if he does then this question is semi-pointless and you'd have to be retarded to do anything but just take the B box
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Post by BlueDolphin on Apr 13, 2007 18:34:42 GMT -5
I agree that Box B is the most rational choice. But I'm going to be devil's advocate and say that taking both has some merit.
There are two rational ideas at work here. One is the Maximized Expected Utility. Under MEU, taking box B has the highest expected payoff.
The other one is the Dominance Principle. When choosing, shouldn't one choose between two higher rewards than two lower ones?
When you enter the room, either Box B has a million or it does not. Either way, you will be better off taking the extra thousand. Since the money can't be removed once you are inside, taking both boxes would always leave you better off than if you took just B.
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Post by Arachis on Apr 14, 2007 5:57:40 GMT -5
It depends on how well you believe the predictor can predict. If you believe he can predict perfectly, take only box B. If you believe he can predict imperfectly, pick both. The problem is that if you try and pick both after having planned to pick only box B, the predictor should have predicted it and not placed the money in the box. Hence, the choice is only based on how much you trust the predictor to predict your action.
Religious people should pick box B.
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Post by Random on Apr 14, 2007 5:58:57 GMT -5
the Dominance Principal bit is irrelevant if box b will be empty if you intend to take both and the predictor will accurately predict what you will do 100% of the time, no matter when you actually decide what you're doing
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Post by BlueDolphin on Apr 14, 2007 12:42:39 GMT -5
This is a good argument but what happens once you walk out of the room and find that there was a million inside? Wouldn't you feel bad that you could have snatched the extra thousand and got away with it since the Predictor can't change the contents of the box after entering?
Who voted for taking both boxes?
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Post by Random on Apr 14, 2007 14:49:03 GMT -5
no, again, its the same thing over and over
I wouldn't feel bad about not taking both boxes because if I was going to, no matter when I decided to, there wouldn't be money in box B, period
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Post by Arachis on Apr 14, 2007 16:31:37 GMT -5
I dont trust the predictor, so I chose to take both boxes. Someone would have to prove the predictor works 100% of the time to me.
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Post by Archagon on Apr 14, 2007 17:43:18 GMT -5
But if you "intend" to just take box B, how can you also intend to take both boxes once you go inside?
True, but the problem states that the Predictor is "hyper accurate" -- and in logic land, definitions never falter. ;D
I think the main fault of this problem is that $1,000 pales in comparison to $1,000,000, which gives the subject no real impetus to go for both boxes. If box A could potentially have, say, $10,000, then the problem would be more challenging.
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Post by Arachis on Apr 15, 2007 8:00:26 GMT -5
I still dont understand where the problem lies.
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Post by BlueDolphin on Apr 15, 2007 13:10:50 GMT -5
The argument for taking B is that whatever you do, it would be seen by the predictor. Although he cannot change the contents of the box after you enter, and there is no backwards causation, his ability to see into the future means that your actions in the future do influence the past for all practical purposes.
Because of this taking B "causes" there to be a million inside while taking both would get you only a thousand.
But what if there was more money in the box like Alexei suggested. Would you change your answer for $10,000 or $100,000 in A?
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Post by Random on Apr 15, 2007 16:01:20 GMT -5
the choice is always going to be to take B until there is more money in A than there is in B
I dunno why it needs to keep being said, it doesn't matter when you "decide", the predictor would know what you'll do, and unless you only take B you aren't getting as much as you could've. period.
there is no reason to go after A until theres more money in it than B
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Post by Arachis on Apr 15, 2007 18:24:19 GMT -5
exactly. In my opinion, even game theory is more interesting than this "puzzle".
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