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Icarus
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Newcomb's Dilemma
« on: Dec 21st, 2002, 7:37pm » |
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This is not really a puzzle, but it is an interesting question. Once again it comes from the pages of Martin Gardner. The name refers to William A. Newcomb, a physicist at Lawrence Livermore Laboratory, who came up with it in 1960.
A great advance has occured in the field of artificial intelligence. A computer has been programmed to predict your actions, and has proven itself able to do so with amazing accuracy. You have put it through many difficult and devious tests, yet it has always been correct in its predictions. A certain multibillionaire with a twisted sense of humor has decided to reward you for your great discovery. He take you into a room with two boxes and tells you that box A contains $10,000 while box B either contains nothing, or a certified check for 1 billion dollars. You will be allowed to open exactly one box and keep it contents. The catch is this: Earlier, your program was asked what you would do. If the computer predicted you would open box A, then the 1 billion dollar check was placed in box B. If the computer predicted you would open box B, the box will be empty. Which box should you open?
Note that box B was prepared before you enter the room.
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Jeremiah Smith
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Re: Newcomb's Dilemma
« Reply #1 on: Dec 21st, 2002, 8:13pm » |
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Well, I would take A... if the computer knows I'll take A, it'll stick the big money in B, but I still get ten grand from A. If I decide to have B, though, it sticks nothing in B, and so I get nothing. So, I can either choose between $10,000 or nothing.
Hmmm...beforehand, do you know about what the computer will do in each situation, or are you oblivious to the fact that what's in B is determined by the computer's predictions?
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Icarus
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Re: Newcomb's Dilemma
« Reply #2 on: Dec 21st, 2002, 9:15pm » |
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You are told about the prediction and its consequences. But you are not told what the prediction was.
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Jeremiah Smith
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Re: Newcomb's Dilemma
« Reply #3 on: Dec 22nd, 2002, 3:06am » |
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So then I'd take A 
I think part of the reason this riddle isn't so easy, is that people will usually be greedy and try to find some way to get the billion dollars, instead of realizing that they should just try to get as much as possible.
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towr
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Re: Newcomb's Dilemma
« Reply #4 on: Dec 22nd, 2002, 7:19am » |
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flip a coin..
Let randomness guide 'your' action.
50% chance it'll have you take A, in which case uyou get 10.000. 50% chance it'll have you take B, which can have been predicted by the AI program in 50% of the time, so expectancy of half a billion dollar. So a total expectancy of just short of a quarter of a billion dollars..
Good odds considering the game didn't cost you anything..
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Icarus
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Re: Newcomb's Dilemma
« Reply #5 on: Dec 22nd, 2002, 3:30pm » |
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Good Idea, towr. But just to be onery, if the computer predicts you will give yourself any chance of opening box B, the box will be empty.
The point of this question is about free will. If the computer predicts you will open A, then when you are in the room, B has the 1 billion. Why not just go ahead and take it? Why settle for the 10,000 when the 1 billion is at hand?
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fenomas
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Re: Newcomb's Dilemma
« Reply #6 on: Dec 22nd, 2002, 7:48pm » |
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I think I'd walk into the room, switch the labels on the boxes, and open what is now labeled as Box A.
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towr
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Re: Newcomb's Dilemma
« Reply #7 on: Dec 23rd, 2002, 1:08am » |
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Ah yes.. free will..
The illusion people have about not being predictable.. Actually, being predictable and free will needn't have to do anything with each other.. It can be your own choice to be predictable.
In the end, here, it depends on how to AI program can figure out your decisions.. If it's clearvoyant you can't do very much against it, but chances are it isn't. So it could use rules and statistics.
The problem with rules in this case is: take A, so the billion is in B, so take B, so it's empty, thus take A, etc
If that's how the program reacts it's 50-50 chance. But under the new by-law, any chance of taking B means its empty, so take A. So why would the computer predict any chance for B. In the end the AI is likely to go insane..
Of course the may be rules to guard against going into an infinite loop, just like people have (you get tired of looping eventually).
An interesting question might be, does the AI think like you. If it does, which is likely since it needs to predict your choices exactly, it may be on your side, and say A so you can take B. Of course it'd need to know the situation. But to predict the situation it will think it is you, and some AI program is predicting what it'll do. So you get into another loop, probably ending in 50-50 chance. Which would mean B is empty, so it chooses A, so you should choose B, which it will thus be empty..
I think since any good AI program would always leave the possibility open you'll choose B, it will be empty. Even if you know it has to be empty there's still the chance you pick it cause you're not sure..
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fenomas
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Re: Newcomb's Dilemma
« Reply #8 on: Dec 23rd, 2002, 6:53am » |
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Towr, I think you're talking yourself in circles... Which is clearly what this poser was designed for (I'm assuming this isn't really a "puzzle", with an answer, but something to get us thinking).
In the end, with the "any chance of taking B" addendum, you really can't get the billion dollars without contradicting the setup of the puzzle, which is that the computer is "amazingly accurate", which is to say that it will presumably be correct. It doesn't matter how it thinks- it's a black box as far as the puzzle is concerned. Even cute answers, like switching the labels, or getting someone to hypnotize you into thinking "A" is "B" before you go in don't really count, because the computer should see that too. I don't think the billion is gettable.
So I'm going to go with: you walk into the room and say, "What is love?" or some such deep question, then when the computer gets confused and explodes (a la classic Star Trek- that western episode), you take the money.
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Icarus
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Re: Newcomb's Dilemma
« Reply #9 on: Dec 23rd, 2002, 2:36pm » |
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I stated right at the start that this is not a puzzle. Really, I was hoping to get some people to take the position Gardner says many people took for him, which was that the logical course would be to open box B. I have even tried to throw out some of their reasoning in hopes someone will run with it, and maybe I can gain a better understanding of their point of view (yes, I personally believe you should take A). Maybe someone will yet.
In the dilemma as stated by Martin Gardner, the predictor was an omniscient being, not a computer. But it seemed to me that a lot of the responses he mentioned were nothing more than atheists getting upset about the suggestion that such a being could exist. By making the predictor a computer program, I was hoping to avoid arguments based on religious fervor rather than rational reasoning.
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SWF
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Re: Newcomb's Dilemma
« Reply #10 on: Dec 23rd, 2002, 7:05pm » |
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Perhaps everyone is claiming to take Box A to fool the computer, which presumably has access to this riddle forum, should this situation ever arise.
Suppose this is a TV show and before making your choice a camera inside Box B shows millions of viewers that Box B has $1 billion inside. If you pick B, will the money disappear in front of everyone's eyes? The computer isn't that powerful. All it can do it make predictions At the time of your choice, the money is either already in the box or it is not, and the computer can't change it. Everyone here is saying they will take Box A. Don't they wish they had taken Box B? Remember that every time after Box A was chosen, it turns out there was $1 billion in Box B all along. All those TV viewers must think you are nuts for picking Box A.
This version of the paradox is slightly different from the usual version. In the usual description, the choice is between taking just box B (which the computer stocked with a $1 million if it predicted this choice, otherwise empty) or taking the contents of both boxes (box A always contains $1000). So in Icaraus' description you get rich if you successfully fool the predictor, but in the usual version you get rich if you match the prediction. However, there is the temptation to take both boxes anyway since the contents of both boxes is always $1000 more than just box B.
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lukes new shoes
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Re: Newcomb's Dilemma
« Reply #11 on: Dec 29th, 2002, 4:31am » |
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does the computer know its predection is going to be used to determine the contents of box B?
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Jeremiah Smith
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Re: Newcomb's Dilemma
« Reply #12 on: Dec 29th, 2002, 8:37am » |
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on Dec 23rd, 2002, 7:05pm, SWF wrote:| Everyone here is saying they will take Box A. Don't they wish they had taken Box B? Remember that every time after Box A was chosen, it turns out there was $1 billion in Box B all along. All those TV viewers must think you are nuts for picking Box A. |
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Yes, but theoretically, the computer or the deity would analyze your brain wave patterns and thought processes and think "Hmmm...he's gonna think about taking A, so the billion will be in B, and then he's gonna switch and take B at the last second."
I think a lot of the paradoxes seem to stem from thinking the predictor isn't omniscient regarding what you'll do.
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BNC
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Re: Newcomb's Dilemma
« Reply #13 on: Dec 29th, 2002, 11:56pm » |
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The way I read the dilemma, you cannot fool the computer / deity (let assume that is the sci-fi manner, the AI has a time machine in which it observes your future actions). Given that, I totally agree with the previous posts – take box A.
note to self: when designing my omniscient AI machine, leave a loophole for allowing me to select the 1 billion.. 
BNC
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James Fingas
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Re: Newcomb's Dilemma
« Reply #14 on: Jan 2nd, 2003, 9:57am » |
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BNC,
That's exactly it! You can never win picking box B, because if you were to pick box B, then the computer would have predicted it. Even with this weird prediction thing, it's still cause-and-effect:
1) You decide to pick box B
2) The computer realizes (before the fact, but whatever!) that you'll pick box B
3) There is nothing in box B.
Therefore, you get $0 if you pick box B, and $10 000 if you pick box A. The fact that $1 billion is in box B is not helpful to you--the only reason it's there is because you're taking the $10 000.
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SWF
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Re: Newcomb's Dilemma
« Reply #15 on: Jan 3rd, 2003, 6:37am » |
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on Dec 29th, 2002, 8:37am, Jeremiah Smith wrote:
I think a lot of the paradoxes seem to stem from thinking the predictor isn't omniscient regarding what you'll do. |
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Yes, the arguments for taking box A are jumping to the conclusion that the computer is omniscient, even though the question only states that it has never been wrong in many tests. I guess it depends on how easily one is convinced that the program will always be right in the future. If instead, one cent was in box A, would anyone change his mind to box B? If so then, isn't that admitting that there is still some possibility that the computer will fail? Even $10,000 vs. $1 billion is a factor of 100,000 difference, so I guess a streak of "many" convinces some people that there is a least 100,000 to one chance of the streak being broken in a given test.
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BNC
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Re: Newcomb's Dilemma
« Reply #16 on: Jan 4th, 2003, 1:59am » |
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on Jan 3rd, 2003, 6:37am, SWF wrote:
Yes, the arguments for taking box A are jumping to the conclusion that the computer is omniscient, even though the question only states that it has never been wrong in many tests. <snip>
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That's an interesting point. As I posted before, I read this dilemma as if the computer was omniscient (like in other posted versions of the dilemma). But all this version of the dilemma stated was that the computer had an amazing accuracy.
I guess that you may assign a value to the probability of "the AI being right" P, were P<1. In that case, the expected value of box B would be (1-P)x10^9. So a good choise of box B would be if (1-P) > 10^5.
But then it only gets more complicated. I think that in such cases, it would be safe to assume the P is not constant for all predicted cases. E.g., P would be larger for the question "what will you have for breakfast?" (happend a lot of times in the past) than it would for the question "would you save your worst enemy from being eaten by a magical, soul-eating, dragon?" (probably didn't hapen more than once or twice before...)
If that is indeed the case, we will need to estimate P for the question in hand. Now, let's assume that whoever designed an "almost omniscient" AI program, has a good understanding of math and logic. In fact, we may even assume he / she is a member of this very board. So P wouldbe calculated, not for the first time question "what box do you pick?", but rather for the more general question "how do you choose based on statistics?". The program would assume you to do the math!
So P would be dependant on P. The larger P is, the larger it would be. That a positive feedback in action. P will reach 1 very rapidlly. Thus, (1-P)x10^9 -> 0.
In conclusion, I would still pick box A.
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mook
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Re: Newcomb's Dilemma
« Reply #17 on: Jan 4th, 2003, 10:24am » |
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After I ask the computer which box he predicted me to open, I open the other box. Why should I think so hard when I have discovered this great artificial intelligence?
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Jeremiah Smith
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Re: Newcomb's Dilemma
« Reply #18 on: Jan 4th, 2003, 12:53pm » |
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on Jan 4th, 2003, 10:24am, mook wrote:| After I ask the computer which box he predicted me to open, I open the other box. Why should I think so hard when I have discovered this great artificial intelligence? |
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Because the AI doesn't tell you what box it predicted you'd open.
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Kozo Morimoto
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Re: Newcomb's Dilemma
« Reply #19 on: Jan 4th, 2003, 6:22pm » |
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on Jan 3rd, 2003, 6:37am, SWF wrote:
If so then, isn't that admitting that there is still some possibility that the computer will fail? Even $10,000 vs. $1 billion is a factor of 100,000 difference, so I guess a streak of "many" convinces some people that there is a least 100,000 to one chance of the streak being broken in a given test.
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This raises an interesting investment philosophy: would you take the $10k (guaranteed) or pick the box with 1 in 100,000 chance of getting $1b and 99,999 in 100,000 chance of getting $0? (sort of like Who Wants to be a Millionaire when you can guarantee a walk-away money, or pick 50-50 for a chance to double your walk-away money)
Both choices give you and E(payout) of $10k, however the latter box has a higher standard deviation or in investment terms risk. Current theory states that give the same expected return, pick the investment with the lowewr risk.
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mook
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Re: Newcomb's Dilemma
« Reply #20 on: Jan 4th, 2003, 8:33pm » |
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on Jan 4th, 2003, 12:53pm, Jeremiah Smith wrote:
Because the AI doesn't tell you what box it predicted you'd open. |
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But the riddle doesn't tell you that you can't ask.
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SWF
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Re: Newcomb's Dilemma
« Reply #21 on: Jan 4th, 2003, 8:45pm » |
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I agree with mook, you can ask and if the computer answers it is setting itself up to fail or be a liar. I was thinking in terms of building an exact copy of the computer, and after the contents of Box B have been set, ask it what is inside Box B. If it says the Box B is empty, pick Box A. If it says it contains a billion dollars, pick Box B. One of the two infallible computers must have given an incorrect answer. I wonder if this was one of the devious tests mentioned in the question for which the computer was successful.
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Icarus
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Re: Newcomb's Dilemma
« Reply #22 on: Jan 5th, 2003, 1:45pm » |
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Been away for awhile... You can examine this problem from both the point of view that the computer can be wrong on occasions, or from the point of view that it is always correct. Obviously, if it is occasionally inaccurate, your best expected return may come from opening box B, depending on how accurate the computer is.
So consider the computer to be always accurate. Asking the computer (or a copy of it) ahead of time what box it will predict runs afoul of this logical conundrum: You can either know exactly what your future will be, or have freedom to decide what you will do, but not both. If the computer is infallible, it will not answer your question. Neither the original nor any copy.
Quote:| This version of the paradox is slightly different from the usual version. In the usual description, the choice is between taking just box B (which the computer stocked with a $1 million if it predicted this choice, otherwise empty) or taking the contents of both boxes (box A always contains $1000). |
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Yes, I tried to write it out from memory and didn't realize that I had changed it. Maybe that is why no one is arguing the position equivalent to the one some of Gardner's readers took for that version: the logical action is to take both boxes even though that would give you less money. These people were not trying to outsmart the predictor, they were actually somewhat upset that those making the "right" choice would get less money than the others. This is the point of view I was hoping someone would take so that I could come to understand it in discussions. (I doubt I would ever agree with it, but I would like to know what the thought behind it is.) I may have blown it though by changing the problem. 
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rmsgrey
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Re: Newcomb's Dilemma
« Reply #23 on: Apr 24th, 2003, 10:53am » |
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The problem assumes some form of determinism - therefore there is no reason to assume my choice to be logical. For that matter, what happens when I take a box with a button on it into the computer's consultation chamber and ask whether I will press it or not in the ten seconds after I hear the machine's answer, having resolved to do the opposite? For the machine to always be accurate, something must happen to frustrate my intentions - maybe I pass out or get distracted immediately after hearing the answer that I won't so don't, or maybe I accidentally press it somehow before the time limit having heard I will. Either way, as soon as the computer makes its decision (if not sooner) I lose free will. In which case, the question of which box I should open is irrelevant. Of course, if I genuinely possess any free will in the matter, then it seems that it should be possible to fool the computer (maybe by using a perfect random number generator - though the upgraded version means the computer is only fooled when you pick box A and B is empty )
Anyway, in the Gardner version, the reason people take both boxes (apart from lacking any choice) is that they don't really accept the time-reversed causation. If you require consistency in all time-like loops (vital for infallibility of machine) then the contents of box B are sort of like Schroedinger's Cat - making your final decision collapses the waveform so that it's "always" been that way - the audience always saw the contents of box B that way, but until you gave your final answer, the audience itself was in a superposition...
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andrewc32569
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Here is what I think.
The obvious choice is A, right? Wonrg.
I would choose B BECAUSE The machine would most likely predict me to choose A.
Here is the reason:Before you meet up with the rich guy, he would have checked the machine,ALTHOUGH,the machine did not know that the rich guy was going to tell you that it already predetermined your fate, THEREFORE, the machine would think I would choose A, knowing most anybody goes for a sure thing. But since you know that he asked the machine , you can determine statistically, that you have a high chance of getting a billion dollars.
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