Newcomb's Problem
Offline The following is a paradox first introduced by Robert Nozick in his book The Nature Of Rationality. This paradox is a paradox of decision. Unlike most paradoxes which arise in either mathematics, epistemology, or metaphysics, this paradox develops when one asks, in this case, what aught person X do? Here is the problem:
Imagine before you are two boxes. One box is transparent, while the other is not. In box one there contains $1,000 dollars; box two either contains $1,000,000 or is empty. Moreover, there is a highly reliable predictor who has predicted you actions. Moreover, assume he is correct in his predictions 95% of the time. You also know that you can either take both boxes, or just box 2. You also know the following two conditionals:
(i) if the predictor predicted that I take both boxes, he would have left the second box empty.
(ii) if the predictor predicted I would only take box two, he would put the $1,000,000 in it.
the question is, do you two-box or one-box?
Argument for Two-Boxing
(1) either the predictor put $1,000,000 dollars in box two, or he left it empty [LEM]
(2) Assume he put $1,000,000 in box two
(3) If (3) is correct, then it would be most rational to take both boxes, for then I would have $1,001,000 instead of just $1,000,000.
(4) assume left box two empty
(5) If (4) is correct, then it would be most rational to take both boxes.
Ergo, either way, I achieve the maximum payout by taking both boxes.
Argument for One-Boxing
(1) The predictor is very reliable
(2) If I were to pick both boxes, the predictor would have left box two empty (with all probability)
(3) If i were to pick only box two, then the predictor would have put $1,000,000 in it.
Ergo, it is most rational to only take one box
Alright, solve the problem people!
I would one-box...and I will justify that after I hear some possible solutions to this paradox.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
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Ah... I've come across this before.
I'm a 'one box' person.
If the predictor is as good as he's supposed to be then there's only one way that there will be a million in that second box.
I think the 'two box' argument makes a similar fallacy to the fatalist.
The fatalist:
Either I will die of lung cancer or I won't.
If not then there's no harm in smoking.
If I do then I might as well smoke.
They ignore the fact that the 'dying' is dependent/linked to the 'smoking'.
See the similarity?
(is this similar to your reason for picking one box?)
Take box two every time. Heres why:
You take 'box two' at all times, no matter what his prediction might have been, right or wrong, because....
If he is wrong with the second conditional, in his prediction, you win anyway, cause you always just take 'box two'.
Of course this problem changes if 'box one' contains more than $1000, as I would gladly give up that sum for a guaranteed million.
I'll just be waiting outside for one of you smart folks. lol.
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Toss the predictor for a loop and don't pick either box.
Well, my reasoning is simply that he is reliable. The probability the predictor predicted the correct answer is high. Therefore, given the high probability of my predictor predicting the right answer should force me to only take box 2. For if I were to take both boxes, the predictor would have predicted this and left it empty.
I am actually suprised that this is a paradox. The fatal flaw of the "two-box" argument is that it assumes a disjoin between my actions and the predictors prediction. Therefore, with this confusion, one assumes they can "trick" the predictor. However, this line of thinking with have already been predicted (in all likelyhood) by the predictor.
The "Two-boxing" argument also rests upon the fallacious assumption that "well, the choice has already been made...since it has already been made, I mine as well choose both boxes; I mean, it isn't like there is backwards causation." Once again, this assumption is highly dubious. It is not a matter of backwards causation, but whether or not box two is empty is directly preportional to the predictors analysis of your behavior. Thus, thinking that "well, the choice has been made, I should take both" is demonstrably false. Yes, the choice has been made. However, the choice is directly preportional to your disposition.
To elicidate this exaple, assume there existed an omnipotent predictor. Then, obviously, my line of reasoning would hold. For if he is infalliable, then it is logically impossible that his prediction is wrong. Now, if the predictor is less than infallable, say 95% accurate, why do we think we can "trick" him/her? We have a 5% chance of getting it right. Therefore, one-boxing is most rational.
We know that the following two conditionals hold:
(1) If I were to one-box, the predictor would have predicted it
(2) If I were to two-box, the predictor would have predicted it
We know that the above two propositions are true, atleast 95% of the time. With this in mind, why two-box? It's like buying a lottery ticket and believing it will win (which brings us to the lottery paradox, which I will expond on next. The lottery paradox is one fucking menacing paradox. What it shows, is that fallable knowledge requires more than mere high probability)
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
Well, your reasoning seems to be favored by many people. This is called the Dominance Principle. Do what is most favorable under all conditions. However, this is a dubious decision-theoretic principle. Once again, this assumes a disjoin between the predictors prediction, and your decision. It is impossible to get around the fact that if you make decision D, the predictor would have predicted it (with all probability). Thus, in the end, your get the suckers payout...only a $1,000 dollars.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
Oh c'mon todangst, let's hear you serious answer. I am curious as to what it is.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
Check out this site for further information. I especially like the theological implications of this game, but it changes it immensely.
http://www.leaderu.com/offices/billcraig/docs/newcomb.html
That is the serious answer. It defeats the predictor.
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
There's no reason why the predictor can't predict you picking no box.
How about a quick re-wording of the original paradox:
If the predictor predicts both boxes being taken then box two is empty, otherwise the second box has a million inside of it.
What would you do now smartass?
Except that the original phrasing of the 'paradox' requires that he predicts that we either pick 1 or both of the boxes. "Zero boxes chosen" isn't an option, hence I don't see how he can predict it.
Basically, there's an assumption there that there is no loss involved in picking either one or both boxes. It is held that the cash prize is motivation enough to select either option. Hence, picking neither box seems to be thinking outside the box... both figuratively and literally.... so I don't see how the predictor can predict it, if the predictor doesn't even include it as a possibility. And I'm willing to give up 1,000 for a nice "fuck you" to someone claiming that they can predict my behaviors.
Well now, you've affirmed what I just said: that the paradox needs to be reworded - not clarified, but reworded, changed, to deal with my new contingency. If so, then my response appears to be a way around the problem.
Pick neither, and still defeat the challenge, because it still screws up his prediction, as far as I can see. Sometimes the only way to win is to not play the game.
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
You know if the goal is to just make money knock the guy out take any money out of all of the box and his wallet. Of course that raises ethical concerns...
If you can grab both boxes then go for it, is there something to lose? If you can only get one go for the one you know has money.
Now if the goal is to screw with the guys prediction I'd say pick none or point out how it would be odd for someone to basically have a mystery box and not be up to something.
Far enough...
Not really.
If you pick the 2 boxes then the second box is empty.
Otherwise (which includes one and no boxes) the million is in the second box. So there's room for him to predict you picking neither and there being a million in the box.
So if you walk away then he predicted it and there was a million in the second box.
I don't think there's a way to tie up the predictor now.
All that's left is what prize you walk away with.
If you're not one for the money then perhaps substitute with something you do want?
Well, not if your goal is to make the greatest amount of money - which the questioner seems to assume will be the goal of every person given the offer. In that case, then picking neither is the worst option.
What I want is to avoid being placed in a situation of constraint. I think not choosing at all does that.
Anyway the predictor here supposedly has a 95% success rate.... which means that he is wrong 5% of the time. Well then, what's the value of a 5% chance at a million? $50,000. Seems that the value of box two is therefore 50,000, whereas the value of box one is 1,000.
I guess the debate here is whether a 50,000 value of possibility is really equivalent to 1,000 dollars of certainty....
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
The version I was given was where the predictor was spot on, the point of the paradox being as Chaoslord described it - the 'two box' and 'one box' arguments both seeming to make sense leaving you wondering what one ought to choose. (assuming they're looking for big money!)
I think we've agreed that the 'two box' argument is fallicious and ignores the connection between the player's decision and the predictor's prediction. (A bit like the fatalist's error)
So the question/paradox is more about two intuitive but conflicting strategies rather than mathematically working out a strategy to play the game the best. If we were devising a mathematical strategy, I think you botched up your numbers!
The second box would have a value of 950,000 (because the 95% of the time the predictor will be right and a million will be in the box) when chosen on its own and 50,000 (a million the 5% of the time when the predictor is wrong) when chosen with the second box. So picking just the second box would have value of 950,000 and picking both boxes would have value of 51,000.
This is what Game Theory's 'Utility Theory' is all about.
I guess you'll be quite familiar with that with your background in psychology.
Is this the same paradox that's in Jeffery's 'Formal Logic: Its Scope and Limits'? I'm looking forward to this!
Except it isn't a serious answer. Since "no-boxing" is not an option, this can hardly be called anything but a red herring.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
Only only using the Dominance Principle. The Dominance Principle states that if some decision X fairs well in most, or atleast equally well in the possible outcomes, then we should favor it over the competitors. Hence, since two boxing ALWAYS carries with it a monetary reward, it should be favored over decision of "one-boxing" which leaves the "possibility" of being left empty handed.
However, this paradox turns on which principle one adopts. This is a very myopic principle in many cases, and should be disregarded. Rather, the principle of maximize expected value states that one should do what is best not on all possible situations, but should choose the decision which carries with it the value that is most probable...even though it is not "fail-safe" like the dominance principle.
Two-boxing does indeed seem intuitively correct. However, one boxing is superior...for reasons argued above.
this is irrelevant. Select ANY type of payout you like, and plug it into Newcomb's problem...let if be world-peace, for example. Unless you a dipshit politician (ah la Bush) most people want the maximum amount of world peace.
Money is merely an example to illustrate the abstract example. Furthermore, we can say "if you desire the most money, then what ought you do?"
Sorry, thats not an option. Think of it like this: remember middle school playing the "what if" games? Since I was born to be a philosopher, I loved these fucking games. The games go something like this: Who would you rather have sex with, Janet Reno, or Jerry Falwell? And of course there would be that one kid who didn't appreciate the "what if" games by saying: "neither, hahahahahahah." Ok, ok, we know neither option is particularly appealing. However, give ONLY these two options, what would you do?
Newcomb's Problem is analogous to this. It is doubtful that this has any real world applications, since it would postulate the existence of psychics...which we know don't exist.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
Or, "money" was merely an example. Obviously you can subsitute any kind of payout you would desire; be it dildo's used by a playboy bunny, or whatever. What do you desire? We can plug it in and get the same paradoxical results.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
Except that it is. Learn to think outside the box(es)
Sure it is, choice is not compulsory. I pick NONE, Mr. Predictor! Ha ha! So whether you put a million or not in the box is meaningless to me.....
Except that it's not a red herring. Choice is not compulsory, and it's possible to not choose any of the boxes. And it may be possible that there's an intrinsic reward that outweighs any extrinsic reward that could be placed in the box.
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
What if the desire is to not be constrained to the options given?
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
No, no, you're thinking along the lines of picking either one or both boxes, and I am saying that this assumption is predicated on the belief that there there is nothing lost in picking either one or both, instead of picking NONE.
My point is that there is an assumption that one would choose either one box or both boxes, and that the assumption is in error. One could lose the sense of 'free will' by entering into the process, and avoid this by not choosing any boxes. In fact, one may even affirm their free will by acting in this fashion...
Pretty expensive way to do it, however...
What is the payout I most desire of all is the sense of freedom that can only come from removing the constraint automatically entailed in picking either one or both boxes? This payout cannot be placed in the boxes.
Sorry, it is. Unless the paradox is "you are going to be given either one or two boxes no matter what you do, the only choice you have is whether you choose to take one of them or both"
The very fact that there is a enticement placed in the box speaks to the possibility of not choosing any boxes at all. And if there is an intrinsic enticement that exceeds any material object, then picking 'none of the above' is a way to screw up the predictor.... he doesn't seem able to predict someone choosing to swipe both boxes off the table and telling him to to pound salt....
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
It's quite simple...
Pick something you'd like quite a bit, (like your favourite snack) then something you'd really like (like a night with a really hot lass?).
Replace the thousand with the first and the million with the second.
Then there are four outcomes, from least to most preferred/valued:
Walking away and getting neither.
Getting just the snack.
Getting the lady.
Getting the snack and the lady.
Those are all the options from the game (including a refusal to play).
If you are fully satisfied in everyway and would rather earn your snacks/lasses the old fashioned way then imagine that Mr Black is on the TV show, that he has the values as assumed, and now tell us what he should do to get his best result?
A perfect predictor makes more sense to me, and that's how I thought I had heard it before... but Chaos' paradox states only a 95% success rate.
But what about the 5% failure rate?
Yes, I read it backwards... I thought you were only guarenteed the 1000... but the paradox actually guarentees the million as long as you only take the 'million dollar box"
Yes! Well done. So it's a matter of 950,000 vs 51,000. I mistakenly believed that only the grand was certain (but you can't pick just the grand, that's not an option) It's actually the million dollars that is certain (well, 2 standard deviations from the norm of a bell curve certain) and you only lose it if you get greedy over a measely thousand dollars....
So the whole point is this: once the 'million dollar box is before you, it already has what it has in it, so why not pick it up? But as you claim, this leaves out the fact that the predictor is somehow privy to your present behaviors, making the contents of the million dollar box contingent upon your own current behavior....
Yes, and now that I have the odds correct (thanks!) I think we can now discuss that issue.
950,000 vs 51,000
Well, those odds are rather clear
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
Again, what if what I prize most is protecting my sense of free will?
Can't stuff that in either box.
Again, this presumes that there is nothing lost by choosing, and I argue that there is a potential loss.
Sorry, but I'm really trying to explore this avenue, as much as it brings consternation to the board.... the game assumes that everyone would play... and with a guarentee of a million, I can see why the presumption is made.
But what if there is no motivator that exceeds the intrinsic motivation of the sense of free will? If so, then the predictor fails.... and while that's not a big deal with the 95% predictor, I think it does screw up a 100% predictor...
A refusal to play offers the protection of one's sense of self efficacy and freedom, particularly if the predictor works at a 100% success rate. That said, walking away from a million, rather than a grand, is... let's say, a bit less likely...
Pick none of the above, Mr. Black!
"Hitler burned people like Anne Frank, for that we call him evil.
"God" burns Anne Frank eternally. For that, theists call him 'good.'
But Mr Black wants prizes!
Your advice to him is as bad as a Christian's who advises you to get a Bible over a philosophy book!
If the scene is reworded so the predictor can predict you walking away and choosing neither. (in which case the million is placed in box two as if he'd predicted you choosing one box)
So walking away doesn't screw up the predictor in this scenario.
Perhaps you mean 'make no choice' as in refuse to walk away or pick the boxes and just stand there undecided?
Then imagine there's a 10 second time limit to make the choice and after this limit you are ejected from the scene. (The predictor can also predict you doing this as well)
If you like the sound of being ejected then perhaps the prizes could be more impressive ejections?
Perhaps we should just move on to the lottery paradox!
this is not part of the problem. It is irrelevant. This is importing superflous material into the problem.
Who said it was? This is not about what you WILL do, but a problem about what you ought to do.
Assuming this is part of the problem...which it isn't, so what? This is irrelevant. This is not a matter of what you actually do, only what you ought to do. So this whole line of reasoning is irrelevant. This is a paradox of decision, meaning, what OUGHT someone do. Obviously you can be irrational - but this isn't the point.
There has been some confusion. I ment something tangible. Unless I am mistaken, you cannot put the above desire into a box. Morever, this desire does not come in degrees like money does.
Interesting thought though. Im going to think about this, this is interesting.
Not quite. The assumption is that if one is rational, one ought to either choose two boxes or one-box. The paradox comes in when it is not clear what one ought to do if one is rational.
However, yes there is an assumption that one will choose a box...this is part of the dilemma. If we change the dilemma, we change the problem. This might be it's downfall. Some have argued that the paradox is incoherent. I disagree, but that's another matter.
Well, free-will is incoherent anyway
It makes more sense this way. The solution to the infallible predictor is straightforward. If one weakens it just a little, it seems to have more of a bite. Thats my view. Anyway, this was how it was presented to me in my Seminar class on paradoxes. I mean, assume some omnicient being existed and preformed this. Since he is infalliable, he prediction cannot be wrong. If his prediction cannot be wrong, then it seems intuitively obvious (damn Raijo) to me that one-boxing is the only option.
I like to use the Newcomb's Problem as a reductio against those who hold as true free-will but also an omnicient being. This is logically impossible, it leads to a contradiction; and if we accept classical logic, the reductio holds. If you don't believe me, I will preform the reductio.
"In the high school halls, in the shopping malls, conform or be cast out" ~ Rush, from Subdivisions
All in time my dear boy.