T|S One Box or Two Boxes (Newcomb's Paradox)

or THIS one

http://www.writerswrite.com/journal/jun04/robert_newcomb.gif

??

And, predictably, taking only box B is not in the poll.

P.S. Why is this considered a paradox?

XP obviously the choice is either only taking Box B or taking both Box B and Box A. It wouldn't make any sense to only take Box A.

The paradox is that, assuming he predicts your choice correctly, you need to pick Box B to get the money. But the logical course of action is taking both boxes. You're hemmed in by a paradox in prediction/free choice.

but it's flawed in its formulation; since we are told the results of his predictions and since his predictions are highly accurate (some versions say "100% accurate"), knowing that 1 box = $100k means you always take 1 box

Can box be prurient slang for vagina? I would take both in the hopes that one was empty cause YOW! papercut pussy is not my thing.

Wait, do you get to open the boxes repeatedly, or just once?

Just once. And HI DERE, that means that you've forfeited your free will -- because once you're committed to always taking Box B, you might as well also take Box A for the extra money.

the logical course of action is taking both boxes.

Not as formulated in your explanation. There is no logical connection between which amount of money is in box B, my actions or and Bob's predictive ability. But given that such a connection is posited and I am assured it is entirely reliable within the confines of this fanciful tale, then logic dictates the choice I made, taking only Box B, rather than taking both boxes.

I'm confused still as to why this is a paradox, even after you explained it.

That's because it isn't a paradox.

This reminds me of that thread about some gloating study about people's responses to a "paradox" about incest, but less gross.

Can't wait for the end of this thread when we all meet up in a church and a bright light comes through the doors.

From wiki:

The problem is called a paradox because two strategies that both sound intuitively logical give conflicting answers to the question of what choice maximizes the player's payout. The first strategy argues that, regardless of what prediction the Predictor has made, taking both boxes yields more money. That is, if the prediction is for both A and B to be taken, then the player's decision becomes a matter of choosing between $1,000 (by taking A and B) and $0 (by taking just B), in which case taking both boxes is obviously preferable. But, even if the prediction is for the player to take only B, then taking both boxes yields $1,001,000, and taking only B yields only $1,000,000—taking both boxes is still better, regardless of which prediction has been made.
The second strategy suggests taking only B. By this strategy, we can ignore the possibilities that return $0 and $1,001,000, as they both require that the Predictor has made an incorrect prediction, and the problem states that the Predictor is almost never wrong. Thus, the choice becomes whether to receive $1,000 (both boxes) or to receive $1,000,000 (only box B)—so taking only box B is better.

this is an incest thing?

I think we may take it that Newcomb's point about free will in this story means that God is masquerading as Bob, and if God has foreknowlege of outcomes in the same way Bob does, then free will is impossible, and if God does not, then such little matters as prophesy and omniscience are forfeited.

To which I say, who the hell cares? This is undergrad fiddle-faddle.

But taking both boxes is clearly NOT preferable if it means you have $999,000 less in $$free money$$$.

I mean, I think that overrides "but I didn't get to pick both!" in anyone sane.

And HI DERE, that means that you've forfeited your free will -- because once you're committed to always taking Box B, you might as well also take Box A for the extra money.

This is not true because, based on how the problem is set up, if you pick both boxes, Box B has nothing in it. You have no free will in either case aside from your actions determining how much money you will get, which is either $100K or $1K.

how is this a paradox? take both boxes.

Taking both boxes is the only guaranteed option, and that guarantee is $1K. As the problem has been stated, if Bob is wrong you will get an extra $100K but Bob is almost never, if ever, wrong.

where is "kick Bob in the nuts" option

The first strategy argues that, regardless of what prediction the Predictor has made, taking both boxes yields more money.

As you see, the whole thing hinges upon whether, in the universe the tale takes place in, there is a connection between the prediction, the action and the amounts of money in each box. Since it is impossible for such a universe to exist, in real life, the "take both" strategy works.

But the impossibility of a universe existing is no impediment to acting consistently with its rules, and under the rules we must take as a given, Bob's prediction has been made, and will be quite near to infallible, and there is a known link between his prediction and the outcome.

Here are the rules of that universe:

If Bob predicts that you'll only take one, Box B will have $100,000 in it. If Bob predicts that you'll take both boxes, Box B will have $0 in it.

This is irrational, but we seem to be in another universe where this is real.

Second point.

If, by acting consistently with the irrational rules of this irrational universe, we make a consistent choice in this case, then it by no means implies that in other cases we have no free will to exercise, as those cases may not have such strict rules, or such obvious rewards. Even then, we are free to punish ourselves... or maybe we already have $1,000,000,000.00 and don't need the money.

Aimless OTM, the only paradox here is in this stupid hypothetical universe where Bob determines the contents of the boxes

x-post

While taking only one box is risky assuming that Bob might be wrong, the problem setup goes to great lengths to remove the accuracy of his predictions from the equation; he is basically a given.

Essentially, this boils down to take 1 if you think Bob is right, take 2 if you think Bob is wrong. It's still more advantageous to take 1 because, if you are wrong, you have left $1K on the table, whereas if you take 2 and you are wrong, you have lost $999K.

how can you have lost what was never there in the first place?

hate bob so much right now

because, according to the rules of the universe, it would have been there had you made the other choice

this universe doesn't make any fucking sense.

the money's either in the box or it isn't - if you take both, you haven't lost anything, because you have already taken all that was there to begin with

like what is this magical universe where, if you leave a box behind, $100k magically appears in it

This is a pure thought exercise that has nothing to do with real life.

The amount of money is in flux until you've made your choice; it is determined by whether the number of boxes you chose matches Bob's prediction. It's like Schroedinger's Cat.

The issue isn't about free will etc, it's about understanding the rules of this hypothetical universe and what the best strategy for success in them is. Since Bob can accurately predict your decisions, you make the choice where his prediction of your behavior gives you the largest amount of money, which means only taking box B.

he can predict your decisions *almost* perfectly

yeah what's with the "almost" - sometimes the laws of this universe don't work? what's that about?

Right, so if you look at the probabilities, it is more likely he is right than wrong:

(UNLIKELY) he predicts 1, you take 2: $101,000 payout
(LIKELY) he predicts 1, you take 1: $100,000 payout
(LIKELY) he predicts 2, you take 2: $1000 payout
(UNLIKELY) he predicts 2, you take 1: $0 payout

You guarantee yourself $1000 by always taking 2; you give yourself the most chance for a large payout by taking 1.

Also, if you take 1 when you should have taken 2 (ie, his prediction was wrong), you are missing out on $1000 extra dollars. However, if you take 2 when he should have taken 1 (ie, his prediction was right), you miss out on $99,000.

this is by definition not a paradox, sorry

it is a logic puzzle, or at best really watered down game theory

^^^

watered down game theory

yep

I kind of like the definition of "paradox" as "annoying thought experiment" though

I think the problem is that lack of free will is being considered paradoxical, but within the structure there cant be actual free will (in fact it's kind of a decisive example of reverse causation, in other words, the choice made in the present causes the choice made by bob in the past).

both variants (100% accurate bob vs. almost always accurate bob) seem to fail as well - 100% relies completely on the free will paradox fallacy i just mentioned, and almost always becomes a really strange betting against the odds gambling problem indicator.

guys

just take box A and then hope that Bob gives you some of the $100,000 out of the goodness of his own heart

Another thing that bothers me about this is it starts out with "Bob can predict your actions almost perfectly," and then shares his predictions about the box contents. The question actually never says he can predict accurately the contents of a box.

He's not predicting the contents of the box. He's the one stocking the box.

This is making me feel illiterate, and I know I'm not. -_-

in other words both boxers are arguing in favor of determinism and one boxers are arguing in favor of reverse causation.

The problem is intended to be about expected-utility principle vs. dominance principle, and it works if it creates a scenario wherein both principles are equally valid. If both principles are equally valid in this scenario and they both lead to different choices, then there is an apparent paradox.

I don't think the mechanism for the reliability of the predictor is important, because the chooser can't know how or why the predictor is reliable. He could be right because he is prescient. He could be right because he has a lot of information, and he's dropping science. He could have been calling heads or tails right, without any special knowledge, every time up until now.

Am I causing the boxes to be in a particular state by making a choice, or is the state of the boxes fixed before I make my decision? There is no evidence contained within the problem to make me choose one way or the other. The question is whether I accept that he is a reliable predictor.

Given that I do accept that he is a reliable predictor, do I apply the expected-utility principle, or the dominance principle? What is the most rational choice?

Am I causing the boxes to be in a particular state by making a choice, or is the state of the boxes fixed before I make my decision? There is no evidence contained within the problem to make me choose one way or the other.

Not as stated in this thread, but it is written into various formulations. Sometimes it's stated that Bob puts the money in the boxes e.g. an hour before you make your choice. Also the version where your friend knows what's in the boxes obviously requires the amount to be pre-determined.

One can make the problem about free will, but that makes it rubbish. If your choice reverse-causes the outcome then determinism doesn't get a look in, you should always two-box.

You mean one-box, right? If you're reverse-causing, then go for just Box B.

woops, yeah.

Found the original articles on the problem and they clearly state that the super-predicting being puts the money in the boxes, then you make your choice.

http://books.google.co.uk/books?id=XOVelCewRMIC&lpg=PA45&ots=D9GeealvwJ&dq=%22Newcomb's%20Problem%20and%20Two%20Principles%20of%20Choice&pg=PA45#v=onepage&q=%22Newcomb's%20Problem%20and%20Two%20Principles%20of%20Choice&f=false

I don't think the mechanism for the reliability of the predictor is important

True enough. It is far more important to know Bob's actual accuracy, which ought to be measurable more exactly than "almost always", than the mechanism of prediction. However, the mechanism is of interest in that it establishes what sort of universe we are inhabiting, and that allows us to judge whether Bob's methods are as likely to be accurate in the matter of boxes filled with cash as they are with other, past actions he has predicted.

BTW, Bob's would appear to be a magical universe, in that there is as yet no imaginable mechanism for predicting my actions in this universe with such near infallibility, without invoking magic, or a diety with magical propoerties. However, if this magical universe is inherently as predictable in as a lawful one, then the mechanism is of no importance, for they will act commensurately. IOW, the magical process must follow laws just as strict and as predictable as physical laws.

I am presuming that, for the purpose of this trial, Bob and I have not already been though this process of choosing hundreds of times already, but that it is novel.

Why is the friend advising you to take both boxes?

Am I causing the boxes to be in a particular state by making a choice, or is the state of the boxes fixed before I make my decision? There is no evidence contained within the problem to make me choose one way or the other.

Not as stated in this thread, but it is written into various formulations. Sometimes it's stated that Bob puts the money in the boxes e.g. an hour before you make your choice. Also the version where your friend knows what's in the boxes obviously requires the amount to be pre-determined.

― literally with cash (ledge), Wednesday, May 26, 2010 5:30 PM (12 minutes ago) Bookmark

If the predictor is prescient, then it doesn't matter when the cash goes in the box--it's still a matter of reverse-causality. I agree that the problem is basically bullshit if the thought-problem is about a being who is infallible.

Why is the friend advising you to take both boxes?

― Marni and Louboutin: coming to Tuesdays this fall on FOX (HI DERE), Wednesday, May 26, 2010 5:54 PM (55 seconds ago) Bookmark

Because he gets a cut of every 100K that doesn't make it into box B.

It's just, if the friend has your best interests at heart and is telling you to take both boxes, then the friend is changing the parameters of the scenario and makes Bob's prediction null and void; the assumption becomes that Bob always puts the $100K into box B and you should always take both because your friend who is, by definition of the problem, not attempting to screw you over knows that the money in the boxes.

actually i dont see any case where the timing of when the cash goes in the box matters. i think what some people are missing is that reverse-causation doesn't imply that the money is actually literally in flux until the instant your decision is made, but functionally thats the only way to view it - the whole thing hangs on the inherent difficulty of prediction wrt linear time. the gap between when the prediction was made/when the cash was put in the box is immaterial really.

xposts

still lolling that the three of us are in hardcore agreement here

Having read the original formulation of the problem by Newcomb (link above), he glosses over the mechanism as irrelevant, and also glosses over what sorts of experience the person asked to make the choice has had with prior predictions, stating only that you know the being (aka Bob):

"has often correctly predicted your choices in the past (and has never so far as you know made an incorrect prediction about your choices) and furthermore this being has often correctly predicted the choices of other people, many of whom are similar to you, in the particular situation to be described below".

I especially like how he plays both sides of the street by saying that you do not know of any predictive errrors in your own case, but that you know (with equal emphasis) that the being's track record in this regard is only "often" correct. Which looks to me like a contradiction: either you know of some errors, or you don't know the being's record is only "often" correct. These can't both be true.

That sort of hand waving makes the problem suck as an exercise in logic or problem solving.

yeah frankly i still feel like the almost always correct (or worse, "often") is just kind of a cheap trick to muddle the obvious one box answer.

To the point of causality, if the predictor is prescient and infallible, and free will still somehow exists, then the state of the cash in box B is "both" until the chooser chooses.

all sorts of xposts

jjjusten, I think the argument is supposed to be that a rational decision-maker would always choose both boxes unless there was a high enough probability that choosing box B will a deliver a big enough reward, and that a statistically reliable predictor is supposed to force a clash between these two rational approaches in decision-making.

I'm not sure how I feel about it, because my decision is supposed to be based on the fact that I accept that there exists a statistically reliable predictor of my behaviorwho is neither prescient nor just waiting to be wrong the next 100 flips of the coin.

http://www.resort.com/~banshee/Misc/8ball/images/bob-ball.jpg

actually i dont see any case where the timing of when the cash goes in the box matters. i think what some people are missing is that reverse-causation doesn't imply that the money is actually literally in flux until the instant your decision is made

yeah i was kinda making that mistake tbh. still pretty sure that reverse causality is not a feature of the problem though.

It's just, if the friend has your best interests at heart and is telling you to take both boxes, then the friend is changing the parameters of the scenario and makes Bob's prediction null and void;

it's not that he actually tells you, but that if he - or anyone else who could see into the boxes - did tell you, they would tell you to take both, because that will always maximise your payoff. it's a thought experiment within the thought experiment!

I'll give Bob $50,500 if he predicts one box. Now, who's on the hot seat, Bob?

"Bob is dead."

-- Friedrich Nietzche --

okay I finally get the "take both" argument

basically it depends on the prediction not mattering at all; either one box is empty, so you get $1K if you take both, or neither box is empty, so you get $101K

But if the mechanism of the prediction is predicated on some causal connection to the choice predicted (which seems to be a necessity, really, to get to near-perfect accuracy) then it would be impossible to dismiss the prediction as not mattering. The causation then would not truly be "in reverse", any more so than the event of an eclipse causes the prediction of an eclipse.

don't see how reverse causation figures in here. we don't know what causes bob's prediction, and it doesn't matter anyway. we only know that whatever our eventual decision might be, it is very likely to have been correctly predicted by bob. therefore, however many boxes we take, we can be reasonably confident that bob saw it coming, and that the amount contained in box B will have been predetermined accordingly. this creates a situation that might seem to resemble reverse causation, but only in a superficial sense. fundamentally, the puzzle has less to do with the manner in which the box contents are determined than the manner in which we make decisions based on our supposed foreknowledge of someone else's supposed foreknowledge.

we can take box A, knowing that we will get $1,000. we can take box B, knowing that we will probably get $100,000. or we can take both boxes, knowing that we will certainly get $1,000, and that we run a slight chance of getting $101,000. i suppose that the decision we make will be determined most of all by how much money we have and need. if we have very little and desperately need $1,000, then it might be best to take both boxes -- that at least guarantees a return of some kind. but if we can live with the chance that we might get nothing, then it's obviously best to take only box B.

agree with whoever said that the puzzle suffers for the absence of a precise measure of bob's accuracy. as stated here, it's mostly a measure of how we interpret the phrase "almost perfectly," and how we balance risk with benefit in monetary gambling. no matter how you slice it, though, there's no "paradox" i can see at any level. a (very inelegant) paradoxical formulation might work like this:

1) you can pick one and only one box.
2) box A contains $1,000, but only if bob fails in predicting your pick.
3) box B contains $100,000, but only if bob succeeds in predicting your pick.
4) if the above conditions are not met, the box contents are reversed.
6) bob predicts that that you will pick the box containing the least of the two amounts.

which box do you pick?

As I understand it, the paradox is as follows:

1. [Using the rules mentioned in the first post on the thread]
2. You should take both boxes, since Bob already made his prediction and taking both boxes maximizes your profit.
3. But if you take both boxes, that means Bob probably predicted you'd take both boxes (since you're clearly the type of person who would take both boxes), and therefore Box B is empty.
4. So you should really just take Box B, because a person who would take Box B would get $100,000
5. But if you're the type of person who would take Box B, you might as well take both boxes, since the amount in them is predetermined.
6. But if you're now the type of person who would take both boxes, then Box B is empty (ie: back to step 3)

So it's an infinite loop.

5. But if you're the type of person who would take Box B, you might as well take both boxes, since the amount in them is predetermined.
6. But if you're now the type of person who would take both boxes, then Box B is empty (ie: back to step 3)

this is the part that doesn't work for me as a paradox. i don't buy the psychological inference made in your point #5, and nothing in the setup implies that bob's predictions wouldn't take such a thing into account in the first place anyway. if you take box B, then box B is almost certainly going to contain $100,000. period. so you might as well take box B, accepting that you really are a box-B-taking kind of person.

i mean, if you go ahead and take both boxes knowing A) that the near-infallible bob has predicted your choice in advance -- and B) that IF bob has correctly predicted that you would choose both boxes, then box B will be empty -- then you're pretty much a moron. and you have to credit bob with knowing that you're not a moron, right?

Wrong. Because if you take both boxes there's no reverse-correlation. It might mean you are the kind of person who would take both boxes, but you haven't damned yourself to less money because you took them in the moment. You were damned from the moment Bob made the prediction. Any chooser should simultaneously want to be the kind of person who would only take Box B, and recognize the impossibility of being that kind of person (because at the moment of choice, you are totally free to take both boxes). A similar paradox that explains this problem is Kavka's toxin puzzle.

An eccentric billionaire places before you a vial of toxin that, if you drink it, will make you painfully ill for a day, but will not threaten your life or have any lasting effects. The billionaire will pay you one million dollars tomorrow morning if, at midnight tonight, you intend to drink the toxin tomorrow afternoon. He emphasizes that you need not drink the toxin to receive the money; in fact, the money will already be in your bank account hours before the time for drinking it arrives, if you succeed. All you have to do is. . . intend at midnight tonight to drink the stuff tomorrow afternoon. You are perfectly free to change your mind after receiving the money and not drink the toxin.

The problem is similar to the one here. In Kavka, you simultaneously want to have intended to drink the poison and realized that any practical person would not drink the poison. Similarly, you want to be the kind of person who would only pick Box B, but must grapple with the fact that at the moment of choice, you'll inevitably take both boxes.

Because if you take both boxes there's no reverse-correlation. It might mean you are the kind of person who would take both boxes, but you haven't damned yourself to less money because you took them in the moment. You were damned from the moment Bob made the prediction. Any chooser should simultaneously want to be the kind of person who would only take Box B, and recognize the impossibility of being that kind of person (because at the moment of choice, you are totally free to take both boxes).

but that assumes things that aren't stated in the puzzle's premises. nowhere is it said that bob's prediction is indirect, based on the kind of person you are, or the kind of person bob takes you to be. it's instead an "almost perfect" estimate of what you will actually do. it therefore can't be circumvented by speculating about the kind of person that bob envisions or the kind of person you actually might be. no matter what you choose or why, no many how much analysis you subject the choice to, bob's prediction remains "almost perfect." and it is therefore almost perfectly certain that box B will be empty if you take both boxes -- no matter what rationale you use to arrive at that choice.

kava's toxin seems similarly non-paradoxical. it's only when one begins to question whether or not one should actually drink the toxin that the attainment of the money comes to be in jeopardy. therefore, the real question is not the wormhole implied by the hidden paradox, it's a straightforward, "should i drink the toxin?" and the answer is a similarly straightforward, "yes, you should." if one puts aside all thought of what one might gain by NOT drinking the toxin and instead simply plans to do it, then one remains assured of gaining the money.

strike

"...no many how much analysis you subject the choice to..."

sub

"...no matter the analysis to which you subject the choice..."

working through the booze here

i mean, i get what you're saying: if you choose to take box B and really mean it, then bob very likely predicted that. okay, so having made that sincere choice, what's to prevent you from changing your mind and taking both boxes, thus somehow "fooling" the supposedly near-infallible bob?

two things:

1) if it's a truly sincere choice, then once made, it cannot be undone. i.e., sincere choice is irrevocable. i say this because any mental decision that IS revocable can be described as a part of the pattern of consideration that might eventually lead to a real and final choice, and that's not what bob seems to be predicting.

2) although reverse causation cannot be assumed, we must still act as though reverse causation is in effect. i say this because we do not understand the actual mechanism that governs bob's predictions. that's what i meant earlier. we only know that the act of taking both boxes seems to drastically reduce the likelihood that box B will contain anything, and given the absence of any other information, we might as well go with what we've been given.

There's certainly a correlation between taking both boxes and Box B not containing anything. Not a causation though. (The causation is that Bob predicted you'd take both boxes, that's why Box B doesn't contain anything. That you took both boxes is incidental.)

OT: I kinda want to run a bunch of other polls in a similar vein (A priori knowledge: Yes/No, Abstract Objects: Platonism/Nominalism, etc). Peeps be interested?

There's certainly a correlation between taking both boxes and Box B not containing anything. Not a causation though. (The causation is that Bob predicted you'd take both boxes, that's why Box B doesn't contain anything. That you took both boxes is incidental.)

yeah, i get that. but as a chooser, you have to assume a quasi-causal relationship between the choice you make (the only part of this situation you can control) and the outcome you hope to receive. you cannot know how bob came to possess this almost perfect understanding, after all. nor can you know what bob has predicted. you only know that whatever choice you ultimately do make, it is very likely to have been correctly anticipated by bob. therefore, by making a choice, and only from your own perceptual standpoint, you more-or-less "cause" the outcome. this has to do with the nature of time. in the scenario described, bob has predicted the future existence of something that did not yet exist at the time of prediction. in other words and regardless of what bob has predicted, prior to your actually making a choice, your choice does not exist. since it asks you (dear reader) to render a decision, this puzzle assumes the existence of free will. therefore, in the act of choosing, you validate (or invalidate) bob's prediction, and your choice IS causal in that sense. the problem is that you cannot possibly know how to invalidate bob's prediction, which makes it prudent to assume that bob has predicted things correctly and to make the choice that will provide maximum benefit under that circumstance.

the problem is that you cannot possibly know how to invalidate bob's prediction, which makes it prudent to assume that bob has predicted things correctly and to make the choice that will provide maximum benefit under that circumstance.

This is my reasoning as well.

The only thing that violates this is the friend who can see into the boxes, and the interesting thing is that if you assume Bob is near-infallible, the odds that you will get $101K after your friend looks at the money goes down dramatically.

contenderizer otm

Automatic thread bump. This poll is closing tomorrow.

I kinda want to run a bunch of other polls in a similar vein (A priori knowledge: Yes/No, Abstract Objects: Platonism/Nominalism, etc). Peeps be interested?

yeah, there ain't enough philosophy in this place.

Automatic thread bump. This poll's results are now in.