Newcomb's paradox

This paradox is named after William Newcomb, a physicist who thought it up in 1960 while playing with the prisoner's dilemma. I paraphrase from Martin Gardner's fine book "Knotted Doughnuts and Other Mathematical Entertainments" (1986) available at fine booksellers near you.

Newcomb's Paradox
There are two closed boxes, B1 and B2, on a table. B1 contains $1,000. B2 contains either nothing, or $1 million. You do not know which. You have a one-time, irrevocable choice between only these two actions:

1) Take what is in both boxes.
2) Take only what is in B2.

But, of course, there is a catch. :)

Some time before you entered the room, a superior Being (god, alien intellegence, supercomputer from the future, whatever) has made a prediction about your choice. That Being has always been correct in all its past predictions about people, and it is almost certainly correct about you.

So here's the catch: If the Being expects you to take both boxes (choice #1), it placed nothing in B2. If the Being expects you to only take B2 (choice #2), it placed the $1 million in B2.

The boxes are now well sealed, you're not allowed to touch them until you've decided, and there is no way you can determine what is inside of them. You understand the situation fully, and the Being knows that you do. So:
Which choice do you make?

:confused: :D

Find that god, superbeing, alien, computer or whatever and make them hand over the money for being a smartass!

I had to think a bit just to figure out what the catch really meant.

I'd take choice #2, collecting B2 and my $1 million; that thing better be right...

I take choice 1. betting on the fact that the thing thought I would take choice 2.

If I'm wrong I'm $1000 better off anyway so it's all good.

100% B2 all the way.

I figure that $1,000 is not that much money and I could get that in Bingo, horse racing, or a good night in Vegas.

But how often do you have a 50/50 chance at 1 million dollars?

For me it's a no brainer. Perhaps if I was raised an only child I would instantly think to take both boxes.

well, since I am a safe person and always take the sure thing. I would take choice number 2 and collect my 1 million :)

how do I know I would get the million? because I always take the safe bet and never gamble. This tendency I have, the super alien/god/computer would know. So I go against it for the first time in my life and voila, I am a million dollars richer :flash: :flash: :flash:

:smoka:

Originally posted by marc49
I always take the safe bet and never gamble. This tendency I have, the super alien/god/computer would know. So I go against it for the first time in my life and voila, I am a million dollars richer :flash: :flash: :flash:Wouldn't the Being know you were going to do that?

Originally posted by jay@af
Wouldn't the Being know you were going to do that?

Reread the Paradox. :D
Its not really a paradox, as there is a correct answer. As Marc said, take box Two.

To make it a Paradox you would need to add a few extra conditions, like the Being was evil and didn't want you to get any money.

well if the being knew what you were going to do, then it wouldn't really be a "prediction". and if that was true, then everybody would have to pick the 1000 bucks because you are guaranteed that.. if he knew exactly what you were going to do, then it would be a 50/50 shot at the million, it would be a 0% chance..

Hehehe... Sure it would make sense that people would choose the first box, because it's logical to want to pick the option where you're guaranteed a return. But people are rarely so logical in tha face of such a decision. Ever see "Let's Make A Deal?" :p

damn, beat me to the reply moppie. lol

I'd tell them "look over there!", then take both boxes and run.:D

B2, its all or nothing.

however, what would have made this more interesting is if you hadnt told us the "catch" Fritz. see, if you had just said, "there is a being that knows what your going to choose" and explain that to us, then told us what would have happened if we picked 1 or 2 later on in the thread, we would have known what our circumstances would have been. just a thought, im probably wrong.

Originally posted by Moppie
Reread the Paradox. :D
Its not really a paradox, as there is a correct answer. As Marc said, take box Two.

To make it a Paradox you would need to add a few extra conditions, like the Being was evil and didn't want you to get any money.
Nope. It is a paradox. If the Being didn't want you to have money, it would just never put any money in B2 - and that would make it so there was no paradox. In the paradox, the Being is fair. It makes its honest prediction and follows the rules.

Here's the counterpoint to what's been voiced here: The Being has mad it's decision beforehand, let's say one week ago, and the boxes are now sealed - the million is either in B2 or it is not. If the money is already in B2, it will stay there whichever you choose; it's not going to disappear. If it's not already there, it's not going to suddenly appear if you only choose B2. There is no "backward causality" - your present actions cannot alter what the Being did last week. So why not just take both boxes? If B2 is filled, you get $1,001,000; if B2 is empty, you get $1000. If you are so foolish as to only take B2, you can't get more than $1 million, and you might even get nothing! Clearly it is to your advantage to take both!

It's funny, I posed this question to a group of friends about a year ago, and they all answered opposite of the consensus here; also stating that it wasn't much of a paradox. ;) That is the neat thing about this. Everyone almost immediately thinks they have the right and obvious answer, but they're usually split right down the middle about which choice they make.
:smoker2:

PS> Some seem to have missed a very important point of the paradox statement. Your two choices are: 1) take BOTH boxes, or 2) take JUST B2. If the choice was to take just B1 or just B2, there would be no paradox.

MTBN - taking both boxes is choice #1.

jay@af - taking just B1 is not an option.
:cool:

Originally posted by fritz_269
Clearly it is to your advantage to take both!Originally posted by jay@af
But people are rarely so logical in the face of such a decision. Ever see "Let's Make A Deal?" :p :right: I hope the "Being" has seen "Let's Make A Deal," anyway...

ok, your counterpoint clears things up slightly. it is definitly to our advantage to take both, however, im sticking to my guns and going with just B2.

There are two variables: Your Choice and the Being's accuracy.
If the Being expects you to take both boxes (choice #1), it placed nothing in B2. If the Being expects you to only take B2 (choice #2), it placed the $1 million in B2.
That makes four possible outcomes:

First choice:
B1 & B2 and the Being is right: $1,000 + $0 = $1,000
B1 & B2 and the Being is wrong: $1,000 + $1,000,000 = $1,001,000

Second choice:
B2 and the Being is right: $1,000,000
B2 and the Being is wrong: $0

About the Being's accuracy:
Some time before you entered the room, a superior Being has made a prediction about your choice. That Being has always been correct in all its past predictions about people, and it is almost certainly correct about you.
"Always been correct" makes it sound like the Being knows a bit about people. "Always been correct" is a pretty darn good track record. I presume that the Being knows that I know the parameters of the situation, including the fact that the outcomes depend on what it put in B2, which in turn depends on its prediction. If the Being is so darn good at making predictions about people, then certainly it considers all my waffling before my final choice.

But, we're not told how many predictions the Being has made. I've made assumptions because of the phrasing "almost certainly correct about you." But technically, it would make a difference if I was the 10th prediction it made, or the 10 billionth.

I think it's funny that I say that it depends on whether the Being is right or not, when really, the dissapointment comes if I don't live up to the Being's prediction. Oh, that sounds a bit like fate, doesn't it?

Or is it that I have to make a prediction about the Being's prediction? And while the Being may "always" be right, I'm not always right. But wouldn't the Being account for that in its prediction as well?

I still pick B2. :p

Originally posted by jay@af
I think it's funny that I say that it depends on whether the Being is right or not, when really, the dissapointment comes if I don't live up to the Being's prediction. Oh, that sounds a bit like fate, doesn't it?

Or is it that I have to make a prediction about the Being's prediction? And while the Being may "always" be right, I'm not always right. But wouldn't the Being account for that in its prediction as well?
BINGO! :D

The more you think about it, the more confusing it gets! :p I can totally convince myself of one answer, and wake up the next day completely convinced I was wrong.

This paradox actually has a lot to do with our core beliefs in determinism (fate) vs. free-will.
:cool:

I still believe that what I stated would work for me :finger: :frog: :flipa: :smoka: LOL

Damn, out whitted by a physicist. :( :o :p :finger:


But I still have a problem with the way its worded, let me get some sleep and I'll see if I can work out what it is. I believe Jay may be close.
I think it has something to do with the being being fair, and playing by the rules.

If the being is truly infallable, I'd have to go with #2.

BTW, do I know that if I take both #2 will have nothing before I enter the room? Or is that information kept a secret?

Originally posted by mtxzx2
If the being is truly infallable, I'd have to go with #2.

BTW, do I know that if I take both #2 will have nothing before I enter the room? Or is that information kept a secret? You have no way of knowing what the Being has decided. But the decision has been made, the money has or has not been placed into the B2, the boxes are sealed, and you get to pick - Both boxes or just B2.

And the Being is not truly infallable, just "almost certainly correct".
:cool:

Originally posted by fritz_269
You have no way of knowing what the Being has decided. But the decision has been made, the money has or has not been placed into the B2, the boxes are sealed, and you get to pick - Both boxes or just B2.

And the Being is not truly infallable, just "almost certainly correct".
:cool: In that case, I still have to look at it with a gambler's perspective..It's a 1000% return on an initial bet of $0 on a 50-50 chance. Go for the big bucks ;)

Originally posted by fritz_269
You have no way of knowing what the Being has decided. But the decision has been made, the money has or has not been placed into the B2, the boxes are sealed, and you get to pick - Both boxes or just B2.

And the Being is not truly infallable, just "almost certainly correct".
:cool: Which is why I made a point of its track record. I don't really think the Being's prediction prowess is akin to flipping a coin, which has a true 50% of being right on any independent test. e.g., if you flip a (fair) coin 100 times and it's landed on heads every time, the next time you flip that coin it still only has a 50% chance of coming up a particular way, regardless of what has come up before. The fact the the Being is a "superior Being" implies that it has some insight beyond simple intuition, e.s.p. or just guessing with dumb luck. Hopefully it learns from every test and uses the information in gains in the next prediction. But, since it had been right from day one, it may already have all the information about people's reactions that it needs.

I shared this paradox with some friends last night, and they all eventually came to the same result; take only B2. The interesting part that they did was debate whether the Being was using its knowledge of all of humanity or only its knowedge of the individual in question in making its prediction. I hadn't even thought of it that way.
Originally posted by mtxzx2
In that case, I still have to look at it with a gambler's perspective..It's a 1000% return on an initial bet of $0 on a 50-50 chance. Go for the big bucks ;) Actually, since you invest nothing, it's an incalculatable return... free money. ;)

P.S. remind me of the prisoner's dillemma. It's been a few years since I've seen it... :)

Originally posted by jay@af
Actually, since you invest nothing, it's an incalculatable return... free money. ;)

P.S. remind me of the prisoner's dillemma. It's been a few years since I've seen it... :)

I know, but "losing" the bet would be getting $1000..I figured it out from that :cool:

I would choose choice 1. Sure bet of atleast something.

Originally posted by jay@af
P.S. remind me of the prisoner's dillemma. It's been a few years since I've seen it... :)
from: http://wings.buffalo.edu/soc-sci/pol-sci/courses/psc102/webpage/pdgame/pdframe.htm
The prisoner's dilemma story is about two criminals, Bert and Ernie, arrested for a minor crime -- car theft. They are brought downtown and put into separate cells where they cannot communicate. The police detective in charge of the case believes that Bert and Ernie are both guilty of a more serious crime: the murder of a security guard during a micro-chip heist. The detective wants the two suspects to "rat" on each other (i.e., to defect and turn the other in). If neither rats (i.e., they cooperate with each other by maintaining their innocence) they both get one year in the state penitentiary. If they both rat and implicate each other, they both get ten years. If one rats and the other stays quiet, then the one giving up the information goes free and the other takes the entire rap - 20 years in prison. The dilemma is whether to rat or not rat.

The above link has a very detailed explaination and the math behind the game theoretical analysis. Here's the first step, make a payoff matrix:

Ernie Ernie
Cooperates Defects
Bert Cooperates 1,1 20,0
Bert Defects 0,20 10,10
Rat or don't rat? :cool:

it dosent say anything about Burt and Ernie being friends huh? in that case, its simple. if i was either one of them and i was not friends with the other, i would rat out the other guy. however, if we were both friends, i would not rat and stay a year.

Originally posted by SickLude
it dosent say anything about Burt and Ernie being friends huh? in that case, its simple. if i was either one of them and i was not friends with the other, i would rat out the other guy. however, if we were both friends, i would not rat and stay a year.
I'm not sure if you really got the idea!?
Don't Rat = Cooperate
Rat = Defect
Remember, you're in seperate rooms, you don't know if your partner is ratting on you or not!

If you Rat you get either 0 years (if your partner Doesn't Rat) or 10 years (if your partner Does Rat).

If you Don't Rat, you get either 1 year (if your partner Doesn't Rat) or 20 years (if your partner Does Rat).

Friend or not - you're looking at 20 years in prision if you keep your mouth shut and your friend squeals. And he's thinking the same thing about you!

Of course, even if you're not friends, you both know that if you both manage to just keep your mouth shut, you'll only spend 1 year inside.
:cool:

we went over this in a politics class that i am taking... but we used

0,0_______20,0


0,20______life,life

i found it was easier if you read it with box 1 having the title and keys to the car/truck/whatever you most want, and box 2 having title/keys to one that you would also like, but, that is worth a hell of a lot more, plus some money... then doing the same paradox

Originally posted by ac427cpe
we went over this in a politics class that i am taking... but we used

0,0_______20,0


0,20______life,life
Your politics professor needs to check up on his math if he thought that was a dilemma. That payoff matrix will result in a best strategy of ALWAYS cooperate. No dilemma there at all. The penalty for double defection must be less than the penalty for cooperate-defection to make things interesting.

Here is the ordinal matrix for the classic dilemma:

Ernie Ernie
Cooperates Defects
Bert Cooperates 2,2 4,1
Bert Defects 1,4 3,3
Defect-Cooperate must be worse than Defect-Defect for one player, and better than Cooperate-Cooperate for the other player. Otherwise, the best move is obvious.

Back to Newcomb's paradox - sure, you can substitute anything you want into the boxes. Dollar amounts seem to make it easier, since they are numbers and we can do some computations with them (as some who posted above have done). But it's also possible that they are just a distraction to the key questions... :cool:
:cool: