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Heroes Community > Other Side of the Monitor > Thread: Newcomb's Problem
Thread: Newcomb's Problem This thread is 3 pages long: 1 2 3 · NEXT»
mvassilev
mvassilev


Responsible
Undefeatable Hero
posted June 22, 2013 04:24 AM

Poll Question:
Newcomb's Problem

Imagine one day you're walking along, minding your own business, when a small flying machine buzzes by you. It turns around and lands in front of you, with two boxes in its clawed hands. Looking at the boxes, you see that one of them is labeled "A" and the other is labeled "B". It appears to turn towards you and says, "Hello, [your name]. I am Omega. No doubt you've heard about me already." You remember seeing stories on television that for the past few years, there have been several thousand instances of this machine landing in front of people. You've heard that it offers people a choice between two boxes (always the same choice), and asks people to make a choice. You also remember that Omega predicts what the person will choose, and that it has never been wrong.
"So, what's the choice?" you ask.
"I've already predicted what you'll choose, and I've never been wrong. Not surprising, given that I'm a superintelligence," Omega says, "But I'll tell you anyway. I'm going to leave these two boxes here and fly away, and you're free to take one or both of them. They're yours. I guarantee that the contents of Box A are a thousand dollars. Box B is either empty or contains a million dollars. I've already put the money in the box or boxes, and I'm not going to add anything to or remove anything from them. My decision rule for filling Box B is the following: if I think you're going to take both boxes, I put nothing in Box B - it'll be empty. It'll also be empty if I think you're going to choose randomly. If I think you're only going to take Box B, then I put a million dollars in it. The only additional bit of information I'll give you is that I've given this identical choice to thousands of other people, (all of whom have had the same incentives you have now), and I've always predicted their choice correctly. So, choose wisely." Then it flies away, leaving the boxes there.
What do you do?
To explain the relation of predictions, choices, and payoffs more compactly -
If Omega thinks you're going to take both boxes, and you choose to take both boxes: $1000.
If Omega thinks you're going to take both boxes, and you choose to only take Box B: $0.
If Omega thinks you're going to only take Box B, and you choose to take both boxes: $1,001,000.
If Omega thinks you're going to only take Box B, and you choose to only take Box B: $1,000,000.

Also, keep in mind that you only have one goal: to maximize how much money you get. So don't try to give answers like "I don't care about money" or "I want to mess with Omega".

This thought experiment was created by William Newcomb, and popularized by Robert Nozick.

____________
Eccentric Opinion

Responses:
take both boxes
take only Box B
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friendofgunnar
friendofgunnar


Honorable
Legendary Hero
able to speed up time
posted June 22, 2013 04:45 AM
Edited by friendofgunnar at 04:45, 22 Jun 2013.

The only way that there will be a million dollars in Box B is if I can rationally explain why I would leave behind the box with a thousand dollars, which would seem to be impossible given that the a priori goal is to maximise my profit...

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mvassilev
mvassilev


Responsible
Undefeatable Hero
posted June 22, 2013 04:53 AM

You can rationally explain why you'd leave Box A behind - because if you don't, you don't maximize your income. Proof by contradiction: suppose the optimal strategy is to take both boxes. Both you and Omega know this. Then Omega will only leave money in Box A, and you'll only make $1000. You have not maximized your income, so taking both boxes cannot be the optimal strategy.
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Eccentric Opinion

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Zenofex
Zenofex


Responsible
Legendary Hero
Kreegan-atheist
posted June 22, 2013 08:25 AM

How can Omega think that you can make either choice, for example take box A, then you make a different choice - take box B, and the assumption that Omega is always correct remain true?

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friendofgunnar
friendofgunnar


Honorable
Legendary Hero
able to speed up time
posted June 22, 2013 08:32 AM

Quote:
You can rationally explain why you'd leave Box A behind - because if you don't, you don't maximize your income. Proof by contradiction: suppose the optimal strategy is to take both boxes. Both you and Omega know this. Then Omega will only leave money in Box A, and you'll only make $1000. You have not maximized your income, so taking both boxes cannot be the optimal strategy.



However Omega, being the supreme mind that he is, knows that 99.999% of humans do not concoct "proofs by contradiction" to arrive at their preferred mode of behaviour.  Thus he knows that people will nearly always take both boxes, thus he never puts anything in B.  


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mvassilev
mvassilev


Responsible
Undefeatable Hero
posted June 22, 2013 08:44 AM

Zenofex:
That's the whole crux of the problem. The reason Omega can predict your actions is because there is an optimal strategy to follow, and it predicts that you will follow it, given that you want to maximize your payoff. You can't really pick either choice, because you have the goal of maximizing your payoff and there is only one strategy that satisfies that goal.

FOG:
Perhaps it observes people before giving them the choice, so it knows how good their strategic thinking is.
Or maybe an unstated assumption is that everyone in this problem is perfectly rational.
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Eccentric Opinion

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master_learn
master_learn


Legendary Hero
walking to the library
posted June 22, 2013 09:42 AM

That's interesting and fine choice a person could get here.
He can't loose whatever his choice is!

So,you summarise it with two choices with four different outcomes.

Personally I would take the box A.
My choice would be in the line of thought that 1000 $ is very good ammount for an advertising strategy-something connected with letter Omega and happy customers(which is perfectly rational in my view).
I frankly I would believe a flying machine would put only 1000 $ or just nothing,because none can force it whether the machine is wrong or just playing with you.

Back on the choice-if I take for granted that Omega is not wrong and I am maximizing my profit,I would take the B box.
Because that's the maximum sum I would receive if both me and Omega think the same.

If Omega thinks I would take the B box and I take the two of them,it would be a contradiction with the assumption,so it would be out of the question.
If I take box B and Omega thinks I take the two of them,I receive 0 $,but that would be also contradiction.


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Adrius
Adrius


Honorable
Undefeatable Hero
Stand and fight!
posted June 22, 2013 11:19 AM
Edited by Adrius at 11:23, 22 Jun 2013.

GraaAARRRGH my head. I like this problem.

The optimal thing to do that I can think of is to decide to take B, really rational thinking and everything, focus on it, make Omega believe that is what I have decided, what I would choose if it were only up to me.

Then I flip a coin and let that decide whether I take only B or both. He shouldn't be able to predict that.

It should cover these two:
Quote:
- If Omega thinks you're going to only take Box B, and you choose to take both boxes: $1,001,000.
- If Omega thinks you're going to only take Box B, and you choose to only take Box B: $1,000,000.


It's the only way I can think of to give me a chance at the maximum amount. I don't think this is allowed though...
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master_learn
master_learn


Legendary Hero
walking to the library
posted June 22, 2013 11:31 AM

Coming to my mind is a clever decision.
I think its nothing wrong if I call a friend to take the box A after my choice to take the box B.
I could later persuade him to give it to me.
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Adrius
Adrius


Honorable
Undefeatable Hero
Stand and fight!
posted June 22, 2013 11:35 AM
Edited by Adrius at 11:43, 22 Jun 2013.

I don't think that's allowed.

In fact I don't even think my coin is allowed.

EDIT:

It seems impossible to "win" this to me with the incentive I have... but then again WANTING both boxes is perhaps different from CHOOSING both boxes.... **** I don't even know....

It seems to me that the experiment somehow favours irrational people... people that Omega perhaps cannot predict, but the statistics of Omega predicting previous contestants with 100% certainty speaks against such people even existing.
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Zenofex
Zenofex


Responsible
Legendary Hero
Kreegan-atheist
posted June 22, 2013 12:10 PM

I'd say there's a flaw in the wording of the whole exercise and from there - its logic. If Omega can always predict what you will pick with 100% success rate, then you will never pick something which Omega has not predicted, thus no matter what you think you're picking, you'll always pick exactly what Omega has predicted and respectively left in the boxes. There's no real choice here, only an illusion of choice. If however Omega is prone to mistakes, although very rare, then the task will have some meaning.  

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artu
artu


Promising
Undefeatable Hero
My BS sensor is tingling again
posted June 22, 2013 12:18 PM

You're really close Zenofex.

Spoiler

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mvassilev
mvassilev


Responsible
Undefeatable Hero
posted June 22, 2013 07:21 PM

To those wondering about the "illusion of choice", consider a simplified problem that has a more obvious answer. Imagine there is no Box A, only Box B. Your choices are now to take Box B or to leave without taking it. If Omega thinks you're going to take Box B, it puts a million dollars in it. If it thinks you're going to leave without it, it puts nothing in Box B. The optimal strategy here is clear, and you will always leave with a million dollars. Does that mean you don't have a "real choice"?

Adrius:
If the optimal strategy involves flipping a coin, then Omega will know that's the optimal strategy, and leave Box B empty. As it said, "It'll also be empty if I think you're going to choose randomly."
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Adrius
Adrius


Honorable
Undefeatable Hero
Stand and fight!
posted June 22, 2013 08:49 PM

Ah I missed that because it wasn't in the summary.
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Zenofex
Zenofex


Responsible
Legendary Hero
Kreegan-atheist
posted June 22, 2013 09:10 PM

Quote:
To those wondering about the "illusion of choice", consider a simplified problem that has a more obvious answer. Imagine there is no Box A, only Box B. Your choices are now to take Box B or to leave without taking it. If Omega thinks you're going to take Box B, it puts a million dollars in it. If it thinks you're going to leave without it, it puts nothing in Box B. The optimal strategy here is clear, and you will always leave with a million dollars. Does that mean you don't have a "real choice"?
That's bypassing the actual problem - is Omega infallible in its predictions or not? If yes, then the content of the box is determined entirely without the participation of the person who seemingly makes a choice. It doesn't matter if he/she knows this or not from the perspective of the content itself - it is there or it is not there no matter what. If however Omega actually can make mistakes AND as a result of that mistake the content of the boxes can be changed - or in other words it is a variable, not a constant - then making a choice is possible.

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mvassilev
mvassilev


Responsible
Undefeatable Hero
posted June 22, 2013 09:13 PM

You only know that Omega has done this many times before, with perfectly strategic people. You don't know what they chose, but you know that it has always predicted their choice correctly. You don't know if Omega is infallible, but you have reason to believe that it's at least a very good predictor.
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Zenofex
Zenofex


Responsible
Legendary Hero
Kreegan-atheist
posted June 22, 2013 09:41 PM

That's a completely different story then. If Omega is known to have always predicted the choice of the people before the person currently choosing between the boxes but there is still doubt that Omega's predictions are not guaranteed to always be correct (like it will most likely be in the real world), then the choice will be genuine.

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Lexxan
Lexxan


Honorable
Undefeatable Hero
Unimpressed by your logic
posted June 22, 2013 09:46 PM

I'd take both boxes, because you'll get money anyway.

if Omega knows this, he'll predict this correctly for me.

Therefore, to maximize profit, i'll *have* to take both boxes, sticking with Omega's prediction, lest i go home with NOTHING.

that's my solution to the problem.

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Coincidence? I think not!!!!

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JollyJoker
JollyJoker


Honorable
Undefeatable Hero
posted June 22, 2013 10:02 PM

Ok, it makes no sense to pick A, because A gives you 1.000 - but not more.
However, if you chose to pick them both, you'll get 1000 dollars minimum, but have a chance for a million more, so "both" is better than A, no matter what.

However - the only chance to get the million is Omega guessing you picking ONLY B. With Omega being right always until now the best strategy is obviously to pick ONLY B, even if that incurs the risk of getting nothing - but only if Omega guesses WRONG, which didn't happen.

Which means, you'll pick B - solely based on the information that Omega pick always RIGHT, and this will leave you with the most money IF THAT'S TRUE.

Is there a choice?

No. If Omega is always right, he can't go wrong and the option where he goes wrong are just illusions.

Betting on him BEING ABLE to be wrong isn't gaining enough for the risk incurred (the win sums would have to be different), so I don't see the problem actually.

B is the right choice no matter what.

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JollyJoker
JollyJoker


Honorable
Undefeatable Hero
posted June 22, 2013 10:33 PM

Edit:
After posting that I read the spoiler, and I don't thionk I agree with the analysis.

That's because win/loss ratio is incongruent.

Practically spoken - it's more or less A BET, not a mathematical or philosophical problem.

As it is, the problem is one of comparing the CERTAINTY of winning a low sum with a very high probability of winning a much higher sum and a very low probability of getting nothing.

From a BETTING point of view, there really is no decision to make here.

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