Newcomb's Problem

[El_Machinae]

I'm posting as a "B picker" so that when Omega reads this thread (currently being beamed at the speed of light, I suspect), he'll know to put a million bucks in my box.

 

[brennan]

Look at it this way. Imagine that both boxes have a transparent side that's facing away from you, and friend of yours is on the other side. That is, they can see what's in the boxes, and you can't. What do you think they would tell you to do?

He'd tell me to change my mind. But then if we reverse the situation, he's only getting a thousand lousy bucks anyway

 

[AbuDhabi]

I think this is a scam. I think Omega cannot predict what choice I make. I think my choice will not alter the contents. I choose both boxes.

I also believe this is an annoying waste of time.

Happy now, Erik?

 

[scy12]

Are there any two boxers who had a change of heart ? Or who haven;t changed their opinion on the matter. I think there can't be a more obvious question as the problem here.
And i repeat that the most likely scenario is that Box B has a donation to your account from person A of a million and Box A has 999000 you owe to person A .

 

[lovett]

Precommitting to being a one-boxer implies a) saying/voting/etc that I will choose one box, b) choosing one box, and c) favoring one box in whatever other ways are appropriate.

If I've precommitted to choosing one box, then I get a million dollars in box B no matter what Omega is doing - cheating by manipulating the boxes, making good predictions based on observations of me, putting money into the boxes based on what I said in this thread, or doing something else.

Wait, Im not sure if I understand.

Are you pre-committing to one box on the off chance that Omega will actually read this thread and therefore put a million $ in box B?

 

[brennan]

Wait, Im not sure if I understand.

Are you pre-committing to one box on the off chance that Omega will actually read this thread and therefore put a million $ in box B?

No, on the evidence that Omega can succesfully predict that I am a one boxer.

 

[Erik Mesoy]

Wait, Im not sure if I understand.

Are you pre-committing to one box on the off chance that Omega will actually read this thread and therefore put a million $ in box B?

No, I'm precommitting to general one-box-ness for all problems that are similar to Newcomb's problem. Does that make any sense?

A person who is precommitted to box B (or the equivalent) gets a million dollars (ditto) for any route that Omega (ditto) uses to determine what to put in the boxes (ditto), as described above: reading the thread, cheating, quickly slipping the money in after I make my choice, running a computer simulation of me...

The only vaguely plausible route I can see to getting the hypothetical $1001000 is to act as though you're a one-boxer right up to the moment when you're asked to choose, and then suddenly pick both boxes. This is difficult at best, and even so, I should pretend to be a one-boxer when discussing this. Whereas planning to take both boxes, and then taking both boxes, is a quick and easy way to end up with $1000.

And i repeat that the most likely scenario is that Box B has a donation to your account from person A of a million and Box A has 999000 you owe to person A .

And I repeat that Box A is transparent and visibly contains $1000.

 

[scy12]

And I repeat that Box A is transparent and visibly contains $1000.

Unfair ! This is another game .... But actually not that different when i explain my reasoning. We are working here knowing the result , because someone who is always right has told us what it is. The question is how have we reached that result not of which is the best choice.

Here are it.

A+ B = R(result)

1000 + B = 1000 , So B = 0

B= 1000000 , Sp B = 1000000

Both are indisputably correct.

What changes is that when you choose A , then B has nothing.

Now lets attempt some explanations.

There very different ways this mechanism may work.
One of them is that When you select Box B a mechanism inside the box turns to true and when that happens from a device (any device you wish) you get a "You win a million" (Their are countless ways this could happen. If Box B and Box A are selected by any different sequence you wish (i.e First B then A, etc) then Box B is set to false and you get nothing from it.

If it is this explanation or timetravel which one you think to be the more plausible ?

The only vaguely plausible route I can see to getting the hypothetical $1001000 i

You can never get 1001000. Omega doesn't predict what you will do. He predicts what you will get if you choose something. And i can do it also.
I can call it predicting what you will do if i wish and you couldn't tell the difference.

And as a running gag i still claim that Omega is not an alien.

 

[Kennigit]

Let me pose more questions:

Do you believe that the only possible way to get the one million dollars is to choose box B (thus contradicting that the value of the boxes does not change according to my personal choice as explained by the rules of the game?

or Do you believe that the only possible way to get a million dollars is if Omega predicted that you would choose box B (thus making your choice irrelevant, meaning that if the money is either there or not and you should take both boxes).

Again, I pose my question before about how predictive prowess by Omega means anything. Has anyone asked this to someone else? More importantly, were you correct in guessing what they would respond? I strongly believe that an ordinary person, meaning anyone here on cfc, can predict the response about 80% of the time if you know the people you ask relatively well.

 

[scy12]

Let me pose more questions:

Do you believe that the only possible way to get the one million dollars is to choose box B (thus contradicting that the value of the boxes does not change according to my personal choice as explained by the rules of the game?

or Do you believe that the only possible way to get a million dollars is if Omega predicted that you would choose box B (thus making your choice irrelevant, meaning that if the money is either there or not and you should take both boxes).

Again, I pose my question before about how predictive prowess by Omega means anything. Has anyone asked this to someone else? More importantly, were you correct in guessing what they would respond? I strongly believe that an ordinary person, meaning anyone here on cfc, can predict the response about 80% of the time if you know the people you ask relatively well.

Do you believe that the only possible way to get the one million dollars is to choose box B (thus contradicting that the value of the boxes does not change according to my personal choice as explained by the rules of the game?

Yes because the rules are contradictory. We are either to believe that Omega is an alien that is using magical powers to succeed with no explanation how or that their is a simple mechanism involved with the boxes. And whatever we choose to believe the rules say we get a million if we choose box B. So whether i flip a coin , believe in magical omega , believe in mechanisms involved if i choose box b i get the million because that is what the rules say.

So i choose the more plausible -logical scenario to see why i get the million.

Unless someone can prove to me that those rules are correct and that Omega is an alien and explain to me the method he is using which is more unlikely than the method i suggested that he is using. But that will not make me not choose box b.

 

[Kennigit]

I fail to see how Omega's ability to predict has any relevance at all. So what if he predicts my choice? If I two-boxed and found only $1,000, then good for Omega, but that meant that at the second that I chose, I could only win $1,000 no matter what I did.

 

[scy12]

I fail to see how Omega's ability to predict has any relevance at all. So what if he predicts my choice? If I two-boxed and found only $1,000, then good for Omega, but that meant that at the second that I chose, I could only win $1,000 no matter what I did.

I agree but i also believe that if you choose one box you would get a million.

 

[lovett]

No, I'm precommitting to general one-box-ness for all problems that are similar to Newcomb's problem. Does that make any sense?

A person who is precommitted to box B (or the equivalent) gets a million dollars (ditto) for any route that Omega (ditto) uses to determine what to put in the boxes (ditto), as described above: reading the thread, cheating, quickly slipping the money in after I make my choice, running a computer simulation of me...

The only vaguely plausible route I can see to getting the hypothetical $1001000 is to act as though you're a one-boxer right up to the moment when you're asked to choose, and then suddenly pick both boxes. This is difficult at best, and even so, I should pretend to be a one-boxer when discussing this. Whereas planning to take both boxes, and then taking both boxes, is a quick and easy way to end up with $1000.

I suppose it makes sense, but it seems, well, a little bit insane.

That is, your commitment to taking one-box is, if im correct(?) predicated on the assumption that the scenario you outlined could actually occur. Hence it is best to act like it will occur, and that Omega (or 'The Predictor' or 'God' or
'Laplaces' Demon') is actually assessing, at this moment, whether you are a one boxer or a two boxer.

It just seems an odd way of viewing it

 

[warpus]

I agree but i also believe that if you choose one box you would get a million.

There was only $1,000 in one of the boxes, he couldn't have gotten a million.

 

[scy12]

There was only $1,000 in one of the boxes, he couldn't have gotten a million.

In this scenario when one chooses one box that box is B. You can't get only A.

 

[warpus]

In this scenario when one chooses one box that box is B. You can't get only A.

Yeah, but, if there isn't a million in one of the boxes and you pick one box.. you don't get a million.

 

[scy12]

Yeah, but, if there isn't a million in one of the boxes and you pick one box.. you don't get a million.

Omega always gave a million to those who choose one box. There has never been a case when one choose Box B and didn't take a million. The future is always uncertain but the 100% certainty we had so far is the furthest one can get. It is also possible that a giant dragon will eat me tomorrow but i think this will never happen.

 

[warpus]

Omega always gave a million to those who choose one box. There has never been a case when one choose Box B and didn't take a million. The future is always uncertain but the 100% certainty we had so far is the furthest one can get. It is also possible that a giant dragon will eat me tomorrow but i think this will never happen.

Yeah, but still... If there isn't a million in one of the boxes, and you pick one. You're not getting a million.

That is a fact.

 

[scy12]

Yeah, but still... If there isn't a million in one of the boxes, and you pick one. You're not getting a million.

That is a fact.

Are you serious or are you joking with me ? This may be undetectable sarcasm laughing at my persistence to discuss this matter.

You do not pick one of the boxes . You pick either B that is supposed to have a million always or both. If B doesn't have anything you don't get the million that is correct. But your supposed to trust 100% predictions for the same reason you trust that the computer will not mutate into an human-eating alien, from the film the thing and kill you in exactly fifteen minutes and 45 seconds.

 

[Elrohir]

I started out leaning towards taking both boxes - the idea that you can't change what's already there was pretty convincing - but the more I've thought about it, the more sure I am that the answer is just taking B.

Now, we don't know how Omega makes this choice. That isn't given to us. But the probability of getting 100 guesses in a row correct if he's just going randomly are infinitesimally small. (I could figure out exactly what those odds are, but there's little point. Everyone can see that the probability is very, very low) For the sake of argument, though, let's say that Omega is right 99% of the time - we can't know for sure what it is, but with definite numbers we can reach a definitive conclusion. (In reality the probability that Omega is wrong in any given 'game' must be less than 1%, but I don't want to deal with fractions of a percentage point, especially when I'm not sure how small of a fraction it actually is) The fact is, it's naive to believe that Omega is guessing; it's only rational to believe that he does indeed have a system, and a pretty darn good one as well. What that system is, be it time travel or computer simulations or just a wicked brain is utterly irrelevant - whatever it is, it works. And assuming that it is 99% effective, the problem seems to me to be reducible to a simple expected value problem:

Do you choose A&B with a 100% chance of $1000 and a 1% chance of $1m? Or do you choose B with a 99% chance of $1m? At this point, it seems like a very simple expected value problem.
(A&B) 1*1000 + .01*1,000,000 = 11,000.
(B) .99*1,000,000 + 0*.01= 990,000.*
Therefore, since $990,000 > $11,000, you should choose B, and only B.

As an aside, thanks for posting this Erik. I skimmed through the entire thread, and it's a very interesting debate, which has really reminded me why I love this place. In between trolls and the spam and angsty teens, you can lose sight of how many utterly brilliant people we have here. On a more negative note, my evening is gone, and I now have philosophical dissertation and a wiki article on quantum suicide to read, that I didn't have before.


*

Spoiler :

The explanation for this is very simple. The $1000 in A is guaranteed, so there's a 100% chance that it's there. And since Omega is right 99% of the time, the probability that he would guess that you would choose B, but you really chose both is 1%.

On the other side, since he's right 99% of the time and you indeed chose just B, the odds of you getting the $1m are 99%.