Newcomb's Problem

[WillJ]

What defines "fated"? Does it mean by definition, a course of action/events that will happen regardless of what reasons and arguments are brought against it?

Either that, or any reasons or arguments brought against it were fated to be brought (i.e. they'd be brought regardless of what's brought against them, unless what's brought against them was fated to be brought, and so on).

In that case I don't think Omega's success record gives us any reason to think the person's decision is fated.

Well, I think it has to be one of the two possibilities I mentioned (if my distinction makes any sense, which maybe it doesn't).

About "weird" physics: there's nothing weird about physics that has determinative relations extending both forward and backward in time. Newtonian physics is like this. For example, from the total momentum of a colsed system today, you can equally well derive the total momentum of the system yesterday, or tomorrow.

Yes, a conservation law can be seen in either direction, but as far as I know there's not a case where if you change something, something in the past will change.

 

[brennan]

I'm afraid I haven't read the whole 14 pages (sorry Erik) but I find Omega's success rate suggests he has a pretty reliable way of getting me that million dollars. Er, I mean figuring out that i'll pick box B.

Can I take mine in pounds sterling please, this funny foreign currency looks odd...?

 

[BCampbell]

I'm not sure it's a "difficult" choice. I think the answer is obvious and it appears that you do so to.

After talking to a few people about it, I agree that it's not a difficult choice at all. The answer that an individual comes to is usually pretty quick, it's easy, and they're relaly sure they're right!

But yes, it comes down to how you look at the problem, which is an interesting bit of psychology. I'm a 2-boxer and I find it impossible to explain to people who "trust" the predictive powers of our extraterrestrial friend that whatever's in box B is already there and your choice doesn't actually change it. Their reliance on "fate" seems to me like an expectation that present actions can change past occurrences. But when I think of the wording of the problem, I understand where they're coming from, I'm just looking at it from the other end.

 

[brennan]

Two boxers are treating it as a random choice and deciding that to pick both boxes is the best way to get a win, as it were - half the time they get $1000, half the time they get $1,001,000; average win $501,000. One boxers are relying on the (rather strong IMO) evidence that it isn't a random choice and expect to win $1,000,000 each time.

 

[shortguy]

They aren't treating it as a random choice; the point of the two-boxers is that there either is or isn't money in box B by the time you choose (that is, the prediction has already been made and the money has been placed), and either way you get more money if you choose both boxes (you get $1,001,000 instead of $1,000,000 if there's money in B, and $1,000 instead of $0 if there isn't).

 

[brennan]

They aren't treating it as a random choice; the point of the two-boxers is that there either is or isn't money in box B by the time you choose (that is, the prediction has already been made and the money has been placed), and either way you get more money if you choose both boxes (you get $1,001,000 instead of $1,000,000 if there's money in B, and $1,000 instead of $0 if there isn't).

Ok. So i'm Omega and you are clearly a two boxer. What do you think is in your box B?

 

[warpus]

It doesn't matter.

It's already been established that if you were predicted to have picked box B only - then that's exactly what you're going to pick.

If you were predicted to pick both boxes - then you will.

You have a choice in the matter only BEFORE the prediction. You do not have a choice when the boxes are presented in front of you.

That little sublety is causing a lot of confusion.

 

[brennan]

It doesn't matter.

It's already been established that if you were predicted to have picked box B only - then that's exactly what you're going to pick.

If you were predicted to pick both boxes - then you will.

You have a choice in the matter only BEFORE the prediction. You do not have a choice when the boxes are presented in front of you.

That little sublety is causing a lot of confusion.

It is not that you have no free will or that the decision is already made, but that the prediction of your behaviour is extremely good: given that the odds of Omega randomly making 100 correct predictions in a row are 1 in 2^100 = mindbogglinglylow; it's a safe bet given the situation as posed that his prediction method is reliable. Assuming this, then you'd be a fool to pick both boxes as this is bound to yield only $1,000 instead of $1,000,000.

I think the confusion arises from the fact that this situation is not plausible in the real world. In the real world I seriously doubt that the 100 correct guesses situation could arise as I very much doubt that behaviour could be predicted with such accuracy. But in the situation as given, with the information we have about the 100 correct guesses, it's a no-brainer.

 

[Kennigit]

Imagine that you, for whatever reason, have to bet money on a football game. You look up some pundits and their opinions on the game:

Pundit 1 has predicted 20/100 games correctly, and thinks that team A will win.

Pundit 2 has predicted 80/100 games correctly, and thinks that team B will win

Would you bet on team A or team B? Whichever team you bet on, you will not influence the outcome of the game, and neither will the pundits. All any of you are doing is predicting! But you can endeavor to match your predictions as closely as possible to observed patterns.

It is a more appropiate analogy that the game has already been played, and I have a bet on which team already won the game. Pundit two had been correct 80/100 games correctly in the last 100 games, and Pundit 1 had predicted 20/100 games correctly. Now, those statistics have absolutely nothing to do with what happened in the game.

To fit it with our analogy, lets say I can bet on eonly team B or bet on team A and get a free bet on team B for the same amount. If team B won ($1,000,000) and I bet on team B, then yay for me, I won the bet! But if team A won or I bet on both teams, then no matter what I win (and get the $1,000,000 as well).

Similarly, has anyone told the problem to anyone else? I bet cfc could get atleast an 80% correct prediction if you ask your close friends/family, especially when predicting the A + B boxers.

Does that mean that if I played the game with you and was right 10 out of 10 times that you would take just box B? And because I have good predicting skills makes you believe I time traveled or have sim perfs or whatever? Or are you much more likely to agree that the value of the boxes don't change, no matter what I predicted, and there is no destruction of universes and so forth.

 

[brennan]

Now, those statistics have absolutely nothing to do with what happened in the game.

To say that the statistics have no effect on the game is the wrong way around. The games have effects on the statistics, then the statistics are used to model future games as accurately as possible. That's how bookmakers make their money after all.

 

[scy12]

It is a more appropiate analogy that the game has already been played, and I have a bet on which team already won the game. Pundit two had been correct 80/100 games correctly in the last 100 games, and Pundit 1 had predicted 20/100 games correctly. Now, those statistics have absolutely nothing to do with what happened in the game.

To fit it with our analogy, lets say I can bet on eonly team B or bet on team A and get a free bet on team B for the same amount. If team B won ($1,000,000) and I bet on team B, then yay for me, I won the bet! But if team A won or I bet on both teams, then no matter what I win (and get the $1,000,000 as well).

Let's change it.


Pundit two had been correct 80/100 games correctly in the last 100 games, and Pundit 1 had predicted 20/100 games correctly. Now, those statistics have absolutely nothing to do with what happened in the game.

Pundit two predicts that if you choose one of the two teams you win the million while if you choose both you don't.

The game already happened but Pundit two may know something which would cause you for example to lose 999000 if you bet on team A.

Infact i think it is a quite easy solution. If you take box B you win a million. If you take both boxes you win a million due to box B but you lose 999000 due to Box A. So one can always predict the result.

 

[warpus]

Brennan, you either didn't read, or didn't understand my post.

 

[Kennigit]

Might I ask all one boxers: What do you believe puts a million dollars in box B?

Do you believe that your individual choice by picking B puts a million dollars in it?

or

Do you believe that Omega put the money in beforehand and does not change it via time travel or teleportation or something else.

If you believe, as I do, that Omega put the money in beforehand and does not change it (as explained in the rules of the game), then why not choose both boxes?

 

[scy12]

Might I ask all one boxers: What do you believe puts a million dollars in box B?

Do you believe that your individual choice by picking B put a million dollars in it?

or

Do you believe that Omega put the money in beforehand and does not change it via time travel or teleportation or something else.

If you believe, as I do, that Omega put the money in beforehand and does not change it (as explained in the rules of the game), then why not choose both boxes?

What do you believe puts a million dollars in box B?

I believe there are always a million dollars in box B or when i choose a mechanism allows me to get them. I don't think that Omega has any magical powers. Or that he is an Alien.

Do you believe that Omega put the money in beforehand and does not change it via time travel or teleportation or something else.

He either does not change it or there is a simple perfectly explainable mechanism involved.

If you believe, as I do, that Omega put the money in beforehand and does not change it (as explained in the rules of the game), then why not choose both boxes?

Because i don't know what is in Box A. Omega is always correct so your choice to get Box A is quite likely to be the reason you lose 999000 . What is in Box A ? It could likely be Paper that show Money you owe to someone due to Omega having connections.

 

[Erik Mesoy]

Might I ask all one boxers: What do you believe puts a million dollars in box B?

My precommitment to being a one-boxer, which Omega can observe and base his prediction on.

Do you believe that your individual choice by picking B puts a million dollars in it?

or

Do you believe that Omega put the money in beforehand and does not change it via time travel or teleportation or something else.

The rules of the situation specify the latter. The money is already in the boxes (or not) when I choose.

If you believe, as I do, that Omega put the money in beforehand and does not change it (as explained in the rules of the game), then why not choose both boxes?

Because that's incompatible with precommitting to being a one-boxer.

 

[Ayatollah So]

Might I ask all one boxers: What do you believe puts a million dollars in box B?

A person who faithfully tracks my choices.

Erik's answer is good, too.

 

[BCampbell]

It is not that you have no free will or that the decision is already made, but that the prediction of your behaviour is extremely good: given that the odds of Omega randomly making 100 correct predictions in a row are 1 in 2^100 = mindbogglinglylow; it's a safe bet given the situation as posed that his prediction method is reliable. Assuming this, then you'd be a fool to pick both boxes as this is bound to yield only $1,000 instead of $1,000,000.

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?

 

[BCampbell]

Because that's incompatible with precommitting to being a one-boxer.

Why?

Sounds like a stupid question, but I'm serious.

 

[aneeshm]

First, you work out the probability that an alien who has been right a hundred times out of a hundred will be right the next time. Basically, find the improbability of 100 correct answers arising from pure guesswork. Call this P. This will give you the chance that the alien is simply guessing. If he is guessing, the chance that he is wrong is given by P/2.

Now, there are four cases:

a) Alien right, you pick B
b) Alien right, you pick both
c) Alien wrong, you pick B
d) Alien wrong, you pick B

a) If the alien is right, and you pick B, you have a reward of 1 million. The value of this case is (1-P/2)*(10^6).
b) If the alien is right, and you pick both, then the value of this case is (1-P/2)*(10^3)
c) If the alien is wrong, and you pick B, then you get nothing. The value of this case is (P/2)*0 = 0
d) If the alien is wrong, and you pick both, then you get the jackpot, valued at (P/2)*1001000

The condition of balance is: Val(a) + Val(c) = Val(b) + Val(d)

which is:

(1-P/2)*(10^6) + 0 = (1-P/2)*(10^3) + (P/2)*1001000

Which gives P = 0.999.

That is, both choices are equal only when the probability that the alien will be wrong 0.999 times every times he makes a choice - or, in layman's terms, that he is wrong every 999 out of 1000 times.

Now again, there are two choices. Either he knows, or he is guessing.

The probability that he is guessing is, or has made a hundred correct choices purely by guess work, is 2^(-100).

As this is clearly less than the required value of 0.999, we can safely conclude that the case in which we take only the box B is the correct one to choose in this scenario. It's not guaranteed, of course, but it's valued far more highly. Much more than trillions of times more highly, in fact.









Was that rough proof of correctness enough of a justification for me saying that we should pick choice B?

And do I win this thread?

 

[Erik Mesoy]

If you believe, as I do, that Omega put the money in beforehand and does not change it (as explained in the rules of the game), then why not choose both boxes?

Because that's incompatible with precommitting to being a one-boxer.

Why?

Sounds like a stupid question, but I'm serious.

That you're serious doesn't stop it sounding like a stupid question, though.

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.

If I choose both boxes, I wasn't precommitted to being a one-boxer.

Spoiler spoiler'd probability calculations for brevity :

First, you work out the probability that an alien who has been right a hundred times out of a hundred will be right the next time. Basically, find the improbability of 100 correct answers arising from pure guesswork. Call this P. This will give you the chance that the alien is simply guessing. If he is guessing, the chance that he is wrong is given by P/2.

Now, there are four cases:

a) Alien right, you pick B
b) Alien right, you pick both
c) Alien wrong, you pick B
d) Alien wrong, you pick B

a) If the alien is right, and you pick B, you have a reward of 1 million. The value of this case is (1-P/2)*(10^6).
b) If the alien is right, and you pick both, then the value of this case is (1-P/2)*(10^3)
c) If the alien is wrong, and you pick B, then you get nothing. The value of this case is (P/2)*0 = 0
d) If the alien is wrong, and you pick both, then you get the jackpot, valued at (P/2)*1001000

The condition of balance is: Val(a) + Val(c) = Val(b) + Val(d)

which is:

(1-P/2)*(10^6) + 0 = (1-P/2)*(10^3) + (P/2)*1001000

Which gives P = 0.999.

That is, both choices are equal only when the probability that the alien will be wrong 0.999 times every times he makes a choice - or, in layman's terms, that he is wrong every 999 out of 1000 times.

Now again, there are two choices. Either he knows, or he is guessing.

The probability that he is guessing is, or has made a hundred correct choices purely by guess work, is 2^(-100).

As this is clearly less than the required value of 0.999,

we can safely conclude that the case in which we take only the box B is the correct one to choose in this scenario. It's not guaranteed, of course, but it's valued far more highly. Much more than trillions of times more highly, in fact.


Was that rough proof of correctness enough of a justification for me saying that we should pick choice B?

I doubt it. Because according to the two-boxers, there will be still be money in box A that you have passed up.

And do I win this thread?

No. You win this thread once you convince people to stop thinking that the answer is obvious and you're wrong. (Going "but it's obvious and they're wrong, because of XXX!" will not help, as everyone and their sister has done that.)

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?

Depends on the mindset of my friend and the contents of the boxes.