Newcomb's Paradox: Decide What to Do?

[moving finger]

well known paradox, goes something like this :

Marvo the magician has come to town. Marvo claims that he can see into the future. You go along to his show and volunteer to help with one of his acts. Marvo offers you two steel boxes, one is closed, the other is open. You and everyone else can see that the open box contains $1,000. Marvo tells you that you may choose EITHER to take only the closed box, OR to take both the closed and the open box (no other options are possible). However, Marvo also tells you that he KNOWS IN ADVANCE what you will choose, and if you take only the closed box you will find that it contains $1 million, whereas if you take both boxes you will find the closed box is empty. You are allowed to keep the money (Marvo has no need of money because his ability to see into the future has already made him a billionaire).

Marvo assures you that he has performed this experiment 100 times in the past, and every time he has been proved right - when the subject has chosen only the closed box it contained $1 million, whereas whenever the subject chose both boxes the closed box was empty. You have independently checked Marvo's claims prior to coming to the show, and indeed he is right - he was indeed able to predict the subjects' choices correctly 100% of the time.

(Please take this as a thought experiment, please let us NOT get into arguments about "how is it possible for Marvo to predict the future? - this is impossible" - please accept the premise in the spirit in which it is intended)

Now it is time for you to choose... what do you do? Take just the closed box, or take both boxes?

Before you decide, think on this :

Logic dictates that, if you really believe Marvo can predict with 100% accuracy, then you should take only the closed box, since this is the only way that you will end up with $1 million.

However, at the moment of your choice, the closed box is necessarily either empty or it contains $1 million. Logic dictates that nothing that you do at that moment can change that. The contents of the closed box are fixed, therefore surely your subsequent decision whether or not to take the open box as well cannot affect the contents of the closed box. Whatever the closed box conatins, logic dictates that you will be $1,000 better off by also taking the open box... hence surely you should take the open box too?

The worst case is that you choose only the closed box and you find it is empty - in which case you end up with nothing. The best case is that you choose both boxes and find that the closed one contains $1 million (but even if it is empty you will still walk away with $1,000 by taking both boxes).

This is the paradox. One path of logic suggests that you should take only the closed box, yet another path of logic suggests that you will always be better of by taking both boxes. Which one is correct?

What would you do?

I have inserted a questionnaire to the thread, where you are asked to choose from one of the following 4 options :

1 - I believe that Marvo can indeed predict the future and I will take only the closed box
2 - I believe that Marvo can indeed predict the future but nevertheless I will take both boxes
3 - I do not believe that Marvo can predict the future and I will take only the closed box
4 - I do not believe that Marvo can predict the future and I will take both boxes

Cheers

MF

 

[Tide]

let us NOT get into arguments about "how is it possible for Marvo to predict the future?

If Marvo has knowledge of future events, i.e. the outcome, then you cannot talk about probabilities and expected values.

 

[moving finger]

If Marvo has knowledge of future events, i.e. the outcome, then you cannot talk about probabilities and expected values.

Hi Tide

It all hinges on that "if" word, doesn't it?

What would Tide do in this situation?

Would you believe that Marvo possessed the power he claims? IF you do, then logically you should take only the closed box. But in doing this you are implicitly acknowledging that Tide has no free will - because Marvo must have been able to know infallibly your decision in advance. IF you acknowledge that Marvo can infallibly predict your decisions, where is your free will?

On the other hand, IF you genuinely believe that you possesses free will then you must also believe that Marvo cannot predict your decisions infallibly, and despite all the evidence to the contrary (that he has never failed in 100 previous attempts) you must harbour some doubt that he can predict this particular decision correctly. Your logic would then (logically) run like this : At the moment of your decision, either the closed box contains $1 million or it does not, nothing in your free will decision can change that, therefore what do you have to lose (in fact you have everything to gain) by taking the open box as well... The only reason you might have for NOT taking the open box as well is IF you believe Marvo can indeed predict your choice in advance, but in this case you are giving up your belief in free will...

It is not obvious that either solution is the correct one, it all depends on one's beliefs.

"If" is a very big word in some cases.

Are you prepared to say what Tide would do?

Cheers

MF

 

[Tide]

mf,

Marvo can claim whatever he wants. He is an actor, a showman and a billionaire from which I infer he has a fairly good grasp of human nature and will set up his act for maximum impact and self-gratification. I would simply be another person who would help him achieve that. I know precisely what I would do but if I reveal that here then it would not be a fair test of Marvo's abilities.

With all due respect, I am not completely confident that you or others here won't telegraph my intentions to Marvo were I state to them in a public forum. I can tell you, however, that I know precisely what Marvo will do - and I haven't been wrong yet! :)

 

[loseyourname]

I'm taking the closed box. Making this decision isn't going to cause me to have no free-will. I either do or I don't, prior to ever hearing of Marvo, and I'd rather be a millionaire than fret over the metaphysical status of my volition.

By the way, isn't this a dilemma? The only way it can be construed as a paradox is if you insist that we truly can make a free decision that proves we are not free. I don't see how this situation can possibly warrant such a claim, however.

 

[moving finger]

mf,

Marvo can claim whatever he wants. He is an actor, a showman and a billionaire from which I infer he has a fairly good grasp of human nature and will set up his act for maximum impact and self-gratification. I would simply be another person who would help him achieve that. I know precisely what I would do but if I reveal that here then it would not be a fair test of Marvo's abilities.

With all due respect, I am not completely confident that you or others here won't telegraph my intentions to Marvo were I state to them in a public forum. I can tell you, however, that I know precisely what Marvo will do - and I haven't been wrong yet! :)

party pooper!

 

[moving finger]

Hi loseyourname

I'm taking the closed box. Making this decision isn't going to cause me to have no free-will. I either do or I don't, prior to ever hearing of Marvo, and I'd rather be a millionaire than fret over the metaphysical status of my volition.

If you are entirely confident that you will indeed end up with $1 million this implies you believe Marvo is genuine, that he can perfectly predict your choices, hence by definition you have no free will (If an agent always acts in a predictable fashion then it is in effect behaving 100% deterministically, hence does not have the ability to choose "freely").

By the way, isn't this a dilemma? The only way it can be construed as a paradox is if you insist that we truly can make a free decision that proves we are not free. I don't see how this situation can possibly warrant such a claim, however.

You could be right, but in the literature it is widely quoted as Newcomb's Paradox (check it out).

MF

 

[Nomy-the wanderer]

I chose the 3rd option, 1st of all i think that Marvo cannot predict the future, at least not with a 100% accuracy because anyhow, some of ur reactions can be predictable from ur boday language, eye contact whatever...
Or he might be lucky enough...

I'll choose the closed box only, even if i won the 1000$, having hopes that i'll win an extra million and then not finding it, will be a disapointment anyway, so who cares about the 1000$s

 

[moving finger]

I chose the 3rd option, 1st of all i think that Marvo cannot predict the future, at least not with a 100% accuracy because anyhow, some of ur reactions can be predictable from ur boday language, eye contact whatever...
Or he might be lucky enough...

I'll choose the closed box only, even if i won the 1000$, having hopes that i'll win an extra million and then not finding it, will be a disapointment anyway, so who cares about the 1000$s

Now that is interesting. It seems to me that you tend to believe that Marvo could be genuine, but you are not entirely convinced. But your belief is strong enough that you are not prepared to "lose the chance of maybe winning $1 million" by taking the open box containing the $1,000. May not be a totally logical approach, but OK.

MF

 

[Nomy-the wanderer]

Not that's not what i said, what i said is that choosing the open box with the 1000$ will be meaningless because this is a very small sum comparing it to a million $, so anyway if i didn't find the million i'll be disapointed, even if i had the other box containing the 1000$

I'm not aiming for just money, I'm aiming for a huge sum, for a million$, so taking the open box or not taking it, won't make any difference for me, if I've a 1000$ to spend ion one day, 1$ won't be a significant sum, and thta's my approach to the problem..

 

[moving finger]

Not that's not what i said, what i said is that choosing the open box with the 1000$ will be meaningless because this is a very small sum comparing it to a million $, so anyway if i didn't find the million i'll be disapointed, even if i had the other box containing the 1000$

But logically $1,000 is still better than nothing, and even if I am disappointed I would rather have $1,000 than nothing at all (and if you do not believe that Marvo can genuinely predict the future then there is a chance the closed box will be empty). The only logical reason for "not" choosing the open box with $1,000 is if you suspect that Marvo may be genuine. (the logic runs like this : the contents of the closed box are already fixed at the time of your choice, how can your free will choice to take or not take the open box affect the contents of the closed box? Logic dictates that you are always better off taking the open box...assuming Marvo is not genuine)

I'm not aiming for just money, I'm aiming for a huge sum, for a million$, so taking the open box or not taking it, won't make any difference for me, if I've a 1000$ to spend ion one day, 1$ won't be a significant sum, and thta's my approach to the problem..

As I said, an interesting approach. You are taking a gamble based on probabilities - you are not prepared to gamble on taking the open box as well (even though this will guarantee you at least $1,000) because the payoff of $1,000 is outweighed by your perception of the "risk" that would cause of you not finding $1 million in the closed box.

(You may say this is not the way that you thought about the problem, but I suggest this is the only logical interpretation of your actions, whether the logic was transparent to your consciousness or not).

Look at it this way, if we changed the odds a little, at what point would your decision change? If the open box contained $5,000, would you still choose not to take it? What about $10,000? or $50,000? or $100,000? At some point I suggest you would change your decision and take the open box as well - which shows that the value of receiving the contents of the open box are somehow being "weighed up" in your mind against the perceived cost (in terms of risk to the total outcome) of taking the open box.

MF

 

[Nomy-the wanderer]

I think i misunderstood ur 1st interpretation...Sorry.

It's true if the sum in the open box is a more significant ratio os the amount i may have in the closed box, i'd have chosen the open box also..

 

[loseyourname]

If you are entirely confident that you will indeed end up with $1 million this implies you believe Marvo is genuine, that he can perfectly predict your choices, hence by definition you have no free will (If an agent always acts in a predictable fashion then it is in effect behaving 100% deterministically, hence does not have the ability to choose "freely").

Yeah, what I'm saying is that is isn't because of my belief in Marvo that I have no free will. If I have no free will, then I never had any to begin with, well before I ever heard of Marvo. What I think this is trying to get at is that if one accepts this, it is contradictory to then go on making choices, but I think that is an oversimplification of the free will issue. One can believe that choices are completely illusory, and perhaps they are, but go on making them anyway. It might be more accurate, if we are going to get technical, to say that I do not choose to take the closed box only; rather, I am compelled to take the closed box only. That way we can rid ourselves of the apparent paradox created by the use of the word "choice."

Note: I'm not saying that I actually believe humans possesses no characteristics that might be called free will, or that a Marvo in our world would be genuine. For the sake of this thought experiment, however, it sounds like Marvo is for real, and the future really is deterministically set.

 

[moving finger]

Yeah, what I'm saying is that is isn't because of my belief in Marvo that I have no free will. If I have no free will, then I never had any to begin with, well before I ever heard of Marvo.

I never suggested that it was your belief in Marvo which suddenly robbed you of your free will. I agree with you, either you have free will or you do not (this does not suddenly change when Marvo appears on the scene).

What I think this is trying to get at is that if one accepts this, it is contradictory to then go on making choices, but I think that is an oversimplification of the free will issue. One can believe that choices are completely illusory, and perhaps they are, but go on making them anyway.

I don't think "making choices" is synonymous with free will. A simple machine can make choices, but that does not mean the machine has free will.

It might be more accurate, if we are going to get technical, to say that I do not choose to take the closed box only; rather, I am compelled to take the closed box only. That way we can rid ourselves of the apparent paradox created by the use of the word "choice."

You do not feel that you are compelled to take the closed box only. You choose. And maybe you convince yourself that this choice is of your own free will. But my point is that IF someone else can infallibly predict what your choices will be then this implies your choices are determined, and hence any free will that you feel is illusory.

Note: I'm not saying that I actually believe humans possesses no characteristics that might be called free will, or that a Marvo in our world would be genuine. For the sake of this thought experiment, however, it sounds like Marvo is for real, and the future really is deterministically set.

I accept that, thank you.

Incidentally - my personal "choice" in this thought experiment is " I do not believe Marvo can predict with 100% accuracy and I will take both boxes”. Why do I reason thus? Because though I believe in determinism, I also do not believe that anyone can have the ability to perfectly predict the future (quantum effects and chaos would limit the precision to which future events could be predicted). Therefore I must look at the 100% success rate of Marvo as containing an element of “luck” – there is a possibility that Marvo could be wrong in my case. If there is any possibility that Marvo could be wrong then I prefer to take the safe route of taking both boxes – that way I will walk away with at least $1,000 (whereas if I take only the closed box I might get nothing). I cannot say that my choice is the “right” choice – that is a personal thing.

MF

 

[loseyourname]

I think you're reasoning incorrectly, though. This experiment takes place in a hypothetical universe that may or may not be completely deterministic, without any quantum effects. All we know of this world is what we know from the scenario and so all we know is that Marvo has always been right. It seems more likely from this that Marvo's universe is free from quantum effects than that he is simply getting lucky an awful lot.

But hey, neither interpretation is authoritative. The fact is that we don't know enough about Marvo's universe to be certain. You have your best guess, and I have mine.

 

[moving finger]

I think you're reasoning incorrectly, though. This experiment takes place in a hypothetical universe that may or may not be completely deterministic, without any quantum effects. All we know of this world is what we know from the scenario and so all we know is that Marvo has always been right. It seems more likely from this that Marvo's universe is free from quantum effects than that he is simply getting lucky an awful lot.

But hey, neither interpretation is authoritative. The fact is that we don't know enough about Marvo's universe to be certain. You have your best guess, and I have mine.

Hmmmm. I was not assuming that the universe of this scenario was completely hypothetical, I was assuming that the scenario took place in our universe, subject to our physical laws. I agree with you that if we change the ground rules and remove quantum effects and chaos from consideration then my choice would likely be different (I would probably judge Marvo to be genuine and take only the closed box).

MF

 

[orgmark]

If marvo can't predict the future,
closed box is empty, so picking both will always
result in empty close box / 1,000 open box.
If marvo can predict,
picking close box will always result n
1,000,000 closed box. As marvo can predict,
picking both will always result in
empty closed box / 1,000 open box.
The only way to get the 1,000,000
is to agree marvo can predict and pick
the closed box only.

 

[moving finger]

If marvo can't predict the future,
closed box is empty, so picking both will always
result in empty close box / 1,000 open box.

Not necessarily. If Marvo cannot predict accurately, then the contents of the closed box are not simply related to my choice (ie closed box may or may not contain $1M, irrespective of my choice).

If marvo can predict,
picking close box will always result n
1,000,000 closed box.

Yes, as long as you take ONLY the closed box.

As marvo can predict,
picking both will always result in
empty closed box / 1,000 open box.

Agreed.

The only way to get the 1,000,000
is to agree marvo can predict and pick
the closed box only.

Agreed, but this choice is based on your "belief" that Marvo can predict - you may be wrong.

MF