Newcomb's paradox

[t_w]

Two closed boxes, B1 and B2 are on a table. B one contains £1,000, B2 contains either nothing or £1,000,000.
You have an irrevocable choice between the two:
1. You take what is in both boxes
2. You take what is in only B2.

At some time before the test a superior being has made a prediction about what you will decide. The being's decision are almost certainly correct.
If he predicts you take both boxes, he leaves B2 empty. If he predicts you take only B2, he puts £1,000,000 in it. (If he expects you to randomize the choice, he has left B2 empty).

What should you do?
Clearly it is not to your advantage to flip a coin.
The argument for taking only B2 is as follows: You believe the being is an excellent predicter. If you take both boxes, he will have almost certainly anticipated your decision and left B2 empty. Counterwise, if you take only B2 he will have predicted this and you will almost certainly receive the £1,000,000.
However, the being has made the decision at least a week ago. Either he left the million in B2, or he did not. If the money is already there, it will stay there whatever you choose(it is assumed that no backward causality is in effect). So why not take both boxes and take everything that is there? If B2 is filled, you get £1,001,000. If it is empty you get at least £1,000.

Suppose the experiment has been done many times before. In every case the Being predicted correctly. Knowing this, surely it is wise to take only B2?

Alas, there is an equally convincing argument for taking both. Assuming B1 is transparent and you can see the £1,000. You cannot see B2, but a friend can see into it and knows whether or not it contains the £1,000,000. It becomes evident that whatever is in B2 your friend will want you to take both.

I remind you that the being does not have perfect predictive power. Let's say his chance of being correct is .9.
Taking both boxes is therefore (.1 x £1,001,000) + (.9 x £1,000) = £101,000
Taking only B2 is: (.9 x £1,000,000) + (.1 x £0) = £900,000
By this method, the best decision is only B2.

Is may seem that back-ward causality is acting, but this is nonsense. Once the million is there, a week later your choice has no impact on what is in B2. Therefore, why not take both?

 

[David Gould]

It is not backwards causality at all. It is factoring in someone else's behaviour - in other words, you are predicting what they will predict and working it out from there.

It is exactly the same as why we get up to go to work - it is because we might be fired. This is not backwards causality, either - it is us factoring the information we have available to us now into our decision making.


Further, what relevance does this have to free will?

 

[t_w]

It is not backwards causality at all. It is factoring in someone else's behaviour - in other words, you are predicting what they will predict and working it out from there.

I stated backwards causality is not acting here in the OP. I don't understand why you even bring up backward causality.

Further, what relevance does this have to free will?

We have a situation where we have two choices. Both are equally logical and illogical(if you don't think this at first, as most people do, look at the paradox a little longer). So, something has to give. In this case, it is the predictive power of the entity that does the predicting. Such an accurate prediction(not a completely accurate, but fairly accurate prediction) cannot be possible. So, we come to the revelation that a persons choice, even though it is completely determined, cannot be predicted. This would imply free will.

 

[Casstranquility]

Suppose the experiment has been done many times before. In every case the Being predicted correctly. Knowing this, surely it is wise to take only B2?

I think it is wise to take only B2.

Is may seem that back-ward causality is acting, but this is nonsense. Once the million is there, a week later your choice has no impact on what is in B2. Therefore, why not take both?

I wouldn't want to take both because there's more of a chance that the being predicts correctly then incorrectly. I guess I'd just want to gamble the certain chance for 1,000 for the almost certain chance for 1,000,000.

 

[FSTDT]

Two closed boxes, B1 and B2 are on a table. B one contains £1,000, B2 contains either nothing or £1,000,000.
You have an irrevocable choice between the two:
1. You take what is in both boxes
2. You take what is in only B2.

At some time before the test a superior being has made a prediction about what you will decide. The being's decision are almost certainly correct.
If he predicts you take both boxes, he leaves B2 empty. If he predicts you take only B1, he puts £1,000,000 in it.

The part in bold isn't one of the options. You can either take B1 and B2, or just B2, but you cannot take only B1. Is this just a typo?

 

[FSTDT]

Generally, I think the solution to the paradox works like this:

We have possible options:

1) Choose both boxes. If the being made a correct prediction, we'll win US$1,000 + US$0.

2) Choose both boxes. If the being made an incorrect prediction, we'll win US$1,000 + US$1,000,000.

3) Choose the second box. If the being made a correct prediction, we'll win US$1,000,000.

4) Choose the second box. If the being made an incorrect prediction, we'll win US$0.

The odds of the being making an incorrect prediction are impossibly low, leaving options 1 and 3 are the only rational expectations, so we logically choose the second box and walk away with our US$1,000,000.

 

[kopilo]

Given if this "If he predicts you take only B1" is a typo and should be B2.

If you take both you have a 1/9 chance of attaing 1,001,000
And a 8/9 chance of only ending up 1,000

If you take box2, you have a chance of 8/9 of attaining 1,000,000
And a 1/9 chance of ending up $0

You have a much higher chance of attaining more money when picking box2 only but you increase the risk of ending up with no money by doing so.

If you pick to open both you have a low chance of attaining more then 1,000,000 but you know you will attain 1,000.

Hence:
If you like low risk with high gain you may prefer opening box2 only. If you like a high risk + safty net then you may prefer opening both.

 

[t_w]

The part in bold isn't one of the options. You can either take B1 and B2, or just B2, but you cannot take only B1. Is this just a typo?

Oops, sorry about that - it is a typo.

 

[t_w]

Cheers for the responses.
Most of the people in this thread so far have stated that it is logical to choose only box B2, as if you do so it is very likely there will be the million in it.
However, there is an equally strong argument for taking both boxes. Imagine that the being has made his predictions a week ago, and that the money is either in or not in the box. So in box B2, there is either £0 or £1,000,000. Now, imagine that another person(who wants us to be rich) knows exactly what is in B2. It soons become obvious that he wants us to pick both boxes no matter what is in them!
If there is a million there, he wants us to take both boxes. We will win £1,001,000 which is better than only B2.
If there isn't a million there he wants us to take both. We will win £1000, which is better than only B2.
Bear in mind the choosing is occuring a week later. The money is in the boxes and nothing will change that(there is no backward causality). It doesn't matter what we choose - the fact remains that the money is there and our rationalizing after the prediction is irrelevant.
There is no soluation to this paradox in terms of a strategy for picking a box. The logic you have presented for taking just B2 is absolutely correct; but then so is my logic for taking both. Something has to give; that something is the predictability of our actions. The paradox suggests our actions are not predictable, and therefore are a result of free will.

 

[Casstranquility]

You do make a good case for taking both cases! However, did the being know about this other person before he made the prediction? If he knew about the other person, and knew the logic behind the person wanting them to take both boxes, he would most certainly not put the money in B2. Then his prediciton would always be right, because the person will always pick both boxes. I'd much rather not have this person in the game. I'd rather just take B2. If the person is in the game, I'd take both.

 

[t_w]

I'd much rather not have this person in the game. I'd rather just take B2. If the person is in the game, I'd take both.

Sorry, I didn't make myself clear when I introduced the 'friend' who can see both boxes. He has no contact with the person choosing the boxes, and thus has no real bearing on the paradox. The predicter doesn't need to take him into account as he won't affect in any way which boxes are chosen. I simply introduced him to help explain a certain argument for taking both boxes(whatever is in the boxes, you get more if you take both).

 

[Osiris]

So in box B2, there is either £0 or £1,000,000. Now, imagine that another person(who wants us to be rich) knows exactly what is in B2. It soons become obvious that he wants us to pick both boxes no matter what is in them! If there is a million there, he wants us to take both boxes. We will win £1,001,000 which is better than only B2.
If there isn't a million there he wants us to take both. We will win £1000, which is better than only B2.

Bear in mind the choosing is occuring a week later. The money is in the boxes and nothing will change that(there is no backward causality). It doesn't matter what we choose - the fact remains that the money is there and our rationalizing after the prediction is irrelevant.

Actually, the rationalizing after the prediction is very relevant. How do you suppose the supreme being would make its prediction if not by the predicting the way you will rationalize after his prediction?

If Box 2 is empty it is because the supreme being would know(have predicted) what your intentions would amount to the day of decision through that 1 week.

If the prediction is irrelevant to the subject, how is this a prediction for what one will decide as stated in the OP?

"At some time before the test a superior being has made a prediction about what you will decide."

There is no soluation to this paradox in terms of a strategy for picking a box. The logic you have presented for taking just B2 is absolutely correct; but then so is my logic for taking both. Something has to give; that something is the predictability of our actions. The paradox suggests our actions are not predictable, and therefore are a result of free will.

How does the paradox suggest that our actions are not predictable? It made an assumption that the predictions are not certain...

 

[t_w]

Actually, the rationalizing after the prediction is very relevant.

Perhaps you misunderstood me. Anything we do after the prediction will not change what is in the boxes. As soon as the being makes the prediction, the boxes are sealed and either £1,001,000 or £1,000 is in them. We can rationalize about anything and this will not change what is in the box. My point was that the act of rationalizing does not change the amount in the box. If we rationalize in a certain way the amount doesn't magically change to fit the prediction.

How do you suppose the supreme being would make its prediction if not by the predicting the way you will rationalize after his prediction?

My point was that any rationalizing wouldn't change the value in the boxes. I apologise if I expressed this poorly.

If the prediction is irrelevant to the subject, how is this a prediction for what one will decide as stated in the OP?

Precisely my point. The prediction should logically be irrelevant and yet should logically be relevant(so your premise above - if the prediction is irrelevant....- is invalid). Pointing out a contradiction only strengthens the situation's claim to be paradoxical!

How does the paradox suggest that our actions are not predictable? It made an assumption that the predictions are not certain...

Because if we have a paradox something is wrong somewhere. In this case it must be the predictive power of the being. It suggests that an accurate prediction is impossible. Something must be responsible for the inability of the supreme being to predict. I propose that this something is free will.

 

[kopilo]

Perhaps you misunderstood me. Anything we do after the prediction will not change what is in the boxes. As soon as the being makes the prediction, the boxes are sealed and either £1,001,000 or £1,000 is in them. We can rationalize about anything and this will not change what is in the box. My point was that the act of rationalizing does not change the amount in the box. If we rationalize in a certain way the amount doesn't magically change to fit the prediction.

No, but the prediction may take your rationalisations (even change of) into consideration. As in, predicting what will occur in the future.

 

[Osiris]

Perhaps you misunderstood me.

No, I understood you perfectly...

Anything we do after the prediction will not change what is in the boxes.

I understand, nowhere in my post did I imply that...

As soon as the being makes the prediction, the boxes are sealed and either £1,001,000 or £1,000 is in them.

from: www.dictionary.com
predic: To state, tell about, or make known in advance, especially on the basis of special knowledge.

what you are suggesting is a mere guess... not a prediction.

We can rationalize about anything and this will not change what is in the box.

I agree, it won't...

My point was that the act of rationalizing does not change the amount in the box. If we rationalize in a certain way the amount doesn't magically change to fit the prediction.

The supreme being is not doing a prediction of what you are thinking at the time he is closing the 2nd box. The being is doing a prediction of what your intents will be a week from now. To make such prediction, this being would certainly have to know what you will rationalize through-out the week...

This being will have this information:

He predicts that if you know that there are $1,000,000 in Box 2, then your intentions through out the week will be :

This being will put $0 in Box 2... so, in reality if you know the content in Box 2, what you will know is that it is empty.

My point was that any rationalizing wouldn't change the value in the boxes. I apologise if I expressed this poorly.

no, you explained it correctly...

rationalizing won't change the value... but the supreme being already took the rationalization you will undergo into consideration which will ultimately give the answer of what box you will pick...

Precisely my point. The prediction should logically be irrelevant and yet should logically be relevant(so your premise above - if the prediction is irrelevant....- is invalid). Pointing out a contradiction only strengthens the situation's claim to be paradoxical!

I don't know what you meant here...

but I did a search on google for newcomb's paradox, and the being doing the prediction is and has been 100% certain in all of his predictions.

Because if we have a paradox something is wrong somewhere. In this case it must be the predictive power of the being.

If there is such a being... I don't see what there be anything wrong with that...

It suggests that an accurate prediction is impossible. Something must be responsible for the inability of the supreme being to predict. I propose that this something is free will.

hmmm... no.

an accurate prediction of a being that could predict with 100% certainty would mean that an accurate prediction is possible.

 

[kopilo]

It suggests that an accurate prediction is impossible. Something must be responsible for the inability of the supreme being to predict. I propose that this something is free will.

hmmm... no.

an accurate prediction of a being that could predict with 100% certainty would mean that an accurate prediction is possible.

Even if prediction wasn't accurate, it would make more sense to take into account the beings skill rather then something which varies from person to person.

 

[t_w]

First of all, I don't know where you read that the being's predictive power is 100%. I can say with 100% certainty that this in the version I read about this paradox, from Martin Gardner no less, the being's predictive power was not 100%(in some instances). However, often the predictive power is postulated as 100% to make certain points or draw certain conclusions from the pardox. I actually think a predictive power of 100% makes my point better - because such power is impossible(hence the paradox).

The supreme being is not doing a prediction of what you are thinking at the time he is closing the 2nd box.

Yes, he is. He will use this information to form a deterministic model which will suggest how you will rationalize. He uses information in your brain at the time of closing the boxes.

The being is doing a prediction of what your intents will be a week from now. To make such prediction, this being would certainly have to know what you will rationalize through-out the week...

He doesn't know what you rationalize throughout the week, he guesses based on a deterministic model(of the brain). Remember, he is't always right.

rationalizing won't change the value... but the supreme being already took the rationalization you will undergo into consideration which will ultimately give the answer of what box you will pick...

True.

but I did a search on google for newcomb's paradox, and the being doing the prediction is and has been 100% certain in all of his predictions.

See above. In the version I read, he had never been wrong before
Never been wrong before != complete predictive power.

If there is such a being... I don't see what there be anything wrong with that...

The way I interpret this paradox is that nothing can be completely predicted in the future if a conscious rational being(man) is making a decision. This is an incredibly famous and fascinating paradox and literally hundreds of conclusions are drawn from it.

an accurate prediction of a being that could predict with 100% certainty would mean that an accurate prediction is possible.

Look, you've pointed out another contradiction. It both is possible and isn't. Contradictions really aren't a great way of attacking a logical paradox.

 

[kopilo]

Look, you've pointed out another contradiction. It both is possible and isn't. Contradictions really aren't a great way of attacking a logical paradox.

huh where, how?
Maybe I better restate what Osiris has stated (in another way).
A precise prediction of that beings precise prediciton means, a precise prediction is possible. (Well I think that is what Osiris is saying)

He doesn't know what you rationalize throughout the week, he guesses based on a deterministic model(of the brain). Remember, he is't always right.

I read the op and it doesn't state this, in fact it says "predicts" and has no mention of method.

 

[t_w]

A precise prediction of that beings precise prediciton means, a precise prediction is possible. (Well I think that is what Osiris is saying)

In the paradox we assume that the being has precise predictive power, and then see what happens after making that assumption. We imagine a being with nearly perfect/perfect predictive power. He doesn't necessarily exist.The rresult of this assumption is, without a doubt, a logical paradox. If an assumption causes a logical paradox then that assumption has something wrong with it.

I read the op and it doesn't state this, in fact it says "predicts" and has no mention of method.

It makes no difference if he uses a deterministic model or astrology or anything else that is remotely connected to prediction(I'm not arguing for astrology btw!) - the point is that he predicts. So we can say the being uses a deterministic model and this doesn't change anything. I only brought up the phrase deterministic model to offer an explaination for how he would work out what our rationalizing would be like.

 

[t_w]

Even if prediction wasn't accurate, it would make more sense to take into account the beings skill rather then something which varies from person to person.

No, it wouldn't at all. I haven't specified any characteristics of the being except that it can predict. Since nothing is specified the being could be anything and the paradox would still be present.