Newcomb's Paradox

Probability Level 3

An alien named Omega who can perfectly predict your actions gives you two boxes, A and B. If Omega predicts you will open just A, it will put $1,000,000 in A. But if the alien predicts you will open both boxes, it will put $0 in A. Additionally, Omega will always put $1000 in box B.

You get to keep whatever money is in the box(es) you open. What do you do?

Open both boxes Open just box

A

Impossible to determine

2 solutions

Siva Budaraju
May 12, 2017

This is a famous paradox. There are two ways of thinking about this:

Just choose A. If you choose both Omega will predict it and put $0 in box A, so you will get $1000. But, if you just choose A,Omega will predict it and put $1000000 in box A. So, choosing just A has a higher payoff.
Choose both boxes. When the money is put inside the box, there is a set amount of money inside box A and B. Let's say that the value in A is $x$ . The value in B is $1000. Then, if you choose box A, you get $x$ dollars. If you choose both, you get $x+1000$ dollars. So, it can easily be seen that choosing both provides a $1000 higher payoff.

Both these ways of thinking are perfectly logical, so it is impossible to determine which one we should choose. The answer is impossible to determine .

Zandra Vinegar Staff
Mar 16, 2016

View the newcomb's paradox to understand why the answer is impossible to determine.

You posed the question wrong, you told me the alien could predict my action , knowing that I would select A. And the alien can perfectly predict my action.

Gary Cofer - 5 years, 3 months ago

I did exactly that. IF the alien tells me the rules, OBVIOUSLY I would just open A. Zandra Vinegar made a boo boo on the question.

Eugenio Rios - 5 years, 3 months ago

I agree, The alien must know our action before the box is presented to always be correct. To place the money in the box it must have already made a prediction. Being that his prediction is correct and the person choosing is aware of the stipulations the outcome is fixed.

The question does however ask "What do you do?" so theoretically any answer would be correct so long as you do what you stated in that situation.

Bradley Totaro - 5 years, 3 months ago

Yes. Assuming the goal is to get the highest possible amount of money, the correct answer is "Open just box A," in this formulation of the problem.

Igor Sucupira - 5 years, 3 months ago

Still don't understand. Given:

1) I KNOW the alien can predict my actions 2) If he knows I will choose A he will put 1,000,000 in Box A

Why would I not choose A? If I open both boxes, I know the alien has predicted this and thus will only get 1,000, Likewise if I choose only B I only get 1,000 as well. Why would I not choose A, as long as I know that I will get a guaranteed 1,000,000.

Unless this question is worded incorrectly.

As long as I know this information beforehand, that is. Otherwise If I DON'T know he can perfectly predict beforehand, or can't perfectly predict at all, then yes, I could possibly choose A, B or both (more likely both to be safe).

Even if he PUT the boxes down first, THEN i learned he could perfectly predict my actions, then I should still choose A. If he can perfectly predict my actions, then he should have predicted whatever I was going to do, otherwise it will be false.

Ex)

If I choose A alone but there's no money in it, then Omega CANNOT perfectly predict my actions. If I choose both, then there should be no money in A, and 1000 in B. If I choose B there will always be 1000 in B anyway.

If the question is to maximize my wealth and I ONLY know there MAY be 1,000,000 in A, and 1,000 in B then I should logically choose both.

I guess I just don't understand the paradox completely. If Omega can predict my actions perfectly, then no matter WHAT i choose, I create my OWN outcome. Since predicting perfectly could be akin to a situation like this:

Omega drops the boxes. If you choose A he will place 1,000,000 in A. If you choose B he will place 1,000 in B. If you choose both he will only put 1,000 in B and 0 in A. Prediction has nothing to do with it at all in this case, yet it turns out exactly the same. Otherwise we've proven him false in the fact that he can perfectly predict an outcome.

Tyler Beachnau - 5 years, 3 months ago

There is a contradiction, not really a paradox, (In the problem) in which the alien cannot make sure to predict our actions correctly. Let's suppose we open just A. Since we open just A we'll find some money on it. Then if we find the money we then open B too. We would force the alien predictions to be incorrect.

Then let's suppose we don't find any money. In this case we can also force the alien predictions to be wrong deciding not to open B.

To avoid that contradiction, when we decide to force the alien predictions to be wrong, some money would have to magically appear or disappear in the box A, even if we have already opened it. And in that case, it's better to choose A.

But it's a fact that the propossed solution to the problem as stated here, is wrong.

David Molano - 5 years, 3 months ago

You cannot force the alien's prediction to be incorrect. That violations the condition. Therefore, your decisions are restricted by the alien's prediction. That's the only way I can see to interpret this.

James Wilson - 3 years, 7 months ago

Newcomb's Paradox

2 solutions

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