Newcomb's Paradox

[Anomalocaris]

I can defeat any amount of goodness in his ability to predict my decision by randomizing my decision,   So if he is really good at predicting my decisions, he would predict I would decide to make a random decision that he can not predict except by random chance.

According to the conundrum, the Predictor knows, without possibility of error, which choice you will make. Randomness is not a factor.

When answering a paradox, the respondents are not permitted to add provisos of their own.

Boru

If my choice is not to make the choice myself but let a flip of the coin decide?

[GrandizerII]

https://en.wikipedia.org/wiki/Newcomb%27s_paradox

A lot of you would know about this already. The interesting thing about this puzzle is that even though it seems like there is a very clear correct answer here, there are a lot of people who insist that's not correct ... and I'm taking philosophers, mathematicians, game theorists, and not just laypeople. So I guess that's really where the "paradox" lies.

Anyway, here's the problem to consider:

You have two boxes in front of you. Behind these two boxes is the Predictor, some super-advanced being who is (at the very least)
at predicting beforehand what you would do.

Box A is transparent and contains $1000.
Box B is opaque and either contains $0 or $1000000

You have two options here:

Either choose both Box A and Box B, or
Choose Box B only

The Predictor has already predicted what option you would go for:
If they predicted you would choose both boxes, then Box B will contain $0.
If they predicted you would choose Box B only, then Box B will contain $1000000

Which option do you go for?

I suspect most of us here would choose Box B only, but it would be interesting to hear the different perspectives on this problem.

How good?

Incredibly close to 100% accurate, if not 100% accurate.

From the Wiki link:

Causality issues arise when the predictor is posited as infallible and incapable of error; Nozick avoids this issue by positing that the predictor's predictions are "almost certainly" correct, thus sidestepping any issues of infallibility and causality. Nozick also stipulates that if the predictor predicts that the player will choose randomly, then box B will contain nothing.

[Angrboda]

I feel boxed in.

[Silver]

Just think outside the box.

[GrandizerII]

I misread the OP - choosing Box A only is not an option. In that case, choosing both boxes is a marginally better option, as you’re guaranteed at least $1000. Choosing Box B only gives you a 50% chance of walking away with bupkis.

Boru

I agree that, per the prediction the Predictor makes, two-boxing always yields the better outcome. However, how I see it is like this:

1. If I choose Box B only, there is an incredibly high chance of walking away with $1000000 since the Predictor would've most probably predicted I would do so.

2. If I two-box instead, there is an incredibly high chance of only getting $1000 since the Predictor would've most probably predicted I would do so, and therefore Box B would contain nothing.

Therefore, it seems like one-boxing is the way to go. Sure, two-boxing instead of one-boxing would net me $1001000 if the Predictor predicts wrongly that I would one-box, but it seems to me like there is an incredibly low chance of that happening.

---

The crazy thing about this just now is that while I'm feeling confident about my answer here (and so have posted this), I'm also now in two minds about this. I feel like I contradicted myself, soo let me think about this more to make sure I didn't.

[GrandizerII]

Let's consider the following:

Suppose you are familiar with puzzle and realize it's always better to two-box (since once you're in front of the two boxes, the prediction has already been made, and no matter what the prediction would be, you always net more by two-boxing).

One day, you actually end up in this scenario yourself. So since you're familiar with the puzzle, and you've already concluded that two-boxing is the way to go, you are most likely going to get $1000, which is better than nothing, of course. And if by luck, the Predictor ended up making a wrong prediction here, then you end up with the big gain of $1,001,000.

But this is about odds here as well, and not just about what nets the biggest gain. And you are more likely to get $1,000,000 by one-boxing than $1,001,000 by two-boxing.

Hence, I still go with one-boxing ... for now.

Though I'm seeing more and more what's tricky about this problem.

[BrianSoddingBoru4]

According to the conundrum, the Predictor knows, without possibility of error, which choice you will make. Randomness is not a factor.

When answering a paradox, the respondents are not permitted to add provisos of their own.

Boru

If my choice is not to make the choice myself but let a flip of the coin decide?

That still involves a choice - you have to decide which side of the coin represents which box. The Predictor will still pre-know the outcome.

Boru

[brewer]

I'm not choosing a box.

Have you considered that you might be a box?

[Nay_Sayer]

Ok, Who took all my boxes from my attic?!

[BrianSoddingBoru4]

Ok,  Who took all my boxes from my attic?!

Schroedinger. I suspect that you may or may not be missing some cats as well.

Boru