Newcomb's Paradox

[Bodhi]

A reliable predictor has placed $1,000 in Box A. The same reliable predictor has placed $100,000 in Box B if and only if he predicted that you will choose to open only Box B and leave Box A closed; what's more, the reliable predictor knew that you would be told this information.

Should you open Boxes A and B, knowing that you will earn at least $1,000 and maybe even $101,000, because the predictor has done what he's done and your actions can't affect the past?

Or should you open only Box B in order to maximize your EV, because if you open both boxes the predictor will have predicted that and not put $100,000 in Box B.

[gaming_mouse]

I picked just B. I mean, you said that he's reliable. So if I was going to open both, he would have known that.

gm

[Bodhi]

This problem usually causes ferocious arguments among my friends, so we'll see if everyone else thinks it's so clear cut. [img]/images/graemlins/wink.gif[/img]

[gaming_mouse]

I can see that. The thing is, for me, let's say you do open both boxes, and there is money in both. That means that the assumption "reliable predictor" no longer holds. But specifically told me that he is a reliable predictor, so that's impossible.

The root of the paradox, then, is in the idea of a "reliable predictor." If you assume the existence of reliable predictors, then you have to throw our typical rational assumptions about future events being unable to affect past events. That is, the existence of reliable predictors is logically inconsistent with the idea that the future events cannot affect past events. But I have no problem throwing out that belief, because you never state in the problem that future events are not allowed to affect past events, whereas you do state that a reliable predictor exists.

gm

[MortalWombatDotCom]

assuming "reliable" is used here to mean "100% accurate", i agree. in this case, the condition of the problem wherein the reliable predictor "knew you would be told that" has no bearing on the outcome.

if "reliable" might mean something else, like having a certain large probability p of predicting how you will behave given an accurate model of the set of information you will have at the time you make your decision, then the answer is, it depends on the actual value of p, and also, the "knew you would be told that" clause becomes important again.

so, before i vote, please define "reliable predictor" [img]/images/graemlins/grin.gif[/img]

as an aside, i fail to see a paradox in either case.

[Bodhi]

the reliable predictor predicts correctly greater than 99% of the time.

[mannika]

No one in their right mind would open just Box B. The reliable predictor has already made his choice about what is in each box. As long as the boxes cannot contain negative money, why would you only be opening one box? It is completely ridiculous. However, if this predictor is that great, he knows that you are going to do this, because any rational person would, and therefore would only put nothing in Box B.

So, bottom line, predictor will place $1000 in box A, and $0 in box B, and you should choose both in order to get anything at all.

EDIT: If he/she is indeed a reliable predictor, I think this is a Nash equilibrium.

[gaming_mouse]

Nonesense [img]/images/graemlins/grin.gif[/img]

[mannika]

[ QUOTE ]
Nonesense [img]/images/graemlins/grin.gif[/img]

[/ QUOTE ]

Ah come on, I was expecting a better flame than that. Can I get anyone to agree/disagree with me? I want to feel smart/challenged.

[Cerril]

Well basically if this person is a reliable predictor, then it seems more likely that what we understand as the normal laws of causality don't apply. Knowing ahead of time that if we choose box B alone we're greater than 99% to get 100k, less than 1% to get 0; and if we open both we're greater than 99% to get 1k and less than 1% to get 101k, then the EV of box B alone is greater than $99k while the EV of both boxes is less than $2k, there's no real way to justify opening both boxes unless you have information that the predictor doesn't.

Of course if he's 99% likely to be correct it's far more likely that he has information that I don't, and so if he can somehow predict my actions I might as well choose the action with the best outcome (that is, if I pick A&B AND he is right >99% of the time, is is >99% likely that he had information leading him to believe that I would pick A&B. Ditto with just B).

It seems paradoxical, but only because such things cannot be done in the real world. For the sake of this experiment though, the only laws are those of the assumptions, and it's by those we're bound.