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View Full Version : Newcomb's Paradox

Bodhi
12-16-2004, 06:03 PM
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
12-16-2004, 06:13 PM
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
12-16-2004, 06:15 PM
This problem usually causes ferocious arguments among my friends, so we'll see if everyone else thinks it's so clear cut. /images/graemlins/wink.gif

gaming_mouse
12-16-2004, 06:31 PM
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
12-16-2004, 08:18 PM
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" /images/graemlins/grin.gif

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

Bodhi
12-16-2004, 08:51 PM
the reliable predictor predicts correctly greater than 99% of the time.

mannika
12-16-2004, 11:13 PM
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
12-16-2004, 11:19 PM
Nonesense /images/graemlins/grin.gif

mannika
12-17-2004, 04:08 AM
[ QUOTE ]
Nonesense /images/graemlins/grin.gif

[/ 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
12-17-2004, 04:34 AM
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&amp;B AND he is right &gt;99% of the time, is is &gt;99% likely that he had information leading him to believe that I would pick A&amp;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.

EliteNinja
12-17-2004, 05:26 AM
I choose only box B and get SOMEONE ELSE to open box A for me afterwards.

gaming_mouse
12-17-2004, 05:31 AM
[ QUOTE ]
I choose only box B and get SOMEONE ELSE to open box A for me afterwards.

[/ QUOTE ]

Dude, if you try to do that, the predictor will totally know.

EliteNinja
12-17-2004, 05:41 AM
[ QUOTE ]
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

[/ QUOTE ]

The key word is 'you'.
That means 'I' will choose to keep box A closed.
'My friend' will open box A.

gaming_mouse
12-17-2004, 06:30 AM
Dude. You have know idea. Just trust me. He'll know.

PoBoy321
12-17-2004, 06:33 AM
The reliable predictor is a fraud. It's like telephone psychics. If they're psychic, why didn't they call you?

Bodhi
12-17-2004, 11:47 AM

[ QUOTE ]
...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.

[/ QUOTE ]

Whenever I encounter a paradox I try to look for inconcistencies that will debunk it. Perhaps the paradox is generated because two-box people retain a real-world perspective on the problem, while one-box people are willing to idealize their assumptions? This ambiguity between two rational courses of action is what makes the question so tricky, I think.

Newcomb's paradox has been tormenting philosophers and economists for decades, and so far as a I know there is yet to be any academic concensus on it.

fnord_too
12-17-2004, 02:59 PM
I have seen this question posed before in a couple of forms, and the real argument is "do we have free will or not." If so, then the predictor cannot be 100% accurate, if it is 100% accurate, then we don't. (Also, you could argue that there can be some randomness in our actions even if we don't have free will per se, if current theories surrounding quantum mechanics are correct. That is, that the theorized laws governing many events at the quantum level are purely probabalistic, not deterministic, but I digress.)

Having said that, I only open box B, hoping it is empty!

gaming_mouse
12-17-2004, 03:07 PM
[ QUOTE ]
I have seen this question posed before in a couple of forms, and the real argument is "do we have free will or not."

[/ QUOTE ]

I don't buy this. Free-will and the ability to predict the future are not mutually exclusive. You just have to have a more flexible concept of time to accomodate both concepts.

I am not religious myself, but I think this idea comes up alot for people who are. That is, people who need to reconcile the idea of an all-knowing god with the idea of free will. And I know lots of people believe these ideas can peacefully co-exist.

gm

fnord_too
12-17-2004, 06:08 PM
[ QUOTE ]
[ QUOTE ]
I have seen this question posed before in a couple of forms, and the real argument is "do we have free will or not."

[/ QUOTE ]

I don't buy this. Free-will and the ability to predict the future are not mutually exclusive. You just have to have a more flexible concept of time to accomodate both concepts.

I am not religious myself, but I think this idea comes up alot for people who are. That is, people who need to reconcile the idea of an all-knowing god with the idea of free will. And I know lots of people believe these ideas can peacefully co-exist.

gm

[/ QUOTE ]

The free will thing is where the argument most often gets to.

If the predictor is infallable, then what it predicts will happen, period. If there is only one possible outcome, there is no choice.

I don't think all-knowing necessarily includes the future.

gaming_mouse
12-17-2004, 06:33 PM
[ QUOTE ]
If the predictor is infallable, then what it predicts will happen, period. If there is only one possible outcome, there is no choice.

[/ QUOTE ]

You didn't understand my previous post, I think. The point is that free-choice and predetermination are not necessarily at odds, at least in many people's opinion. That is, many people believe that God is all-knowing, and knows everything that ever has happened and ever will happen. At the same time, they believe God gave human beings free choice. I am not religious at all myself, so I am certainly not proselytizing (sp?) -- my point is that this is a well known philosohpical debate and you are taking one side of it. The other side, as illogical as it may seem, has many proponents. It just requires one to adjust one's concept of past, future, and causality.

gm

jason1990
12-17-2004, 09:52 PM
I think you (or perhaps the religious people you speak of) might need a shave. With Ockham's razor, that is. If expanded notions of time and causality are needed to reconcile the simultaneous belief in free will and determinism, then it is probably better to simply accept that these ideas are contradictory.

gaming_mouse
12-17-2004, 10:13 PM
[ QUOTE ]
I think you (or perhaps the religious people you speak of) might need a shave. With Ockham's razor, that is. If expanded notions of time and causality are needed to reconcile the simultaneous belief in free will and determinism, then it is probably better to simply accept that these ideas are contradictory.

[/ QUOTE ]

I thought I was very clear in stating that none of the religious part of this was my view. I am not religious AT ALL, for the third time. I was using that as an example to illustrate the fact that there is more to the argument than the OP -- and you -- seem to think. It was perhaps misleading to say that determinism and free-will can co-exist.

Rather, the fact that things can be predicted accurately (even 100% of the time) is not inconsistent with the idea of free will, at least not with many people's conception of it, including mine. How would you react if I could predict everything you would say and do? Would you no longer believe you had free will? And don't say it's impossible that I could do that -- I'm making a point about your concept of free will, assuming you believe in it. My point is, if I started doing that, and was consistently right, would you still believe in your own free will? Maybe you would, maybe you wouldn't. But it certainly would not be a clear-cut logical answer, at least IMO.

gm

fnord_too
12-18-2004, 01:16 AM
[ QUOTE ]
You didn't understand my previous post, I think. The point is that free-choice and predetermination are not necessarily at odds

[/ QUOTE ]

My definition of free choice includes that you have a choice and that it impacts future events. By that I mean that there are at least two possible decisions at every decision point, the decider is free to choose between them, and the choice will have an impact.

By my definitions, free choice (will) precludes absolute knowledge of the future. With my definitions, this is provable. If your definitions are different, that's fine. I have argued before with people who tried to maintain free choice and the future being known, but the people on the other end of the argument have never been able to put forth an argument more sophisticated than "It's not like that."

gaming_mouse
12-18-2004, 02:28 AM
Well,

If it's just a difference of definitions, that's fine. No point arguing.

I guess my point is... if someone could predict everything I do perfectly accurately, I would still believe in free choice. I see no inconsistency there, not by my definition. For me, the concept of free choice intersects with many other concepts, like the feeling of responsibility for my actions -- which I would still feel even if my life could be predicted by some God or force or really smart dude or whatever. Also, it has to do with the feeling of being consious, being able to move my hand this way and that, control my thoughts, etc. Determinists would claim the feeling of control is an illusion, but I don't buy it and no amount of prediction is going to change that.

Anyway, we've now veered into the region of personal belief or personal definition, so there's nothing really to argue about.

gm

jason1990
12-18-2004, 01:50 PM
I didn't mean to imply that you are religious. I had already read your two previous denials of that fact. If you inferred that and were offended, then please accept my apology.

[ QUOTE ]
It was perhaps misleading to say that determinism and free-will can co-exist.

[/ QUOTE ]
Well, I was arguing via Ockham's Razor that, in the absence of any real (i.e. non-hypothetical) evidence that they do co-exist, it is logical to assume that they do not. So if I was arguing against an ill-formed statement, then I guess we are not in disagreement.

MortalWombatDotCom
12-18-2004, 03:33 PM
Hypothetically, assume that an all powerful being could reverse time and perform the following experiment.

The being allows you to make a choice and act upon it (like deciding whether to open two boxes or only one, or deciding whether or not to jump off that ledge you are standing on).

Then, the being rewinds time and allows you to make the decision again. Everything is exactly the same. You have no knowledge of the reversal of time, because for you, the "first" runthrough hasn't happened yet.

Do you make the same decision the second time, and every other time this experiment is run?

If so, then you are essentially a machine running a program. You take as inputs all the things you observe, and your memories of everything that you have ever observed, and certain heuristics you have assembled as a result of things you have observed, and you produce the choice and you try to execute that choice. Your "free will" is just your name for the algorithm you use. It will always produce the same choice given the same EXACT inputs, and physics will take care of whether or not you successfully execute it. Why couldn't there be a reliable predictor of your choice?

If not, then you believe that what you do is random. given any particular choice, you might do one thing, you might do another thing, there is some random element that shapes the outcome. What is your free will now? In one trial, you are standing on a ledge, and you decide to jump. In another trial, you are standing on a ledge, and you decide not to jump. Is that really the way it works? That's a reasonable belief (i guess), but i personally couldn't reconcile that with a belief in a god that sends you to hell if you commit suicide but might admit you to heaven if you don't. If you're lucky, you go to heaven, if not, you go to hell. Wow. For what it's worth, I still think in this scenario you are a machine executing a program, but now your program uses as one of its inputs the output of something that is produced randomly. But i am forced to admit that there is a way of defining that random element as "free will". Congratulations. You have free will.

gaming_mouse
12-18-2004, 04:16 PM
This is has now devolved into an argument about whether or not free will exists, which I think is about as pointless to have as an argument about religion.

I would say, though, Mortal, that you're argument has not "proved" anything any more than people's arguments for or against the existence of God prove anything. It is a point of view. My own happens to be different, but I doubt I could change your viewpoint any more than you could change mine, so there's no point in discussing.

gm

KingDan
12-18-2004, 06:13 PM
I'd flip a coin, and decide based on that. Make it random, so the predictor cannot outthink me.

mannika
12-19-2004, 01:12 AM
[ QUOTE ]
I'd flip a coin, and decide based on that. Make it random, so the predictor cannot outthink me.

[/ QUOTE ]

Wouldn't the predictor know what the coin was going to land on? /images/graemlins/grin.gif

(I'm just being a dick now)

EliteNinja
12-19-2004, 02:21 AM
[ QUOTE ]
Dude. You have know idea. Just trust me. He'll know.

[/ QUOTE ]

Okay, I trust you. If what you say is true, I'd play it safe and only pick Box B. Then take that money and GAMBOOOOL!!!! and win the other \$1000.

The coinflip idea is pretty cool, though.