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Platt Inner circle New York 2012 Posts |
You are confronted with a choice. There are two boxes in front of you, A and B. You may open both boxes or else just open B. You may keep what’s inside any box you open but you may not keep what’s inside any box you do not open. The background is this.
A very powerful being who has been invariably accurate in his predictions about your behavior in the past has already acted in the following way. He has put $1,000 in box A. If he has predicted you will open just box B, he has, in addition, put 1,000,000 in box B If he has predicted that you open both boxes, he has put nothing in box B. What should you do to maxize expected utility? What's the rational thing to do? What would you do?
Sugar Rush is here! Freakishly visual magic. http://www.plattmagic.com
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Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
I'm missing something here. Why would I care if the "prediction" is correct if I can open both boxes and get the million if it's in B and come out with a thousand otherwise? Powerful as in good with a NW?
...to all the coins I've dropped here
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Andrei Veteran user Romania 353 Posts |
Well, Jonathan, if you were going to open both boxes anyway, then he would have just let the $1,000 in A, which you will end up with.
If you only decide to open B, and he has predicted it correctly (which he always does), you end up with $1 mil. I'm not saying that's rational behavior, but that's the first analysis. Andrei |
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Poliphilo New user 57 Posts |
I didn't want to reveal my method on here too soon, so I sent you a PM
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Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
I guess we could call this a leap of faith situation and come out with two bits of data by opening just box B. One is the accuracy of the prediction and two is faith in the predictor. Is that utility though?
...to all the coins I've dropped here
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Platt Inner circle New York 2012 Posts |
This is actually a very deep paradox closely related to the prisoner's dilemma. The fact that it's dealing with the supernatural makes either argument a little harder to prove. But there are quite long mathematical equations that lead to one decision being the best for maximizing return. Poliphilo, you were right about the name behind this famous paradox.
Jonathan, here's one way to think about it: If you were watching somebody else confronted with this choice, wouldn't you bet heavily that if they opened both boxes they would end up with just 1,000? And if others were betting on you, wouldn't they be best off betting the same way? So if you were confronted with the boxes, in essence, betting on yourself, shouldn't the same logic apply?
Sugar Rush is here! Freakishly visual magic. http://www.plattmagic.com
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Steve Martin Inner circle 1119 Posts |
This is Newcomb's Problem.
Much written about this on the web. I don't believe in determinism. The boxes are in front of me. My actions cannot affect their contents. My personal response is "b-o-l-l-o-c-k-s to the predictor - he can't possibly know what I am going to do with complete accuracy, as I can do whatever I like." I will take both boxes. That is the "rational " thing to do, as it is irrational to believe that some being can predict what I am going to do. That way, I am guaranteed $1000, and if the predictor (hail, oh great one!) has predicted that I would only choose Box B, then I will get an extra million dollars on top of that.
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
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Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
But Steve, the mighty one might be good with a NW and still be right.
...to all the coins I've dropped here
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Steve Martin Inner circle 1119 Posts |
Regarding the supernatural, God (if you believe there is such a being) sees what we are going to do in future because he sees the whole of history - in time and space - open before him like a book. This does not seem crazy to me, since it is conceivable that God is not necessarily constrained by our experience of time and space. (After all, we read books in which the story takes place in a certain way, yet we do not know what happens until we read the pages. We can skip to the last page and find out what happens "ahead of time" but we cannot change what happens there.)
This is not the same thing as saying that our actions are *pre-determined*. We can do whatever we like. God watches us do what we do. *** If God - reaching into time and space - placed the money in the boxes, he would not be able to make an accurate *prediction* - in my time and space - about what I was going to do. He would only know what I was going to do by virtue of him seeing me carry out the action. And by then it would be too late - "late" in my time and space - to change what he had put in the boxes. __________________ *** Can God influence what I do as we go along? I see no reason why not. After all, even you can influence (sometimes) what I do as we go along!
Any man who reads too much and uses his own brain too little falls into lazy habits of thinking.
Albert Einstein |
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Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
Without getting into absolutes or multiverses, the unknown issue here is whether the "predictor" also desires one to have the million. The rest of the analysis is unclear to me.
...to all the coins I've dropped here
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Platt Inner circle New York 2012 Posts |
I'd open only box "B" if only to get great joy of proving the great predictor wrong for the first time ever. Or if he's right, I get a million bucks. Not a bad alternative. Of course the reason most of us would pick only box B would be the fear of backwards causation. Somehow, I'm guessing, we feel that if we open both boxes, the money that was in box B would magically disappear. Experts on quantum physics just might agree. In the subatomic world this type of crazy dual states, and apparently backwards causation, is a reality.
Sugar Rush is here! Freakishly visual magic. http://www.plattmagic.com
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Psy-Kosh Regular user Michigan 134 Posts |
For the sake if this puzzle, I assume that it is known and certain (or highly probable) that the being really can accurately predict my actions, or somehow arrange things so that the only states of reality allowed to exist are "I only open box B and there's a million dollars there" or "I open both boxes and box B is empty."
This does not seem inherently paradoxical as of yet. Physics, afaik, has yet to really be sure one way or the other on time travel (that is, accessable information from an event ending up in the event's past lightcone), and there's reason to believe that the "paradoxes" of time travel are resolvable, one way via the "spawn off another timeline" resoltion... (short version is you go back in time and kill your grandparent... only it isn't really yours, but the timeline splits, so it all works out) or, more interestingly, it's been shown mathematically that at least in contrived simplified "paradox" situations, there will always exist a self consistent solution. Given all that, seems to me that if one knows that the being in question is able to do this, and also believes that the being in question is honest about its intentions, then the rational choice is to open box B. |
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Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
Do we know the intentions or desires of the great predictor?
...to all the coins I've dropped here
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Platt Inner circle New York 2012 Posts |
Don't discount this quite so quickly psy-kosh. Jonathan, let's assume we don't know the intentions of the predictor. When you throw out the possibilty of backwards causation by using glass backed boxes, the true paradox shines.
Most people would pick box 'B." Even if they know it's for silly reasons- if all the people who picked box "B" before you became millionaires and all the people who opened both boxes became only 1,000 dollars richer, you've got to believe the same will apply to you. Surveys in Scientific America claim over 70% would pick just box "B" Again the game is about getting the most money in your hands. If we change the game and give the boxes a glass backing, and you believe, like most, that you should open only box "B", there's a distinct paradox. If your wife's on the other side of the boxes looking through the glass, no matter what, she has to be hoping you open both boxes. Who's right?
Sugar Rush is here! Freakishly visual magic. http://www.plattmagic.com
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Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
Platt, folks,
I discounted any supposed influence of foreknowledge and treated this as a version of the sucker die box. For that matter, this might make for a presentation of that trick in a fun way. So, if the great predictor were that great, they would know to put the million in box B anyway so I can not only have the million but also have installed some faith in them. Else it's not a win/win and a neurotic pitfall (*IMHO) Funny thing about the simplest and to date most pratical interpretation of quantum physics... there is no "what if", only superimposed states that collapse when you make a measurement. Of course there is much hope that someday some experiment will demonstrate the effect of the viewer upon the viewed... ie mood or belief affects the results.
...to all the coins I've dropped here
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Psy-Kosh Regular user Michigan 134 Posts |
Platt: I'm not sure what you're saying I discounted.
The situation is odd, circular, and unlikely, but I don't see it as actually paradoxical. |
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Platt Inner circle New York 2012 Posts |
Quote:
On 2006-04-05 00:29, Psy-Kosh wrote: I guess that depends on your definition of paradox. Most puzzles that are titled paradox aren't really a paradox but rather puzzles that often lead to incorrect intuitive assumptions- i.e the monty hall paradox. A true paradox, to me, leads to both decisions or conclusions being correct and incorrect at the same time. I'd say Newcombes Paradox fits the bill- The decision to be a "B" boxer and pick up only box "B" is the logical thing to do if you want to get the most money. Clearly if people who pick only box "B" get the big prize every time and those who pick both boxes get only $1,000, you've got to assume if you pick up only box "B" the great predictor would have predicted it that way and you'll be a million dollars richer. At the same time, if the money is already in the box(es) there is absolutely no logical reason to not open both boxes, for the predictor already made his prediction. Both decisions are logical and illogical at the same time. I'd say that's paradoxical. Glass backed boxes- If your wife is on the other side looking in at the boxes, she would always be thinking "pick both boxes!" yet picking just "B" making you a "B" boxer seems to make the most sense from your perspective. You're both thinking logically but can't both be thinking logically. Again, paradoxical. No? If you take the other stance and believe the logical thing to do is open both boxes there's still a paradox. Knowing the predictor has never been wrong, if you were watching another guy make the decision, wouldn't you bet very heavily that if he picked both boxes he would would wind up with 1,000. And if he picked just box "B" he would end up with a million? Wouldn't a third party watching you bet very, very heavily that if you open just one box you'll get the million and if you open both boxes you'll get just 1,000? Wouldn't that be a very, very bright bet? So why when you're opening the boxes wouldn't you have to find your apparently logical decision to open both boxes illogical. Seems paradoxical to me.
Sugar Rush is here! Freakishly visual magic. http://www.plattmagic.com
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Psy-Kosh Regular user Michigan 134 Posts |
If the player's wife was watching, then here's what she'd see:
If the player was going to open only box B, then she'd see that there's a million dollars in box B. If he was going to open both, then she'd see box B was empty. If we accept the hypothesis that self consistend solutions always exist even when time is messed with, then if she tried to signal him in a way to deliberately do the opposite of what the predictor predicted, then the result would either be that he interprets the signal, or the predictors prediction device shorted out and gave the wrong info or or or or or... |
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Jonathan Townsend Eternal Order Ossining, NY 27297 Posts |
But if the predictor's wife is watching, she will make sure he does not put the million in B and tell him to use the NW.
...to all the coins I've dropped here
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flobiwan Regular user 165 Posts |
It seems like only opening box B is a win-win situation.
If the predictor is right, I get a million dollars. If the predictor is wrong, I get numerous guest shots on Conan O'brien, Oprah etc. for being the guy who stumped the infallible predictor and can make my million with my celebrity status. Fredd |
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