Free Will Philosophy Problem
 

My philosophy teacher posed this problem to the class. I've been thinking about it a lot, and I'm fairly convinced I have the correct answer. I want to hear what you guys think about it.

Box #1 is guaranteed to contain $1000 no matter what. Box #2 either contains one million dollars, or it contains nothing. You can either 1) take both boxes, or 2) take only Box #2.

Seems simple enough right now, but there's a story behind Box #2. A brilliant alien psychologist has been studying your every behavior since birth. This hypothetical alien knows you better than you know yourself, and can predict your actions as accurately as possible. This alien is in charge of deciding whether to put the million in Box #2 or not. If the alien predicts you will chose both boxes, he will put nothing in Box #2. If the alien predicts that you chose ONLY Box #2, he will put a million dollars in it.

Like I said, I've pretty much convinced myself of the answer. I'd be interested to hear various arguments on both sides though, because I might end up having to defend myself later in class.

Re: Free Will Philosophy Problem
 

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My philosophy teacher posed this problem to the class. I've been thinking about it a lot, and I'm fairly convinced I have the correct answer. I want to hear what you guys think about it.

Box #1 is guaranteed to contain $1000 no matter what. Box #2 either contains one million dollars, or it contains nothing. You can either 1) take both boxes, or 2) take only Box #2.

Seems simple enough right now, but there's a story behind Box #2. A brilliant alien psychologist has been studying your every behavior since birth. This hypothetical alien knows you better than you know yourself, and can predict your actions as accurately as possible. This alien is in charge of deciding whether to put the million in Box #2 or not. If the alien predicts you will chose both boxes, he will put nothing in Box #2. If the alien predicts that you chose ONLY Box #2, he will put a million dollars in it.

Like I said, I've pretty much convinced myself of the answer. I'd be interested to hear various arguments on both sides though, because I might end up having to defend myself later in class.

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My brain hurts

Re: Free Will Philosophy Problem
 

Since the amount in each box cannot change, take both.

If the second box is empty, there was nothing you could do about it. At least you will have $1000 if you take both. Deposit it all in Party Poker, and send me half of it for giving you this advice.

GG

Re: Free Will Philosophy Problem
 

They will never be able to predict your actions 100% of the time, so it really doesn't matter.

You could out think yourself and go against your expected behavior, only to have the alien make a mistake in guessing your expected behavior and you will be screwed either way.

In the end, you're better off taking both boxes because you will always get something, regardless of any mistakes made.

Re: Free Will Philosophy Problem
 

You both came to the same conclusion as I did. The way I see it, it's always correct to take both boxes. Unfortunately for me, if this situation ever came up, the alien would never put the million dollars in Box #2, because he'd know that I know that taking both boxes is the smartest thing to do. He'd know that I would realize NOT taking the first box is just giving up $1000 no how you choose to look at it.

The only way I could ever expect to gain anything from Box #2 is if I somehow tricked myself into actually believing that taking ONLY Box #2 is logical and correct. And even after that, taking both boxes would STILL be correct, seeing as the million is either in there or it isn't when it comes time to chose.

Re: Free Will Philosophy Problem
 

So basically the alien will give a stupid person a chance at $1mil but anyone with a brain only gets $1k. Liberal arts professors sure are goofy.

Newcomb\'s Paradox
 

This is Newcomb's Paradox. It has recieved a lot of attention in philosophy circles in the last 50 years. It boils down to belief in free will vs. determinism. There is a lot written on this paradox on the web and probably some on this forum. Martin Gardner has wlso written on it in one of his books and Paul Watzlawick gives a treatment of it in _How Reak is Real_. There is no "solution". Your response to the dilemna is entailed by your belief in free will or in determinism.

regards,

raisins

Re: Free Will Philosophy Problem
 

Does the Alien let you off the spaceship?

Re: Free Will Philosophy Problem
 

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You both came to the same conclusion as I did. The way I see it, it's always correct to take both boxes. Unfortunately for me, if this situation ever came up, the alien would never put the million dollars in Box #2, because he'd know that I know that taking both boxes is the smartest thing to do. He'd know that I would realize NOT taking the first box is just giving up $1000 no how you choose to look at it.

The only way I could ever expect to gain anything from Box #2 is if I somehow tricked myself into actually believing that taking ONLY Box #2 is logical and correct. And even after that, taking both boxes would STILL be correct, seeing as the million is either in there or it isn't when it comes time to chose.

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I agree with you. The alien made his prediction before you were presented with the choice. Nothing you can do ex post facto in your choice (or your thinking about the choice) can now change his prediction and thus his decision to put or not put the $1MM in box# 2 (you were who you were pre-decision). You must take both boxes and you will never get the $1MM. But there is nothing you can do about it.

FWIW, I believe in free choice and don't find this hyp too disturbing. I would be interested in hearing more about it though.

Thanks for the post.

Re: Free Will Philosophy Problem
 

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and can predict your actions as accurately as possible

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I think this part of the question is the most interesting. Can someone's actions be predicted 100% of the time and if so, couldn't counter measures be put in place to make them lose no matter what they choose?

Re: Free Will Philosophy Problem
 

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I think this part of the question is the most interesting. Can someone's actions be predicted 100% of the time and if so, couldn't counter measures be put in place to make them lose no matter what they choose?

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Yes, but only if you knew what their choice was. In the problem, you don't know what the aliens choice is so you can't try to defeat his prediction.

There is a good discussion of this problem at the attached link:

Newcomb's Paradox

This is called Newcomb\'s Paradox
 

I already posted it in the probability forum, do a search on "Newcomb's Paradox" to see what others here have already said.

Re: Free Will Philosophy Problem
 

I guess I am a stupid person then, but I'll be a stupid millionaire. I take box #2 only.

The way I look at it, I'm betting $1000 that the alien is correct in his prediction. If he indeed knows me, then he will know that I am an all-or-nothing kind of guy. I make decisions like that all the time. Assuming he is being honest, then it is almost certain he will put the money in box #2.

If there is a million dollars in the box, I don't care about leaving $1000. Big deal. The alien can keep it and give it to the next sucker that takes both boxes. Or take his alien wife out to dinner.

If he was wrong and thought I would take both, then, hell, it would be worth $1000 to laugh at him and knock him down a peg or two. Then I would take pictures of him and sell them and the story to the Enquirer for $1,000,000.

Re: Free Will Philosophy Problem
 

I'd take only box #2.

Either I'd get a million dollars or I'd prove that a brilliant alien scientist wasted 30 years studying my every action instead of doing something far more important (worth every penny).

Hello,gasgod! But BOX# 2 \'s content is a function of...
 

how well the psychologist can predict MY behavior.
I must change gears. That is,I would have to drastically change my behavior pattern of a lifetime. There is an extremely small chance of my doing so UNLESS I'm aware of the psychologist's experiment and his intentions. Given that I will lose 1000.00 if box2 is empty,I won't lose sleep over it.. However,a 50% chance of winning a million and NOT taking it will cause me to lose some sleep. [img]/images/graemlins/confused.gif[/img] So , if I'm NOT aware of the Alien'experiments and intention,I would select BOX2. But I'm speaking for myself. I do not know what anyone else would do. HOWEVER, my GUESS is that MOST of them would do the same as I.
SittingBull

Re: Free Will Philosophy Problem
 

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I'd take only box #2.

Either I'd get a million dollars or I'd prove that a brilliant alien scientist wasted 30 years studying my every action instead of doing something far more important (worth every penny).

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Assuming the only thing that matters is making the decision that will get you the most money from the boxes, how can you turn down that free 1k?

Hello,Happy! The answer depends on knowing your behavior ..
 

pattern of a lifetime. Since U think that the Alien thinks U are a go-for-the-gusto type of guy,he would NOT put the MILLION in BOX2. Hence,U would be out of both 1000.00 and 1million.
In your case,U should go for the 1000.00.
However,if u were an extremely conservative non-gambling person, and U know that the alien know u were that type,then U would go for BOX2--assuming u knew the alien's objectives. You would do a reverse tell on the alien. But your tell is a well-ingrain HABIT. Very difficult to reverse.
SittingBull

Re: Free Will Philosophy Problem
 

The only thing that matters to me is charging the alien the most amount possible to be accurate.

Re: Free Will Philosophy Problem
 

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and can predict your actions as accurately as possible

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I think this part of the question is the most interesting. Can someone's actions be predicted 100% of the time and if so, couldn't counter measures be put in place to make them lose no matter what they choose?

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it's a hypothetical situation.... keyword hypothetical

Re: Free Will Philosophy Problem
 

The choice is laying you 1 to 999 that the alien can predict your action. Only a really bad, super alien would be worse than that. I take box 2.

Re: Free Will Philosophy Problem
 

I assume I've been told about the alien. Suppose the alien can predict my behavior with 99.9% accuracy. If my Final Choice is both boxes the alien will have predicted That choice 99.9% of the time and my EV is $2000. If I my Final Choice is box #2 only, the alien will have predicted That choice 99.9% of the time and my EV is $999,000. Clearly I maximize my EV by taking Box 2 only - Final Decision.

However, we don't know that the alien can predict with 99.9% accuracy. All we know is he "can predict your actions as accurately as possible". Suppose his accuracy is only 50%, achieved by flipping a coin. Then choosing both boxes has EV $501,000 and choosing Box 2 has EV $500,000.

If the alien's accuracy is 50.05% either choice has EV $500,500. So if the alien can predict worth beans at all better than 50.05% accuracy you are better off choosing Box 2 only.

What's all the hubub about free will here? Sklanskytology solves it. Say, do you think this might be worth a Nobel Prize?

PairTheBoard

Re: Free Will Philosophy Problem
 

i don't get it, why wouldn't you choose just box #2 ?

Re: Free Will Philosophy Problem
 

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i don't get it, why wouldn't you choose just box #2 ?

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Because there is essentially a free $1000 on the table. No matter what you think, or what you think the alien thinks, or what the alien thinks you think, nothing changes the fact that once you are given the opportunity to choose, the money with either be in Box 2, or it won't be.

Let's assume you chose only Box #2 and it turns out to contain the million. That means that the million was in the box the entire time. If you could go back in time, you could chose both boxes, and you'd have the million + 1000.

Re: Free Will Philosophy Problem
 

You guys are missing the point. The reason a sophisticated alien is used in the example is just to assume that all information about your life has been accurately gathered and examined.

It's really a question of biological determinism. Do you think that your future choices are wholly determined by the totality of your past experience? If so, you're screwed because it's possible to accurately predict your future action so the alien will take the money out of box #2, so you might as well just take the 1k.

If you don't think we're biologically determined, then you might as well take box #2 since you believe the totality of your past experiences won't add up to any concrete answers as to which box you'll pick. Therefore, the alien has no way of knowing for sure whether or not you'll pick #2.

Re: Free Will Philosophy Problem
 

If you choose box 2 AND the alien is an accurate predictor - better than 50.05% - you will make more money on average than if you choose both boxes AND the alien is an accurate predictor of your choice.

You're assuming that the alien cannot accurately predict your choice.

PairTheBoard

Re: Free Will Philosophy Problem
 

how does this relate to free will/determinism?

hows this, i will simply take the million dollar box. a thousand dollars doesnt mean much to me. if the alien knows that i will simply take the million dollar box then i get the million dollars.

i guess what it boils down to is that if life revolves around free will, then it is correct to take both boxes because the alien can only guess what you will choose. however, if it boils down to determinism then its correct to take the million dollar box, because you will always get the million dollars every time you take this box, and you will never get the million dollars if you take both boxes.

i really dont understand the complexity of the problem. just take the million dollar box.

Re: Free Will Philosophy Problem
 

Moreover, there is a reasonable chance the alien has some cheating mechanism that will skew the study results in his favor.

Like some smoke and mirrors job to hide the million if you pick both.

Re: Free Will Philosophy Problem
 

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Because there is essentially a free $1000 on the table. No matter what you think, or what you think the alien thinks, or what the alien thinks you think, nothing changes the fact that once you are given the opportunity to choose, the money with either be in Box 2, or it won't be.

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this seems to contradict the assumption the alien is always right

Re: Free Will Philosophy Problem
 

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Because there is essentially a free $1000 on the table. No matter what you think, or what you think the alien thinks, or what the alien thinks you think, nothing changes the fact that once you are given the opportunity to choose, the money with either be in Box 2, or it won't be.

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this seems to contradict the assumption the alien is always right

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the problem with this statement is that it sides with free will. if you sided with determinism then it means that picking the box with the million with it will give you the million more often than picking both boxes.

i argue that you should simply take the box of 1 million because we are too stupid to know if life is based on free will or determinism, so why risk it?

Re: Free Will Philosophy Problem
 

i think i am starting to follow now

i argue that assuming the alien knows what we are going to do we don't have free will

Re: Hello,gasgod! But BOX# 2 \'s content is a function of...
 

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how well the psychologist can predict MY behavior.

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This is the flaw. The psychologist has already predicted your behaviour. You cannot change that prediction; it is history. Box 2 may or may not have anything in it. That's beyond your control. Given that, why pass up on a free $1000?


GG

Re: Hello,gasgod! But BOX# 2 \'s content is a function of...
 

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how well the psychologist can predict MY behavior.

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This is the flaw. The psychologist has already predicted your behaviour. You cannot change that prediction; it is history. Box 2 may or may not have anything in it. That's beyond your control. Given that, why pass up on a free $1000?


GG

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I agree. If the alien predictor's actions were made before you could act, then there is absolutely no reason not to always take both boxes because your choice doesn't influence whether or not the money is in box #2. It either already is or already isn't and there is nothing you can do about it.

Re: Hello,gasgod! But BOX# 2 \'s content is a function of...
 

no but see, i argue that this logic is flawed because your logic is that youre passing up on a free $1000 on a decision that doesnt matter either way. the alien knows you will think this and therefore will not give you the million.

however, if you think like me, that you are willing to pass up on the free $1000 because your logic is that the alien thinks you will think that you are more likely to get the million if you only choose the million dollar box, then he will think you will only take the million dollar box and you will get paid.

Re: Free Will Philosophy Problem
 

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I'm fairly convinced I have the correct answer

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And that is precisely why you are wrong. First philosophy course, right?

Scott

Re: Hello,gasgod! But BOX# 2 \'s content is a function of...
 

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no but see, i argue that this logic is flawed because your logic is that youre passing up on a free $1000 on a decision that doesnt matter either way. the alien knows you will think this and therefore will not give you the million.

however, if you think like me, that you are willing to pass up on the free $1000 because your logic is that the alien thinks you will think that you are more likely to get the million if you only choose the million dollar box, then he will think you will only take the million dollar box and you will get paid.

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Why are you using future tense? The alien has made (Note: past tense) his decision. It's wishful thinking to imagine that you can influence the course of events in the past.

GG

Re: Hello,gasgod! But BOX# 2 \'s content is a function of...
 

its ok if you dont agree with me, but its ridiculous if you dont even understand what im telling you.

Re: Hello,gasgod! But BOX# 2 \'s content is a function of...
 

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its ok if you dont agree with me, but its ridiculous if you dont even understand what im telling you.

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Your previous post:

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no but see, i argue that this logic is flawed because your logic is that youre passing up on a free $1000 on a decision that doesnt matter either way. the alien knows you will think this and therefore will not give you the million.

however, if you think like me, that you are willing to pass up on the free $1000 because your logic is that the alien thinks you will think that you are more likely to get the million if you only choose the million dollar box, then he will think you will only take the million dollar box and you will get paid.

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The first sentence is entirely unintelligible. I frankly have no idea how to parse this post. You are certainly correct that I didn't understand what you were telling me. Did you?

GG

Re: Hello,gasgod! But BOX# 2 \'s content is a function of...
 

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The alien has made (Note: past tense) his decision. It's wishful thinking to imagine that you can influence the course of events in the past

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But you did influence his decision in the past. He based his decision whether to put the money in the box on you. So in effect you have already made the choice, at the time he set up the boxes.

When he presents me with the choice, I realize that I have already made my decision - without knowing it at the time - and I am stuck with that.

There is no changing your mind at the last minute. The decision to do that was already part of your predictable state at the time he set up the boxes.

This does not condradict free will. It was my free will that led me to the point in my life that he based his decision on. Free will is not random, I can only choose what seems to be the best choice at the time, for whatever reason.

Taking only box #2 is the rational decision.

Re: Hello,gasgod! But BOX# 2 \'s content is a function of...
 

thank you, you explained it much better than i did.

Re: Free Will Philosophy Problem
 

I flip a coin. Heads I take both, tails just box 2. Beat that alien from another planet.

Krishan