Rational Choice

[Paidion]

Box A only: 0

Both boxes: 0

Suppose you have been chosen to participate in a psychological experiment. You are going to be paid well. First you enter a room which contains a complex computer. You are seated in a chair in front of it, while the operator places electrodes on your head. These electrodes transmit brain waves into the computer.

After removing the electrodes, the operator goes into the adjoining room and returns. Then you are taken into that room where there is a table on which are two boxes labelled "A" and "B". You are told that you may open either Box A, and keep the money which is in that box, or you may open both boxes and keep the money from both boxes.

You are also given the following true information before making your choice. The operator has gotten a prediction from the computer after your brain waves were analyzed. If the computer predicted that you would open both boxes, then the operator placed nothing in Box A, and a hundred dollars Box B. But if the computer predicted that you would open only Box A, then the operator placed ten thousand dollars in Box A and a hundred dollars in Box B. The experiment has already been done with 500 other people, and the computer predicted correctly what the participant chose in all 500 cases.

What will you choose? Both boxes, or Box A alone?

Please relate you choice. It would be great if you explained why you made that choice. But first copy the "counter" from the top of this post to the top of your post, and change the number from zero to one for whatever choice you made. Subsequent choice should add one to the previous number beside the choice which you made.

 

[Vic C.]

Box A only: 1

Both boxes: 0

Pay up bro!

Why would I make any other choice based on the info you gave us? There is no variable in the scenario. I already know Box A is the way to go because you said so.

If you were to say that box A contained either $0 or $10,000 and Box B guarantees me $100, now I have a "gambling" choice to make.

 

[John]

If you were to say that box A contained either $0 or $10,000 and Box B guarantees me $100, now I have a "gambling" choice to make.

for a 50/50 chance at 10,000 I'd take box A I would not lose sleep over 100$


Box A only: 2

Both boxes: 0

 

[Paidion]

Box A only: 2

Both boxes: 0

Thank you for your replies, Gentlemen.

If you were to say that box A contained either $0 or $10,000 and Box B guarantees me $100, now I have a "gambling" choice to make.

I did say that, Vic. You may want to read it again ---- more carefully --- in particular the paragraph beginning with: "You are also given the following true information before making your choice."

 

[Paidion]

Box A only: 2

Both boxes: 0

for a 50/50 chance at 10,000 I'd take box A I would not lose sleep over 00$

Are you sure it's a 50-50 chance? Are you sure there's any element of "chance" at all? Or is there rather one particular "rational choice" which can be made?

 

[John]

Sorry i read it wrong.

But if the computer predicted that you would open only Box A, then the operator placed ten thousand dollars in Box A and a hundred dollars in Box B

Box A still please.

 

[ProphetMark]

Asumption 1: Neither box contains a negative amount of money. Therefore A + B can't be less than A.

Hmm, this is more complicated than it looks.
If the computer predicted I choose only Box A, and was wrong, I get $10,100.
If the computer predicted I choose both boxes, and was wrong, I get nothing.
If the computer predicted I choose only box A, and was correct, I get $10,000.
If the computer predicted I choose both boxes, and was correct, I get $100.

Assumption 2: The computer is highly likely, but not certain, to be right.

If I choose only box A, I either get $10,000 or nothing.
If I choose both boxes, I either get $100 or $10,100

Still not sure, I'll take a chance on the computer being wrong, and see if I can get the $10,100.

Box A only: 2

Both boxes:1

 

[Paidion]

Box A only: 2

Both boxes: 1

Thanks Prophet Mark for your thorough explanation. Thanks to the others who have made your rational choice. I hope that many others also do so, soon.

There is a reason for this survey. I'll explain it when many more results come in.

 

[Adullam]

Box A only: 2

Both boxes: 2

Choosing both boxes guarantees the making of $100 as I see it. If this were a test of greed vs logic then the computer would always pick both boxes. This way the greedy would get nothing and the cautious would make $100.

 

[Vic C.]

If you were to say that box A contained either $0 or $10,000 and Box B guarantees me $100, now I have a "gambling" choice to make.

I did say that, Vic. You may want to read it again ---- more carefully --- in particular the paragraph beginning with: "You are also given the following true information before making your choice."

I read it very carefully. I also did a web search for this math riddle and found a close match. Their problem was presented with a variable, which doesn't exist in yours.

Here's yours:

You are also given the following true information before making your choice. The operator has gotten a prediction from the computer after your brain waves were analyzed. If the computer predicted that you would open both boxes, then the operator placed nothing in Box A, and a hundred dollars Box B. But if the computer predicted that you would open only Box A, then the operator placed ten thousand dollars in Box A and a hundred dollars in Box B. The experiment has already been done with 500 other people, and the computer predicted correctly what the participant chose in all 500 cases.

We're being told right up front choosing both boxes yields $100. Choosing only A yields $10,000. Knowing this, the obvious choice is A only.

Now their problems say that Box A has either $0 or &10,000 and Box B has a guaranteed $100. Choosing only A would give you one of two possible amounts, not known in advance; $0 or $10,000. Choosing both would give you either $100 or $10,100.

Box A is the variable. The problem I present has a hidden factor; Box A may contain nothing. Your problem doesn't have this variable.

But I digress. If I am reading your quiz correctly and I know all that is stated above in the quote and it is indeed true; I still choose Box A.

I get this nagging feeling I'm not reading this correctly.

 

[animal]

The computer makes a prediction before you even know the boxes exist?

 

[stovebolts]

I flipped a coin and picked B just to be different, besides, who wants to think that hard this early in the morning? ;)

 

[Paidion]

We're being told right up front choosing both boxes yields $100. Choosing only A yields $10,000. Knowing this, the obvious choice is A only.

Choosing A only doesn't "yield" $10,000 unless the operator placed $10,000 in Box A. He would have placed the ten grand in Box A only if the computer predicted that you would choose only box A.

I still don't see why you think that you are guaranteed $100 either way. The instructions are:

You are told that you may open either Box A, and keep the money which is in that box, or you may open both boxes and keep the money from both boxes.

If you open Box A only, you may keep the money which is in that box. If there is nothing in that box, you get nothing.

The computer makes a prediction before you even know the boxes exist?

RIGHT! We're assuming that this complex computer can analyze your brain waves and make such predictions even if you don't know what's going on.

 

[Vic C.]

Choosing A only doesn't "yield" $10,000 unless the operator placed $10,000 in Box A.

Correct... and we are being told in your post that the operator will put the money there if the computer predicted I would choose Box A. So based on that foreknowledge, I choose A

I still don't see why you think that you are guaranteed $100 either way.

I don't believe I wrote that.

The instructions are:
You are told that you may open either Box A, and keep the money which is in that box, or you may open both boxes and keep the money from both boxes.

If you open Box A only, you may keep the money which is in that box. If there is nothing in that box, you get nothing.

Cool, now what about the true information we are given before the choice? Could you please post that true information again? I think that is where I am getting caught up. It says the operator would put $10,000 in Box A if the computer predicts me choosing only Box A. Now since there is no real computer here scanning my puny brain and since you are telling us what the operator would do based on this hypothetical computer, I would have to be a lunatic not to choose Box A.

Why is it that John and myself are the only ones reading exactly what it says in your first post?

http://mathforum.org/library/drmath/view/56802.html

 

[lovely]

Box A only: 2

Both boxes: 3

I would choose both boxes, because when I read your OP that's immediately what my brain went to. Two are better than one, if they both happen to contain money that I am free to keep. So, if they could predict what I would do, the computer would predict both boxes.

It seemed contradictory to me, though, because first I am told I can keep the money from 'both boxes', but then later I am told that only 'one' contains money if the computer predicted both. I would still open both for the sake of honesty.

The Lord bless you. I am not good with brain teasers. <sigh>'

 

[lovely]

Oh, it just dawned on me that I would still be given $100.00! Right? So, I would come out ahead.

 

[VaultZero4Me]

The only information that is useful in my decision is that I can keep the contents of A and B if I open both, or only A if I only open A. The outcome is not decided by my actual choice, but by my predicted choice. Unless you believe in pre-determined destiny, at which point the scenerio gets too complicated to rationalize.

The outcome had already been decided before my action, therefore there is either $100 in B and $0 in A, or $10,000 in A and $0 in B. My choice will not make the make the $10k vanish and the $100 appear if I go for both.

If I choose to only open A, then I get $0 or $10,000.

If I choose to open both, I get $10,000 or $100.

Since the contents are not affected by my choice at the time I can make my choice, and if I open both I can keep the contents of either box, I always open both for a net gain.

Unless I read this wrong.

 

[Paidion]

Box A only: 2

Both boxes: 3

Way back in 1966, this question was given to hundreds of people. They were split right down the middle. About half chose Box A only, and half chose both boxes. But virtually everyone felt very strongly that his answer was the only rational choice.

These are two very distinct ways of thinking, and I think there is a relation to theological thinking. When we get some more results, I will register my own choice and explain why I think that one is the rational one. I will also show how thinking about this problem is related to thinking about a particular philosophical or theological problem.

Thanks to all who have registered your choice. If you haven't would you please take a few moments to think it over, and then do so.

 

[VaultZero4Me]

I have read it twice, and I do not see how there is any rational to open just A, since you are allowed to keep whatever is in either box upon opening.

Unless you feel that your actual choice will some how effect the contents of the box (since the money is placed based on the prediction not the action), or are not trying to maximize profit. Either one does not seem rational.

We all want to receive the most of what we can, and thinking your actual choice has any effect on the contents of the boxes, is saying that the future can affect the past. That we know isn't rational.

One of the more interesting posts I have read in a while on a forum. Thanks for the brain teaser and want to see your answer :D

 

[VaultZero4Me]

*edited out