Newcombs's paradox

[Drakim]

You are sitting in a room. Before you stands a machine that's specialized on predictions, especially when it comes to human behavior. It's public established knowledge that this machine is correct 99.999853% of the time in it's predictions.

On a table are two boxes. Box A is open and in it you see 1000$ in it. Box B is closed, but you are told it has two diffrent setup possibilities. Either, Box B has 1 000 000$ or it has 0$. Which one of these two options was up to the machine to decide. The machine did this decision before you entered the room, and is unable to change it now that you are in the room.

You are allowed to keep the content of Box B, or, you can keep the content of both Box A and Box B.

However, the machine declares before you get to make your choice.

"I, the almighty machine, have done an analysis of you before you entered the room. I found out which of these two options you are going to pick, even factored into that I'm making this statement to you right now. All I'm telling you is this: If I predicted that you were going to take both boxes, then I will not have placed the 1 000 000$ in box B. If I predicted that you were going to pick only box B, then I will have placed the 1 000 000$ in box B. That is all"

Now....which of your two options do you pick? Think about this carefully.

[RubberTrucky]

I pick A/both. Cause then I will be sure to have some money.

There is no way to tell what he had picked, I think

[poxpower]

MWAHAHA I WIKIED THE ANSWER I RUINED YOUR FUN HAHAHA

[Drakim]

At 1/22/09 05:32 PM, poxpower wrote: MWAHAHA I WIKIED THE ANSWER I RUINED YOUR FUN HAHAHA

The only thing you ruined was your potential enjoyment you know. You unloaded a bucket of salt on the pudding I had served you to take away the satisfaction I get from pleasing people with treats.

Congratulations, I guess.

[Al6200]

At 1/22/09 05:12 PM, Drakim wrote:

"I, the almighty machine, have done an analysis of you before you entered the room. I found out which of these two options you are going to pick, even factored into that I'm making this statement to you right now. All I'm telling you is this: If I predicted that you were going to take both boxes, then I will not have placed the 1 000 000$ in box B. If I predicted that you were going to pick only box B, then I will have placed the 1 000 000$ in box B. That is all"

Now....which of your two options do you pick? Think about this carefully.

It's a recursive loop. I think the fallacy with his "paradox" is that the machine can predict which box you will choose after you have been told that it is not in the box that you will choose. In predicting, it too should get stuck in a recursive loop just as you did.

Anywho the best bet would probably be to use something arbitrary (like if the 15th digit of Pi is greater than 4) because the machine couldn't predict that ahead of time.

[Drakim]

At 1/22/09 05:49 PM, Al6200 wrote:

At 1/22/09 05:12 PM, Drakim wrote:

"I, the almighty machine, have done an analysis of you before you entered the room. I found out which of these two options you are going to pick, even factored into that I'm making this statement to you right now. All I'm telling you is this: If I predicted that you were going to take both boxes, then I will not have placed the 1 000 000$ in box B. If I predicted that you were going to pick only box B, then I will have placed the 1 000 000$ in box B. That is all"

Now....which of your two options do you pick? Think about this carefully.

It's a recursive loop. I think the fallacy with his "paradox" is that the machine can predict which box you will choose after you have been told that it is not in the box that you will choose. In predicting, it too should get stuck in a recursive loop just as you did.

I tried to deal with by having the ", even factored into that I'm making this statement to you right now." part of the statement. Personally, I don't think it needs to be a recursive loop. The machine would simply have awareness of the prediction as another factor in it's prediction calculation.

If the machine had told you WHAT he predicted, then it would indeed be a recursive loop, but it didn't. It simply said that it had predicted something, which is not a dynamic change, but an absolute unchangable one, thus, not recursive.

Anywho the best bet would probably be to use something arbitrary (like if the 15th digit of Pi is greater than 4) because the machine couldn't predict that ahead of time.

That's one tactic.

[Musician]

I'm sorry, could you clarify what exactly the drawback is for taking both Box A and Box B?

[therealsylvos]

Reminds me of my high school lecture on Calvinism...

Anywho A and B. The fact that it is almost never wrong is irrelevant. Once it makes its prediction I can't do anything about it. Changing my guess after the fact to prove him right won't change his prediction.

[Drakim]

At 1/22/09 09:12 PM, Musician wrote: I'm sorry, could you clarify what exactly the drawback is for taking both Box A and Box B?

Well, the machine, which is almost always right, claims that he will have removed the money from Box B if you are intending to pick both boxes. According to it, you'll end up with only the money in Box A if you pick both.

At 1/22/09 09:15 PM, therealsylvos wrote: Reminds me of my high school lecture on Calvinism...

Anywho A and B. The fact that it is almost never wrong is irrelevant. Once it makes its prediction I can't do anything about it. Changing my guess after the fact to prove him right won't change his prediction.

Yeah, this was the same thing I figured when I first heard it.

[Ravariel]

Sounds to me like if you pick only box B there is an infinitesimal chance that the comp will be wrong and have removed the money... so you have a 99.999 whatever % chance of getting the million if you just choose box B... seems the logical choice given what the comp said. Unless there's something I'm missing.

[ForkRobotik]

At 1/23/09 03:05 AM, Ravariel wrote: Sounds to me like if you pick only box B there is an infinitesimal chance that the comp will be wrong and have removed the money... so you have a 99.999 whatever % chance of getting the million if you just choose box B... seems the logical choice given what the comp said. Unless there's something I'm missing.

The computer already made his choice, so you might as well take both boxes. Statistically i think most people WOULD INDEED take both boxes, so his decision would likely be to put $0 in box B, irrelevant of you being the exception.
Also, this computer supposedly made some sort of analysis on the individual, what are the factors that were given to this machine? Given that there's so little information given to you on this process, you might as well take both. It would be foolish to not, because either way you've either got a million dollars or you don't and the decision has already been made.
Also, anyone that only takes B should get $0 dollars just for being so ridiculous.

[Drakim]

At 1/23/09 03:05 AM, Ravariel wrote: Sounds to me like if you pick only box B there is an infinitesimal chance that the comp will be wrong and have removed the money... so you have a 99.999 whatever % chance of getting the million if you just choose box B... seems the logical choice given what the comp said. Unless there's something I'm missing.

The solution, I belive, is in part of what ForkRobotic said. The decision has already been made. The machine cannot change his mind when you have already entered the room. The decision of wherever you should get the large sum of money or not is already complete. You and the machine cannot influence it, short of having a time machine.

Thus, the choice should be pretty easy. Do you want one box, or both boxes? Knowing that your choice right now is irrelevant to the placing of the money in the boxes? It's not like picking both boxes is going to make the money in Box B go away. If the money is not in Box B, then it never was there in the first place, and you had nothing to lose.

The decision of wherever you should get the money or not was already made before you entered the room. Your choice is actually quite irrelevant. It just decides whever you should get the small sum of money on the side, wheever you win or loose the big bet.

scenario 1, where the machine didn't place the money in box B: You get 1000 or 0
scenario 2, where the machine did place the money in box B: You get 1 001 000 or 1000

Are you really going to pick any of the latter choices?

[ForkRobotik]

oh i forgot to say thanks drakim for posting this i did thinking about it :)

[FUNKbrs]

The whole "fallacy of appeal to authority" applies here.

Ok, so the machine is 99% right. That's great and all, but even if it's record was an even 100% THIS COULD BE THE FIRST TIME IT WAS WRONG.

If the money's in the box; it's already in there. If it's not... IT'S NOT. There's no negative reaction to taking both boxes!

Basically, this machine is using the concept of fate to try and trick you into doing something very, VERY stupid using a fallacious appeal to authority. It can't GO BACK and take the money out of box B! Box B is EMPTY, but the machine is trying to trick you into taking ONLY Box B, so you leave with NOTHING, as opposed to taking BOTH boxes, where you DEFINITELY get the contents of Box A.

[Drakim]

At 1/23/09 10:00 AM, FUNKbrs wrote: The whole "fallacy of appeal to authority" applies here.

Ok, so the machine is 99% right. That's great and all, but even if it's record was an even 100% THIS COULD BE THE FIRST TIME IT WAS WRONG.

That's perfectly okay to take into account. I never said you are forced to trust the machine.

If the money's in the box; it's already in there. If it's not... IT'S NOT. There's no negative reaction to taking both boxes!

Exactly. That's what I'm thinking.

But it can also be argued that since you are thinking this, the machine wouldn't put the money there. Being smart got you punished.

Basically, this machine is using the concept of fate to try and trick you into doing something very, VERY stupid using a fallacious appeal to authority. It can't GO BACK and take the money out of box B! Box B is EMPTY, but the machine is trying to trick you into taking ONLY Box B, so you leave with NOTHING, as opposed to taking BOTH boxes, where you DEFINITELY get the contents of Box A.

The machine knows you are too smart to be tricked and that you will pick both, so he doesn't put the money there. Congrats. : D

[Bacchanalian]

$1000 really isn't much. Assuming you're employed and not a janitor, that's about a week of tax-exempt work.

$1000000 on the other hand is a huge sum of money, about two years worth of tax-exempt work.

Assuming the statistics on the bot's reliability are true...
Assuming I trust the entirety of the situation...
The bigger risk of taking only box B nets a proportionately much much bigger reward than playing it safe.

By taking only box B I stand about a 0.000147% chance of not getting the bigger reward.

Did I read wrong?

[TheReno]

Der both. Risk it all for the chance at 1000 more then a Chance getting a million or zero or change getting 1001000 or 1000. I mean really.

[Tancrisism]

At 1/24/09 03:58 PM, Bacchanalian wrote: By taking only box B I stand about a 0.000147% chance of not getting the bigger reward.

Did I read wrong?

That's the conclusion I came to as well. The bot knows which choice you will make, and if he predicted that you would open box B (which he is right essentially all the time), the bigger reward would be in there. So if you pick box B, chances are that's what he predicted you would pick, and the money is in there. I would thus pick B.

[Drakim]

Hehe, what I love about this question is that many people dissagree. Too many dilemmas has 99% answering the same.

[LazyDrunk]

I don't understand how you are put into a room with a talking machine offering you money to fondle it's boxes.

[Bacchanalian]

At 1/24/09 04:11 PM, Tancrisism wrote: That's the conclusion I came to as well.

Woo!

At 1/24/09 04:12 PM, Drakim wrote: Hehe, what I love about this question is that many people dissagree.

It seems to me the "both boxes" people are simply concerned with "more", while the "one box" people are concerned with "how much more." (I personally think those both box people should take a business class or two)

If you pick both boxes...
- 99% chance of walking away with 1,000
- 1% chance of walking away with 1,001,000

If you pick Box B only...
- 99% chance of walking away with 1,000,000
- 1% chance of walking away with 0

Is it really worth second guessing the machine for $1000 more, when second guessing the machine and taking both boxes will almost surely net you a total of 1,000 instead of 1,001,000?

[Drakim]

At 1/24/09 04:21 PM, Bacchanalian wrote:

At 1/24/09 04:11 PM, Tancrisism wrote: That's the conclusion I came to as well.

Woo!

At 1/24/09 04:12 PM, Drakim wrote: Hehe, what I love about this question is that many people dissagree.

It seems to me the "both boxes" people are simply concerned with "more", while the "one box" people are concerned with "how much more." (I personally think those both box people should take a business class or two)

If you pick both boxes...
- 99% chance of walking away with 1,000
- 1% chance of walking away with 1,001,000

If you pick Box B only...
- 99% chance of walking away with 1,000,000
- 1% chance of walking away with 0

Is it really worth second guessing the machine for $1000 more, when second guessing the machine and taking both boxes will almost surely net you a total of 1,000 instead of 1,001,000?

But how are you sure your thinking is right? There is nothing wrong with your numbers, however, if you look at it from a more practical point of view, you might see it diffrently.

Here is what I'm reasoning:

I am currently in the room, about to pick. The machine has already decided the content of Box B and put it there. That means, he can't just suddenly change his mind and change it now. If the money is in box B, then me picking both boxes isn't going to make the large sum of money turn into air. Likewise, me picking only box B isn't going to make the large sum of money spring into existence. To say it short, the state of box B is already decided. It's not up for changing once you know about the whole situation.

That means, there are two boxes in front of me. I can either decide to take all the money in them, or some of the money in them.

Think of it this way. Right before your pick, we freeze time and reflect upon the two possible scenarios that could unfold:

If the money isn't there, then that's too bad. But that doesn't mean that if I now pick box B, then the money will have suddenly sprung into existence. If the machine decided not to place the money in the box, then it's at this point of time impossible for me to win the large sum of money. You simply cannot collect what is not there. So, in the "money isn't there scenario", I can either choose between both, which gives me 1000$, or just box B, which gives me 0$.

If the money is there, then that's good. But that doesn't mean that if I pick both, then the money will suddenly dissapear. If the machine decided to put the money in the box, then nothing can stop me right now from taking it. So, in the "money is there scenario", I can either choose between both, which gives me 1001000$ or just box B, which gives me 1000000$.

As you can see, in BOTH scenarios, taking both boxes nets a higher reward than just taking one box. The only difference is that one scenario is better than the other scenario. However, which scenario that is reality has already been chosen by the robot. It will not change once you have entered the room.

That's my thoughts, at least.

[Doonie]

I'd choose only box B just to be the 0.000147% and outsmart the machine. Hell, 1000$ is not that much. (Or i'd get a million dollars.)

[Drakim]

At 1/24/09 04:50 PM, Doonie wrote: I'd choose only box B just to be the 0.000147% and outsmart the machine. Hell, 1000$ is not that much. (Or i'd get a million dollars.)

Are you sure the machine hasn't outsmarted you?

Event log:

*Box A has 1 000$*
*Box B has 1 000 000$*

*Doonie enters*
*Doonie takes only Box B*
Doonie: Haha! I have outsmarted you!
*Doonie leaves, leaving 1 000 perfectly fine dollars in the other box*

[Bacchanalian]

At 1/24/09 04:44 PM, Drakim wrote: It's not up for changing once you know about the whole situation.

That is a given in my reasoning as well.

But that doesn't mean that if I now pick box B, then the money will have suddenly sprung into existence.
But that doesn't mean that if I pick both, then the money will suddenly dissapear.

My reasoning also states...

That doesn't mean that if I now pick box B, then the money will have suddenly sprung into existence.
That doesn't mean that if I pick both, then the money will suddenly dissapear.

As you can see, in BOTH scenarios, taking both boxes nets a higher reward than just taking one box.

And this is a disingenuous abtraction, for reasons I already made clear. You're not taking into account the probability of all 4 outcomes.

I'll be more explicit now...

If you pick both boxes...
...there is a 99% chance that the machine predicted this, and therefore you get only 1,000.
...there is a 1% chance the machine predicted that you'd choose only B, and therefore you get 1,001,000.

If you pick box B...
...there is a 99% chance that the machine predicted this, and therefore you get 1,000,000.
...there is a 1% chance the machine predicted that you'd choose both boxes, and therefore you get 0.

Or this way...

The machine has made it's prediction...
... and you pick box B. You have a...
... ... 99% chance the machine was right; 99% chance of getting 1,000,000
... ... 1% chance the machine was wrong; 1% chance of getting 0
... ... 0% chance of getting 1,000
... ... 0% chance of getting up to 1,001,000
... and you pick both boxes. You have a...
... ... 99% chance the machine was right; 99% chance of getting 1,000
... ... 1% chance the machine was wrong; 1% chance of getting up to 1,001,000
... ... 0% chance of getting 0
... ... 0% chance of getting only 1,000,000

Or this way...

Just box B. [VS] Both Boxes...
You will almost certainly get 1,000,000. [VS] You will almost certainly get 1,000.
You will almost certainly get 1,000,000. [VS] You may by the slimmest margin get 1,001,000.
You may by the slimmest margin get nothing. [VS] You will almost certainly get 1,000.

Both Boxes. [VS] Just box B...
You will almost certainly get 1,000. [VS] You will almost certainly get 1,000,000.
You will almost certainly get 1,000. [VS] You may by the slimmest margin get nothing.
You may by the slimmest margin get 1,001,000. [VS] You will almost certainly get 1,000,000.

Where as your logic is...

The machine has made it's prediction...
... (A) and you pick both boxes...
... ... (a) you might get 1,001,000
... ... (b) you might get 1000
... (B) and you pick box B...
... ... (a) you might get 1,000,000
... ... (b) you might get 0
... no matter what you get more by picking both boxes.

Your logic is incomplete because it doesn't take into account the accuracy of the machine's future telling ability, making it meaningless to weigh Ab against Ba. However, once you do take into consideration the machine's accuracy, it does become important to weight Ab against Ba.

It will not change once you have entered the room.

And again. I'm not saying it ever changes.

[Drakim]

At 1/24/09 05:54 PM, Bacchanalian wrote: Your logic is incomplete because it doesn't take into account the accuracy of the machine's future telling ability, making it meaningless to weigh Ab against Ba. However, once you do take into consideration the machine's accuracy, it does become important to weight Ab against Ba.

I'm in the opinion that your logic is incomplete because you don't take into account that the decision of the machine is already made by the time you get to choose.

Think about this. You are standing in the room RIGHT NOW. That means that the state of Box B is already decided. If there is no money there, then there is nothing you can do about that. You can't think your way into making the money come back. If the money is there, then you have won! You just need to collect it. In both these scenarios, picking both boxes is the best choice.

But it could be argued that it's for the very fact that I am thinking about this strategy will result in the machine not putting the money in box B, thus punishing me. D:

[LazyDrunk]

Unless the computer knew anything about you, it wouldn't have the stated probability of prediction, only a 50:50 of stashing a million vs showing a thousand.

The computer is nothing without the program driving it.

...why computers anyway? Why not just some really rich guy, or a figurehead?

[Drakim]

At 1/24/09 06:04 PM, LazyDrunk wrote: Unless the computer knew anything about you, it wouldn't have the stated probability of prediction, only a 50:50 of stashing a million vs showing a thousand.

The computer is nothing without the program driving it.

...why computers anyway? Why not just some really rich guy, or a figurehead?

Because I needed a non-supernatural reason for the prediction. Throwing magic into the equation messes things up.

[LazyDrunk]

At 1/24/09 06:06 PM, Drakim wrote:

At 1/24/09 06:04 PM, LazyDrunk wrote: ..why computers anyway? Why not just some really rich guy, or a figurehead?

Because I needed a non-supernatural reason for the prediction.

Your all-knowing computer isn't supernatural?

Throwing magic into the equation messes things up.

That's probably why I can't follow the "dilemma" here. Either the PC believes you only believe what you see or only believe what you hear.

Seriously, stupid thread.

[Drakim]

At 1/24/09 06:10 PM, LazyDrunk wrote:

At 1/24/09 06:06 PM, Drakim wrote:

At 1/24/09 06:04 PM, LazyDrunk wrote: ..why computers anyway? Why not just some really rich guy, or a figurehead?

Because I needed a non-supernatural reason for the prediction.

Your all-knowing computer isn't supernatural?

It's actually not all knowing.

I mean some form of prediction isn't impossible. I'm just taking it to the extreme by upping the numbers for the benefit of this question.

Why would it need to be supernatural?

Throwing magic into the equation messes things up.

That's probably why I can't follow the "dilemma" here. Either the PC believes you only believe what you see or only believe what you hear.

What?

Seriously, stupid thread.

Seriously, stupid philosophical issues then.