ForumsWEPRNewcomb's paradox

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Einfach
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Einfach
1,448 posts
Nomad

Newcomb's Problem - Please read the first three paragraphs of the link before commenting

What do you do?

Do not say the Being does not exist, because that is assumed in the problem.

  • 78 Replies
Kyouzou
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Kyouzou
5,061 posts
Jester

Perhaps I'm reading this too critically, but the paradox states that one of the boxes contains a $1000 bill, something that doesn't exist at this point in time. When considering this, you take into account that the second box contains a million dollars, with no specific denominations mentioned. Wouldn't you rather take the sure chance of a million dollars, than some monopoly money?

Einfach
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Einfach
1,448 posts
Nomad

@Kyouzou - you're missing the point of the thought experiment - the point is not that a $1000 bill doesn't exist, even in monopoly.

the sure chance of a million dollars


Sure chance is an oxymoron :P
MageGrayWolf
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MageGrayWolf
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Farmer

but the paradox states that one of the boxes contains a $1000 bill, something that doesn't exist at this point in time.


They do exist they just haven't been in circulation since 1934.
http://en.wikipedia.org/wiki/File:1000-2f.jpg
Einfach
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Einfach
1,448 posts
Nomad

OK - I am going to make the case right now that it is better to choose both boxes:

So say you chose both boxes, and the Being predicted that you would. That means that you get $1,000. If you had chosen otherwise, you would have received nothing.

Say you chose both boxes, and the Being predicted that you would choose only the closed box. That means you get $1,001,000. If you had chosen otherwise, you would have only received $1,000,000.

Please note that your choice does not affect the chance of the being putting the million dollars in the box, because either the Being has or the Being hasn't. In either of these cases, it is better to chose both boxes, as you will receive $1,000 more. Your choice is independent of the Being's choice to put the money in the box or not.

Kyouzou
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Kyouzou
5,061 posts
Jester

Mage that's why I said

at this point in time.
Moe
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Moe
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Blacksmith

Your choice is independent of the Being's choice to put the money in the box or not.


That depends on how the being predicts what you will choose.
MageGrayWolf
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MageGrayWolf
9,462 posts
Farmer

at this point in time.


But that's not quite n accurate statement. It's not that we don't have this money at this point, it's just that it's not currently being used.
Secretmapper
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Secretmapper
1,747 posts
Nomad

I'll take the closed box. Yes, I tried reading both the link's contents, and the thread comments, but after page 4, my head hurts..

Moegreche
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Moegreche
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Duke

OK - I am going to make the case right now that it is better to choose both boxes:


I like your setup there, Einfach. And you make a pretty solid case - taking both boxes does, in fact, guarantee that you'll get at least $1000. You correctly point out that by taking only the closed box, it is still possible to receive nothing.

But let's bring in some decision theory to this. Right now, you're basing your decision on the fact that you're at least guaranteed some money. Nothing wrong with that stance, but the proponent of a decision theory based assessment is going to say you should maximize the utility of the situation. In other words, you shouldn't be satisfied with receiving a guaranteed $1K. Instead, you should want to maximize the amount of money you can make.

The assessment is going to be based on the confidence of a particular outcome. In your case, given the parameters of the experiment, it seems okay to say that your confidence of getting at least $1000 is 1 (that is, 100% confident). The outcome space for this event is 2 (getting $1K and getting an additional million) and is fully exhaustive.

But what is your confidence that you'll receive $1,000 versus the confidence that you'll receive $1,001,000? Let's say you have a confidence level of .95 that the being will accurately predict your decision. Thus con($1000) = .95 In other words, the confidence you have in getting $1000 is 95%, and the confidence in getting the extra million is 5%.
Note this is far more conservative than the problem is suggesting, which seems to be a .999 confidence level. I just think that .999 is a little high, and the argument I'm using still works for .95
So, you have .95 confidence that you'll get $1000.
But if you decide to take the closed box (and again, assuming you are 95% certain the being's prediction will be accurate) then you get: con($1,000,000) = .95.
Now, the decision theorist has a way of calculating the "monetary value" of a particular outcome by applying the confidence level to the monetary gain. Since choosing both nets you at least a grand, your monetary value will simply be $,1000 for that event. You're not expecting anything more (nor should you be) and you're guaranteed at least that amount.
For both boxes, the monetary value would be something like $950,000 given your confidence level. You are almost certain to receive a million smackers by choosing the closed box.
The decision theorist wants to argue here that the preferable bet is the one with the greater monetary value - taking the closed box. Otherwise, he would argue, your decision isn't rational because it fails to meet the Kolmogorov axioms of probability (thus leaving you open to Dutch Book bets).

Put simply: isn't it worth taking a slight risk to maximize your utility over getting a sure, but much smaller, amount?
Rodoubica
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Rodoubica
25 posts
Nomad

id chose one box...with a milion $ in it..XD

chang
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chang
846 posts
Nomad

Well this is interesting, I don't want to read through all of the previous pages.
This being claims to know what you will pick. This being claims to put a million dollars in the closed box if he knows you will take it. I propose the following take the closed box but open the closed box so it is now the open box, but the 1 million dollars is already in it because you did take the closed box. But then take the second box which is an open box and close it so it is now a closed box and then take it as well. You know have both boxes except one box is open and contains a million dollars but the other box is closed and contains a 1-thousand dollar bill. So you followed his instructions and took the closed box...BUT TWICE
Mwhahaha

Drace
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Drace
3,880 posts
Nomad

Sorry Moe, I misread the situation. But the answer seems much more clearer to me nonetheless.

If you wanted to maximize utility, why would you not choose the closed box? The probability of gaining the million is almost certain, if not destined.
Given the logical choice, there is no reason not to pick the closed box.
If you took both boxes, he would have most likely have guessed that you would, and you forfeit the one million dollars.

While you mentioned the confidence level of such a risk is .999, it could very well be a possibility that the being's prediction always holds true. Based on induction, we could generalize the statement that the being has been right the past 999 times by stating that he is omniscient. It is obviously beyond chance that the being is able to make such predictions and thus we can conclude that there is a definite answer as to why he is able to do so. ie, it is a predetermined event and the being is always right. Given that, the riddle is useless. But then again, if this reasoning fails, then he could simple be extremely talented at guessing, or just pure lucky up to this point.

The only paradox that is presented is from the decision the being would have to make if he were not omniscient or near omniscient. Then the player and the being would be involved in a mind game over who was going to pick what. "He probably guessed the closed box knowing that I would pick both boxes. But him probably knowing that I know this, I should pick the both boxes...."

But since that doesn't exist, its a useless quarrel. Since the being is certainly likely to pick the box you will choose, its simply "If I pick the closed box, I get a million dollars. If I pick both boxes, I get $1000 and a 1/1000 chance for a million dollars"

sk8brder246
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sk8brder246
740 posts
Nomad

why is everyone making such a big deal out of this choose the closed box get a million dollars. choos the open one get a thousand dollars. its simple choose the closed one. a thousand dollars doesnt really matter when you just snagged a million dollars from a being. thats a good day in my book

Moegreche
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Moegreche
3,826 posts
Duke

If you wanted to maximize utility, why would you not choose the closed box?


And that seems like the most reasonable response. Yet you know that there's another $1,000 in the box right next to it. So by having overwhelming reason to choose the closed box, you suddenly get overwhelming reason to choose both boxes. And thus the paradox takes hold.

Based on induction, we could generalize the statement that the being has been right the past 999 times by stating that he is omniscient.


And inductive principle makes an inference from observed cases to unobserved ones. You're right in that there is induction at play here: the fact that the being has been right 999 times in the past (and hasn't yet been wrong) gives you a very good reason to believe that it'll be right this time. But to infer from this fact that the being is omniscient isn't supported by inference.
Maybe what you're thinking is abductive reasoning, rather that inductive. This is the inference to the best explanation. But I'm not sure that omniscience - even in this limited respect - is really the best explanation. It may be, I'm just expressing a worry about this kind of inference.

Then the player and the being would be involved in a mind game over who was going to pick what.


Exactly. Now, you and I would just take the closed box no questions asked. I mean a million bucks is nothing to sneeze at!
But think about that moment just before you grab that closed box. You know full well that there's $1,000 in that other box. And you know the contents of the box you're about to pick up is already set - there's no changing it. It may be awfully tempting to take that box as well.
For the relevant decision theories under discussion, this possibility can't be ignored. There's an opportunity at the moment before you pick up the box to increase you overall "utility" by 1,000. To not take both boxes at this moment would be, for these theories, an irrational decision.
Now maybe this is just a problem for these decision theories. After doing a bit of work, it looks like Kaplan's Modest Probabilism could offer a way out given the possible state of affairs. But I think I'm going to write a paper on that one, which kind of prevents me from talking about it :P

But let's take decision theory out of it completely. You've decided to take the closed box thinking it's overwhelmingly likely that you're about to be a millionaire. Now imagine an observer who can see the content of both boxes. Wouldn't he think you're irrational for not taking both boxes? Regardless of what's in the closed box, you have another $1,000 within arms reach.
Moe
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Moe
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Blacksmith

But think about that moment just before you grab that closed box. You know full well that there's $1,000 in that other box. And you know the contents of the box you're about to pick up is already set - there's no changing it. It may be awfully tempting to take that box as well.
For the relevant decision theories under discussion, this possibility can't be ignored. There's an opportunity at the moment before you pick up the box to increase you overall "utility" by 1,000. To not take both boxes at this moment would be, for these theories, an irrational decision.


But whats to say the being wouldn't know you would make a grab for both boxes at the last minute?
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