Newcomb's problem

3,293 Views | 59 Replies | Last: 7 yr ago by BusterAg
BusterAg
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AG
Interesting test to see how you view the world:

https://www.theguardian.com/science/alexs-adventures-in-numberland/2016/nov/28/newcombs-problem-divides-philosophers-which-side-are-you-on

From wiki:
Quote:

A person is playing a game operated by the Predictor, an entity presented as somehow being exceptionally skilled at predicting people's actions. The player of the game is presented with two boxes, one opaque (labeled A) and the other transparent (labeled B). The player is permitted to take the contents of both boxes, or just the opaque box A. Box B contains a visible $1,000. The contents of box A, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box A, or both boxes. If the Predictor predicts that both boxes will be taken, then box A will contain nothing. If the Predictor predicts that only box A will be taken, then box A will contain $1,000,000.

What say you R&P?

Take box A, or both? Why?
Martin Q. Blank
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Take box A only. My two options are $1 million or $1000. Why not go for the $1 million? There is nothing to lose.
schmendeler
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AG
I'd be curious to know if any other contestant has actually gotten the $1 million in previous contests.
Win At Life
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AG
schmendeler said:

I'd be curious to know if any other contestant has actually gotten the $1 million in previous contests.
https://www.theguardian.com/science/alexs-adventures-in-numberland/2016/nov/28/newcombs-problem-divides-philosophers-which-side-are-you-on

Quote:

Before making your decision, you do your due diligence, and discover that the Super-Intelligent Being has never made a bad prediction.
Given this knowledge, wouldn't you pick only the unknown box every time?

[note the link switches Box A & B from what OP posted from wiki]
schmendeler
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AG
sure there may be a check for a million dollars. but the other box contains $1000 cash.
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Zobel
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AG
Astro, those outcomes are not properly weighted for probability though. From a distribution point of view, you should come up with an average outcome for the two decisions. If all outcomes are equally probable, B is the correct choice by a slight edge.

The interesting thing is that you're not wagering on your own choice but on Predictor's skill.
BusterAg
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AG
Win At Life said:

schmendeler said:

I'd be curious to know if any other contestant has actually gotten the $1 million in previous contests.
https://www.theguardian.com/science/alexs-adventures-in-numberland/2016/nov/28/newcombs-problem-divides-philosophers-which-side-are-you-on

Quote:

Before making your decision, you do your due diligence, and discover that the Super-Intelligent Being has never made a bad prediction.
Given this knowledge, wouldn't you pick only the unknown box every time?

[note the link switches Box A & B from what OP posted from wiki]
Does the fact that you choose unknown now, after the predictor has already made his decision, have any possibility to impact the predictors prediction?

If not, then you should always choose both.

If so, then you should always choose only the unknown.
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Win At Life
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AG
I'm guessing it's assumed the predictor is motivated to see that you get the least amount of money?

I think that's implied, but I didn't read it anywhere. That would make the paradox make more sense.
BusterAg
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AG
The predictor should be assumed to be motivated to predict correctly.
BusterAg
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AG
There is some truth in this.

Part of the reason it was formed was to examine the determinism / free will thingy. Which is why I thought it would be interesting here.
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schmendeler
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AG
AstroAg17 said:

Let's replace the predictor with an omniscient god, let's replace the million dollars with everlasting life, and let's replace the thousand dollars with sinful pleasures.

If you take the earthly pleasures, god will know and you won't get box A. If you plan on box A and put aside earthly pleasures, you'll get it.

We've just replaced the uncertainty of whether the predictor will correctly guess your choice with the uncertainty of whether such a God exists. The OP was secretly Pascal's wager.
hence my question if it could be shown that anyone actually gets the million dollars.
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Martin Q. Blank
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AstroAg17 said:

Let's replace the predictor with an omniscient god, let's replace the million dollars with everlasting life, and let's replace the thousand dollars with sinful pleasures.
I have never made a choice contingent on God's providence. God has never decreed anything contingent on man's choices. There's no comparison.
Star Wars Memes Only
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Unless we're ignoring causality, I don't see how it makes any sense to do anything but take both boxes. The predictor has picked before my choice is ever made. The predictor choosing and me choosing are independent events. Unless there is some gotcha causal connection here so that the two events are not independent, I don't understand how anything but taking both boxes can be the answer. Is there something deeper here that I'm missing?
Dad-O-Lot
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AG
I would pay $1000 for a 50/50 shot at $1000000

Box A only
Aggrad08
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AG
As long as each predicted event is equally likely you take both. Under no circumstance do you take the 1000. Instead of playing once, play 5 times. Ten times. The answer is clearly go big or go home.

If the big prize was smaller it gets harder to choose.
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kurt vonnegut
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When I read this question, my first thought was of Schrodingers cat. Even though the predictor has already made a prediction, his/her effective inerrancy seems to suggest that the state of box A is only determinedwhen I make a decision to choose. Probably not a perfect analogy to Schrdinger's cat, but this was my first thought.
kurt vonnegut
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AG
And what does 'exceptionally skilled' mean? Inerrant or just above average? Does being right 51% of the time while most people are right only 50% of the time qualify? If so, I'd say the predictor is blindly guessing and my decision has no affect on the outcome - thus, take both boxes.
BusterAg
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dargscisyhp said:

Unless we're ignoring causality, I don't see how it makes any sense to do anything but take both boxes. The predictor has picked before my choice is ever made. The predictor choosing and me choosing are independent events. Unless there is some gotcha causal connection here so that the two events are not independent, I don't understand how anything but taking both boxes can be the answer. Is there something deeper here that I'm missing?
The counter argument is that the predictor will know if you are going to decide to use this brand of logic, and will make sure that box A is empty if you think about the problem this way.

However, if you DECIDE to think about the problem in the way where the predictor has always been right in the past, so he will be right about my decision to choose A only, the predictor will predict that, and you will get the cool $million.

So, if the predictor can predict the way that you will logically address the problem, why not choose the logic that is going to result in a better outcome?
BusterAg
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AG
kurt vonnegut said:

And what does 'exceptionally skilled' mean? Inerrant or just above average? Does being right 51% of the time while most people are right only 50% of the time qualify? If so, I'd say the predictor is blindly guessing and my decision has no affect on the outcome - thus, take both boxes.
exceptionally skilled means he has gotten it right the last 100 times in a row.
Martin Q. Blank
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dargscisyhp said:

Unless we're ignoring causality, I don't see how it makes any sense to do anything but take both boxes. The predictor has picked before my choice is ever made. The predictor choosing and me choosing are independent events. Unless there is some gotcha causal connection here so that the two events are not independent, I don't understand how anything but taking both boxes can be the answer. Is there something deeper here that I'm missing?


The predictor would have predicted this thought process. Only $1000 for you.
BusterAg
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AG
Another aspect of this that I didn't consider until talking to my wife about it has to do with people's willingness to rely on experts.

In order to trust the predictor, you kind of have to acquiesce that he has special knowledge and an ability to reason that far surpasses your own logical / analytical abilities, and trust that his past performance is going to predict his future performance.

If you trust your own logical analysis more, and you are unwilling to admit that he may just be super smart in a way you can't understand, you are always going to take both boxes.
schmendeler
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I don't buy that "skill" alone gives one that much accuracy. at that point, it has to have supernatural ability or power to see into the future. since that's the case, i'll take the one that assures me of the million. I find this hypothetical kind of poor. there's no way anything is that good at just guessing 100 times correctly in a row. there's a fix in place. in which case, using probabilities no longer applies.
Star Wars Memes Only
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Quote:

The counter argument is that the predictor will know if you are going to decide to use this brand of logic


If the predictor knows beforehand what I'm going to predict then there is a causal connection between what I pick and what the predictor picks, and those two events are no longer independent. This certainly changes the optimal strategy, but I feel like this changes the original scenario in an important way too. In the original scenario I think it's natural to assume the two events are independent, which reverts us back to my original strategy. If we force those events to not be independent that kind of seems like a gotcha question to me. To me, the word "predict" seems misleading given the fact that we are assuming the predictor has knowledge.

To me, mathematically this seems to all boil down to whether or not these events are independent. The optimal strategy depends on that.
BusterAg
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AG
dargscisyhp said:


To me, mathematically this seems to all boil down to whether or not these events are independent. The optimal strategy depends on that.
Yeah, I guess this is restating the paradox.

Case 1: If you can believe that the events are truly independent, even based on past performance, then you always pick both.

Case 2: If you do not believe that the events are truly independent, even though you can't understand why, then you always pick the chance for $1 million.

Case 2 requires the player to accept that there is some form of mystery going on here that the player does not understand or does not have the ability to comprehend.

It really is a very interesting test for gauging how a person looks at the world.
Martin Q. Blank
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Quote:

If the predictor knows beforehand what I'm going to predict then there is a causal connection between what I pick and what the predictor picks, and those two events are no longer independent. This certainly changes the optimal strategy, but I feel like this changes the original scenario in an important way too. In the original scenario I think it's natural to assume the two events are independent, which reverts us back to my original strategy. If we force those events to not be independent that kind of seems like a gotcha question to me. To me, the word "predict" seems misleading given the fact that we are assuming the predictor has knowledge.
The predictor doesn't make a 50/50 choice. Somehow, he is exceptionally skilled. How? We're not told. He knows things about you? How you think? How you make choices? How you problem solve? He read this thread before you played the game? Who knows?

The point is, he's exceptionally skilled. So if you're like me, who would take box A only, he'd know that and I'd get a $1 million. If you're like you, who would take both, he'd know that and you'd get $1000.
Martin Q. Blank
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