Newcomb's paradox
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Newcomb's paradox
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Re: Newcomb's paradox
#2Worth mentioning Scott Aaronson's blog post (http://www.scottaaronson.com/blog/?p=30), and a lot of discussion on Less Wrong over the years (http://wiki.lesswrong.com/wiki/Newcomb%27s_problem).
Re: Newcomb's paradox
#3I guess this boils down to whether you believe in determinism.
If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money.
If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.
Re: Newcomb's paradox
#4I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money. If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.
It reminds me of the 'Battle of Wits' scene in The Princess Bride: http://c2.com/cgi/wiki?BattleOfWits
Re: Newcomb's paradox
#5I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money. If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.
That's not really the point of the thought experiment at all. And invoking randomness doesn't make the thought experiment easier, just more complicated. From the link someone posted above:
>(Incidentally, don’t imagine you can wiggle out of this by basing your decision on a coin flip! For suppose the Predictor predicts you’ll open only the first box with probability p. Then he’ll put the $1,000,000 in that box with the same probability p. So your expected payoff is 1,000,000p2 + 1,001,000p(1-p) + 1,000(1-p)2 = 1,000,000p + 1,000(1-p), and you’re stuck with the same paradox as before.)
Re: Newcomb's paradox
#6I think there's a weak echo of this concept that plays out in an election. Except swap in the inconvenience of voting for giving up the $1,000 box.
On the one hand, why bother voting? It's a pain in the ass and my single vote has such a negligible effect. On the other hand, if everyone like me has that same attitude, then I and others like me lose our voice in the election. So should I vote, or not?
Re: Newcomb's paradox
#7I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money. If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.
It's not about changing your mind for the money, it's about the fact that causality doesn't (shouldn't) run backwards in time.
Consider this: when you are faced with the choice, the allotted money is already under the boxes. How could what you choose now affect this outcome? It can't. You must always take both boxes to get the maximum amount of money possible. Either the $1,000,000 is under the single box, or it is not. If you take both boxes, you will get $1000 regardless of anything else, and possibly $1,001,000. If you take the single box, you will either get $0 or $1,000,000, but your action can't possibly change that, unless you believe somehow that causality runs backwards in time.
Re: Newcomb's paradox
#8For the risk-averse:
Make a bet with someone for $500,000.00 that you can prove The Predictor is fallible. Take only box B. If box B contains $1,000,000.00, then you have lost the bet and you are left with only $500,000.00. If box B contains no money, you have wone the bet and are left with $500,000.00.
Re: Newcomb's paradox
#9I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money. If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.
That is not the issue at all. There are two main ways of seeing the problem:
1. If the predictor really has such an awesome predicting talent, you have to wonder why. How much information must she have the means to process in order to make such successful predictions? Do you really think you could outperform her?
2. It doesn't matter what she predicts, because the result is independent of her prediction.
This is a problem about determining what is more important to rational decision-making: newly discovered information advantages, or previously known truths. Do you bet on the powerful new technology, or the tried and true past solution? Do you hire the person with a proven track-record of reliable success, or the unproven one with the ground-breaking earth-shattering new idea?
Re: Newcomb's paradox
#10I guess this boils down to whether you believe in determinism. If you do, then the predictor will always be right, and you have essentially zero chance of fooling it by "changing your mind" later for the extra money. If you don't believe in such a thing, then theoretically some nondeterministic volition of yours could allow you to change your mind in a way that the predictor could not have deterministically forseen.
It's not about changing your mind for the money, it's about the fact that causality doesn't (shouldn't) run backwards in time. Consider this: when you are faced with the choice, the allotted money is already under the boxes. How could what you choose now affect this outcome? It can't. You must always take both boxes to get the maximum amount of money possible. Either the $1,000,000 is under the single box, or it is n…
Your assuming something along the lines of free will. Remember the choice is made independent of what's in the boxes.
So, let's consider a deterministic system. If I write a program that uses pure logic to make the choice and it's non random then it always makes the same choice. EX: hard coding chose (A+B).
Then that choice has in effect already made based on the algorithm selection making the (A+B) prediction basically fool proof. I could of course then run that program after the fact and see (A+B), but barring a low chance random event it's going to give the result of my prediction.
PS: Consider chess, from a math standpoint every possible game already exists with players essentially picking just one game from the set of possible games. So, if you write two deterministic programs and run them the winner is already predetermined based on which algorithms where selected. If you then change one of the programs in such a way that it still chose the same move you know the winner before running the programs.