7 ms·

A solution to Newcomb's paradox

26 points by erwald 5y ago

gatronicus 5y ago
Do not talk about the basilisk.
mef 5y ago
after reading the article, I don't understand why 2-boxing is correct but I'm intrigued to know if anyone else does
- sjburt 5y ago
  With the one box strategy, 90% of the time you get nothing, 10% of the time you get $1,000,000. With 2 box, 90% of the time you get $1,000, 10% of the time you get $1,001,000. More importantly, regardless of how good the computer is, the difference is always $1,000. This is the c term in the expressions at the bottom. If the computer is always wrong, with 2 boxes you always get $1,001,000. If the computer is always right, you always get $1,000. And the one box strategy always averages $1,000 less.
  - mef 5y ago
    Wait, why do you get $1M 10% of the time with the one-box strategy? The article reads: "If it predicted that you would take only B, then they put $1 million in B. " If it predicts that you will take only B, and they put $1M in B, and 90% of the time it's correct, why isn't the one-box strategy 90% likely to get you $1M?
planetsprite 5y ago
The solution is to misunderstand Newcomb's paradox and make yourself think that it's best to take 1 box, decide to take 1 box no matter what, have the machine evaluate your future decision, then read this article and then change your mind and take 2 boxes.
- FeepingCreature 5y ago
  Reading this article is also a decision the machine can evaluate.
drdec 5y ago
What we learned from that article is that Michael Huemer will only be winning $1000 if he is ever lucky enough to play this game. The key to one-boxing is to commit to it early and don't waver when the time comes.
- deleted 5y ago
  [deleted]
JoshTriplett 5y ago
This doesn't seem like an actual solution to the problem as normally stated. The point of Newcomb's problem is that if someone makes decisions on the basis of accurate prediction of your choices, you should commit to making the choice that gives you the maximum payout. In other words, the problem as stated is that if you choose both boxes there will be nothing in the opaque box, and if you choose one box there will be a large payout in the opaque box. Redefining the problem to say "they've already made the decision and filled the box or boxes, so your choice won't change the outcome" is sidestepping the point of the problem.
- remontoire 5y ago
  This is definitely not an actual solution. It's a first order solution to a non-first order problem.
civilized 5y ago
Ok, so now what if the machine is 100% accurate?
- vehemenz 5y ago
  Then you can only get $1M for one box or $1000 for two boxes. The decision becomes even more obvious then. The accuracy of the predictor does not impact the two-boxer's argument from causal independence, which I think is a serious problem for the two-boxer.
  - civilized 5y ago
    People seem to be thinking "if the predictor is not 100% accurate then I don't have to worry about the predictor, since it has already made its decision and now I should just get as much as I can". But if it's 100% accurate, your decision implies (if not causes) how much money you'll get, so shouldn't you make the decision that implies the most money? It doesn't feel right for there to be one argument that applies below 100% and another at exactly 100%.
    - vehemenz 5y ago
      > It doesn't feel right for there to be one argument that applies below 100% and another at exactly 100%. Exactly. The reason to choose one box holds whether the predictor is 90%, 99%, or 100% accurate. I think lowering the accuracy of the predictor makes two boxing look more appealing though.
      - derbOac 5y ago
        The more I think about the problem the more fiendish it is and the more I understand why it's a paradox. I think regardless of whether you agree with the author's conclusions about what is correct strategy, they're correct the paradox arises in that it pits the optimality of two different strategies against one another, where the strategies depend on the causal processes involved. I think the paradox raises a lot of questions about prediction versus causality and free will, and it's fair to ask (as another poster suggested) whether or not the machine in the paradox can ever exist. The problem is that in the case where the machine is 100% accurate, it is still not causing anything. So although it's fair to conclude in that scenario that optimal strategy is the 1-box decision, it doesn't make sense from a causal perspective because you shouldn't have any causal agency over the decision the machine made.
vlovich123 5y ago
The thought experiment part aside, isn’t the premise a logical contradiction? You may choose to flip a coin about your choice and therefore the machine cannot possibly have a 90% accurate prediction of your guess.
- FeepingCreature 5y ago
  The machine predicts that you will not choose to flip a coin. :)
  - lmm 5y ago
    Well if I do then clearly it didn't.
    - FeepingCreature 5y ago
      Exactly, but conversely my point is that the machine giving you a 90% rating is evidence that you will not choose to flip a coin. edit: Oh hang on, this is a machine, not Omega, so I can't say that Omega can just choose to not give you the offer if it can't reach 90%. Idk then. Probably it means that at least 9 out of 10 people don't throw coins.
- jerf 5y ago
  Newcomb's paradox obscures the same basic reason you can't have a Halting-Detection TM, only it covers it over with fuzzy terms and human complications. If you recast the paradox as "There exists a machine scientists made that will determine if any other intelligence will either choose the box or not the choose the box. You are that other intelligence. Do you choose the box or not choose the box?" then you can see that the same principle holds; if you incorporate the logic of the predictor into your own intelligence, you can twist the original machine's logic back on to itself in exactly the same way the Halting problem does. A subtlety to note about the halting problem is that while it is phrased in terms of that particular machine that can twist back on itself, it is itself a generalized proof of impossibility, and via Rice's theorem and lots of other work over the years it extends out into the impossibility of all sorts of other machines as well. The proof simply provides one machine that unambiguously can not be created, it is not limited to that one machine. Similarly, while a human brain that encompasses the same logic as the box-prediction machine may have technical problems in the fuzzy real-world land, the fact that such a brain would be fundamentally unpredictable means that the prediction machine can't exist. If you try to fix up the thought experiment by limiting the size of the predictor and the predictee in various ways, I suspect it isn't that hard to show that the predictor must be exponentially more complicated than the predictee in order to function, and something "exponentially larger" than the human brain doesn't really fit in the universe. And then if you try to escape by allowing arbitrarily large mathematical systems, you're back where I described above. If you try to bound how much larger the predictor has to be than the predictee, you are going to be encountering some really serious mathematical problems doing so (of the "busy beaver" mathematical sequence sorts). Given that the problem intrinsically encompasses a delay between the scan and the decision, I can simply take an ad-hoc hash function of the experiences of the last day and now the predictor needs to have also had information of my entire last day as well, and a simulation sufficiently detailed to have predicted that, too. Even if it can predict the hash function I would use (itself no guarantee since that is also conditionalized on the intervening day, potentially), it can't predict the input going into it. I think most people intuitively sense that the predictor can't really exist; I think people's intuitions are correct. It would require the predictor to have physically impossible amounts of additional resources vs. the predictee if you try to embed it in real space and time, and if you put it in math space it's nothing more and nothing less than the halting problem restated.
georgewsinger 5y ago
If you enjoyed this essay, you might also enjoy the author's fuller book Paradox Lost: Logical Solutions to Ten Puzzles of Philosophy, which covers 9 additional famous logical puzzles and offers solutions to them: https://www.amazon.com/Paradox-Lost-Logical-Solutions-Philosophy/dp/3319904892 https://www.amazon.com/Paradox-Lost-Logical-Solutions-Philos... I personally wasn't convinced by every paradox solution offered in this book, but a few of the solutions were truly stunning, and left me with the feeling that some famous philosophical paradox had been completely and unambiguously resolved (esp. in the first chapter). (I love shilling for Michael Huemer [author of this book/blog] because his philosophical books & essays have been extremely influential/clarifying in my own thinking).
vehemenz 5y ago
The original scenario as imagined by Nozick implies the probability is much higher than 90%, something close to 1. And you can't "outsmart" the machine. This actually makes a big difference when trying to "solve" the paradox, as this author attempts to do. Also, why you should 1 box: https://www.youtube.com/watch?v=Tzi3PCi0WBU https://www.youtube.com/watch?v=Tzi3PCi0WBU
deleted 5y ago
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deleted 5y ago
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sega_sai 5y ago
I don't agree with this calculation. Under the assumption that 1) you think about what to do then 2) you decide which decision to make then 3) the computer learns about it and provides it to organizers with 90% precision then I am pretty sure the the correct answer is what is provided as 'first answer' in the article. (assuming what we care about is expectation). And I think even if our strategy is probabilistic between box B and A+B the box then still chosing B box with 100% is the best stategy.
reactspa 5y ago
Fans of Taleb who are reading this: please share what you think would be the "ergodicity-rational" choice here, and why? (after all, Thales wouldn't have bothered with analysis-schmalysis). I can't share my view (yet) because I'm still not sure I understand the problem properly.
- deleted 5y ago
  [deleted]
- gatronicus 5y ago
  Taleb favours "street smarts" vs "intellectual yet idiot". In this context "street smarts" probably means being a one boxer.
daxfohl 5y ago
It depends. Need to know the algorithm. If it's just that 90% of people choose one, then it can choose that one and be right 90% of the time without even taking your brain scan into account. Or maybe 90% of males go one way and 90% of females go the other way, well that's an easy thing. Or maybe nobody ever chooses one when it's raining, and there's a 10% chance of rain tomorrow. Or, maybe it does a perfect simulation and knows exactly what you'll choose, but flips it 10% of the time just for fun. Any of those would have different ways of optimizing, so it doesn't make sense to speculate without knowing exactly how it works.
- daxfohl 5y ago
  One interesting thing, any scenario I devise where choosing one box wins also implies lack of free choice. IDK if this can be proved, but it seems to be the case.

26 points by erwald 5y ago

gatronicus 5y ago

Do not talk about the basilisk.

mef 5y ago

after reading the article, I don't understand why 2-boxing is correct but I'm intrigued to know if anyone else does

sjburt 5y ago
With the one box strategy, 90% of the time you get nothing, 10% of the time you get $1,000,000. With 2 box, 90% of the time you get $1,000, 10% of the time you get $1,001,000. More importantly, regardless of how good the computer is, the difference is always $1,000. This is the c term in the expressions at the bottom. If the computer is always wrong, with 2 boxes you always get $1,001,000. If the computer is always right, you always get $1,000. And the one box strategy always averages $1,000 less.
- mef 5y ago
  Wait, why do you get $1M 10% of the time with the one-box strategy? The article reads: "If it predicted that you would take only B, then they put $1 million in B. " If it predicts that you will take only B, and they put $1M in B, and 90% of the time it's correct, why isn't the one-box strategy 90% likely to get you $1M?

planetsprite 5y ago

The solution is to misunderstand Newcomb's paradox and make yourself think that it's best to take 1 box, decide to take 1 box no matter what, have the machine evaluate your future decision, then read this article and then change your mind and take 2 boxes.

FeepingCreature 5y ago
Reading this article is also a decision the machine can evaluate.

drdec 5y ago

What we learned from that article is that Michael Huemer will only be winning $1000 if he is ever lucky enough to play this game. The key to one-boxing is to commit to it early and don't waver when the time comes.

deleted 5y ago
[deleted]

JoshTriplett 5y ago

This doesn't seem like an actual solution to the problem as normally stated. The point of Newcomb's problem is that if someone makes decisions on the basis of accurate prediction of your choices, you should commit to making the choice that gives you the maximum payout. In other words, the problem as stated is that if you choose both boxes there will be nothing in the opaque box, and if you choose one box there will be a large payout in the opaque box. Redefining the problem to say "they've already made the decision and filled the box or boxes, so your choice won't change the outcome" is sidestepping the point of the problem.

remontoire 5y ago
This is definitely not an actual solution. It's a first order solution to a non-first order problem.

civilized 5y ago

Ok, so now what if the machine is 100% accurate?

vehemenz 5y ago
Then you can only get $1M for one box or $1000 for two boxes. The decision becomes even more obvious then. The accuracy of the predictor does not impact the two-boxer's argument from causal independence, which I think is a serious problem for the two-boxer.
- civilized 5y ago
  People seem to be thinking "if the predictor is not 100% accurate then I don't have to worry about the predictor, since it has already made its decision and now I should just get as much as I can". But if it's 100% accurate, your decision implies (if not causes) how much money you'll get, so shouldn't you make the decision that implies the most money? It doesn't feel right for there to be one argument that applies below 100% and another at exactly 100%.
  - vehemenz 5y ago
    > It doesn't feel right for there to be one argument that applies below 100% and another at exactly 100%. Exactly. The reason to choose one box holds whether the predictor is 90%, 99%, or 100% accurate. I think lowering the accuracy of the predictor makes two boxing look more appealing though.
    - derbOac 5y ago
      The more I think about the problem the more fiendish it is and the more I understand why it's a paradox. I think regardless of whether you agree with the author's conclusions about what is correct strategy, they're correct the paradox arises in that it pits the optimality of two different strategies against one another, where the strategies depend on the causal processes involved. I think the paradox raises a lot of questions about prediction versus causality and free will, and it's fair to ask (as another poster suggested) whether or not the machine in the paradox can ever exist. The problem is that in the case where the machine is 100% accurate, it is still not causing anything. So although it's fair to conclude in that scenario that optimal strategy is the 1-box decision, it doesn't make sense from a causal perspective because you shouldn't have any causal agency over the decision the machine made.

vlovich123 5y ago

The thought experiment part aside, isn’t the premise a logical contradiction? You may choose to flip a coin about your choice and therefore the machine cannot possibly have a 90% accurate prediction of your guess.

FeepingCreature 5y ago
The machine predicts that you will not choose to flip a coin. :)
- lmm 5y ago
  Well if I do then clearly it didn't.
  - FeepingCreature 5y ago
    Exactly, but conversely my point is that the machine giving you a 90% rating is evidence that you will not choose to flip a coin. edit: Oh hang on, this is a machine, not Omega, so I can't say that Omega can just choose to not give you the offer if it can't reach 90%. Idk then. Probably it means that at least 9 out of 10 people don't throw coins.
jerf 5y ago
Newcomb's paradox obscures the same basic reason you can't have a Halting-Detection TM, only it covers it over with fuzzy terms and human complications. If you recast the paradox as "There exists a machine scientists made that will determine if any other intelligence will either choose the box or not the choose the box. You are that other intelligence. Do you choose the box or not choose the box?" then you can see that the same principle holds; if you incorporate the logic of the predictor into your own intelligence, you can twist the original machine's logic back on to itself in exactly the same way the Halting problem does. A subtlety to note about the halting problem is that while it is phrased in terms of that particular machine that can twist back on itself, it is itself a generalized proof of impossibility, and via Rice's theorem and lots of other work over the years it extends out into the impossibility of all sorts of other machines as well. The proof simply provides one machine that unambiguously can not be created, it is not limited to that one machine. Similarly, while a human brain that encompasses the same logic as the box-prediction machine may have technical problems in the fuzzy real-world land, the fact that such a brain would be fundamentally unpredictable means that the prediction machine can't exist. If you try to fix up the thought experiment by limiting the size of the predictor and the predictee in various ways, I suspect it isn't that hard to show that the predictor must be exponentially more complicated than the predictee in order to function, and something "exponentially larger" than the human brain doesn't really fit in the universe. And then if you try to escape by allowing arbitrarily large mathematical systems, you're back where I described above. If you try to bound how much larger the predictor has to be than the predictee, you are going to be encountering some really serious mathematical problems doing so (of the "busy beaver" mathematical sequence sorts). Given that the problem intrinsically encompasses a delay between the scan and the decision, I can simply take an ad-hoc hash function of the experiences of the last day and now the predictor needs to have also had information of my entire last day as well, and a simulation sufficiently detailed to have predicted that, too. Even if it can predict the hash function I would use (itself no guarantee since that is also conditionalized on the intervening day, potentially), it can't predict the input going into it. I think most people intuitively sense that the predictor can't really exist; I think people's intuitions are correct. It would require the predictor to have physically impossible amounts of additional resources vs. the predictee if you try to embed it in real space and time, and if you put it in math space it's nothing more and nothing less than the halting problem restated.

georgewsinger 5y ago

If you enjoyed this essay, you might also enjoy the author's fuller book Paradox Lost: Logical Solutions to Ten Puzzles of Philosophy, which covers 9 additional famous logical puzzles and offers solutions to them: https://www.amazon.com/Paradox-Lost-Logical-Solutions-Philosophy/dp/3319904892 https://www.amazon.com/Paradox-Lost-Logical-Solutions-Philos... I personally wasn't convinced by every paradox solution offered in this book, but a few of the solutions were truly stunning, and left me with the feeling that some famous philosophical paradox had been completely and unambiguously resolved (esp. in the first chapter). (I love shilling for Michael Huemer [author of this book/blog] because his philosophical books & essays have been extremely influential/clarifying in my own thinking).

vehemenz 5y ago

The original scenario as imagined by Nozick implies the probability is much higher than 90%, something close to 1. And you can't "outsmart" the machine. This actually makes a big difference when trying to "solve" the paradox, as this author attempts to do. Also, why you should 1 box: https://www.youtube.com/watch?v=Tzi3PCi0WBU https://www.youtube.com/watch?v=Tzi3PCi0WBU

deleted 5y ago

[deleted]

deleted 5y ago

[deleted]

sega_sai 5y ago

I don't agree with this calculation. Under the assumption that 1) you think about what to do then 2) you decide which decision to make then 3) the computer learns about it and provides it to organizers with 90% precision then I am pretty sure the the correct answer is what is provided as 'first answer' in the article. (assuming what we care about is expectation). And I think even if our strategy is probabilistic between box B and A+B the box then still chosing B box with 100% is the best stategy.

reactspa 5y ago

Fans of Taleb who are reading this: please share what you think would be the "ergodicity-rational" choice here, and why? (after all, Thales wouldn't have bothered with analysis-schmalysis). I can't share my view (yet) because I'm still not sure I understand the problem properly.

deleted 5y ago
[deleted]
gatronicus 5y ago
Taleb favours "street smarts" vs "intellectual yet idiot". In this context "street smarts" probably means being a one boxer.

daxfohl 5y ago

It depends. Need to know the algorithm. If it's just that 90% of people choose one, then it can choose that one and be right 90% of the time without even taking your brain scan into account. Or maybe 90% of males go one way and 90% of females go the other way, well that's an easy thing. Or maybe nobody ever chooses one when it's raining, and there's a 10% chance of rain tomorrow. Or, maybe it does a perfect simulation and knows exactly what you'll choose, but flips it 10% of the time just for fun. Any of those would have different ways of optimizing, so it doesn't make sense to speculate without knowing exactly how it works.

daxfohl 5y ago
One interesting thing, any scenario I devise where choosing one box wins also implies lack of free choice. IDK if this can be proved, but it seems to be the case.