6 ms·

Newcomb's Paradox Needs a Demon

15 points by sestep 7mo ago

danbruc 7mo ago
The existence of a flawless predictor means that you do not have a choice after the predictor made its prediction, the decision must already be baked into the state of the universe accessible to the predictor. It also precludes that any true randomness is affecting the choice as that could not be predicted ahead of time. I do not think that allowing some prediction error fundamentally changes this, it only means that sometimes the choice may depend on unpredictable true randomness or sometimes the predictor does not measured the relevant state of the universe exactly enough or the prediction algorithm is not flawless. But if the predictor still arrives at the correct prediction most of the time, then most of the time you do not have a choice and most of the time the choice does not depend on true randomness. Which also renders the entire paradox somewhat moot because there is no choice for you to be made. The existence of a good predictor and the ability to make a choice after the prediction are incompatible. Up to wild time travel scenarios and thinks like that.
- halfcat 7mo ago
  A flawless predictor would indicate you’re in a simulation, but also we cannot even simulate multiple cells at the most fine-grained level of physics. But also you’re right that even a pretty good (but not perfect) predictor doesn’t change the scenario. What I find interesting is to change the amounts. If the open box has $0.01 instead of $1000, you’re not thinking ”at least I got something”, and you just one-box. But if both boxes contain equal amounts, or you swap the amounts in each box, two-boxing is always better. All that to say, the idea that the right strategy here is to ”be the kind of person who one-boxes” isn’t a universe virtue. If the amounts change, the virtues change.
  - danbruc 7mo ago
    A flawless predictor would indicate you’re in a simulation [...] No, it does not. Replace the human with a computer entering the room, the predictor analyzes the computer and the software running on the computer when it enters. If the decision program does not query a hardware random source or some stray cosmic particle changes the choice, the predictor could perfectly predict the choice just by accurately enough emulating the computer. If the program makes any use of external inputs, say the image from an attached webcam, the predictor also needs to know those inputs well enough. The same could, at least in principle, work for humans.
    - vidarh 7mo ago
      I agree with you that it doesn't require that you are in a simulation, but a flawless predictor would be a strong indication that a simulation is possible, and that should raise our assumed probability that we're in a simulation.
      - arethuza 7mo ago
        I would think that the existence of a flawless predictor is probably more likely to indicate that memories of predictions, and any associated records, have been modified to make the predictor appear flawless.
        vidarh 7mo ago
        I would say that if we presume memories of everyone involved have been modified, that is an equally strong predictor that we are in a simulation.
        danbruc 7mo ago
        Where does this obsession with the simulation hypothesis come from, it has been so widespread in the last years? It is more or less pointless to think about it, it will not get you anywhere. You only know this universe, to some extend, but you have no idea what a real universe looks like and you have no idea what a simulated universe looks like, so you will never be able to tell which kind our universe is. But what if we discover that our universe is made from tiny voxels or something like that, that will be undeniable evidence, right? Wrong! Who says that real universes are not made of tiny voxels? It could be [1] the other way around, maybe real universes are discrete but their universe simulations are continuous, in which case the lack of tiny voxels in our universe would be the smoking gun evidence for being in a simulation. [1] This is meant as an example, I have no idea if one can actually come up with a discrete universe that admits continuous simulations, which probably should also be efficient in some sense.
- ordu 7mo ago
  > Which also renders the entire paradox somewhat moot because there is no choice for you to be made. Not quite. You did choose your decision making methods at some point in your life, and you could change them multiple times till you came to the setup of Newcomb's paradox. If we look at your past life as a variable in the problem, then changing this variable changes the outcome, it changes the prediction made by the predictor. > The existence of a flawless predictor means that you do not have a choice after the predictor made its prediction I believe, that if your definition of a choice stop working if we assume a deterministic Universe, then you need a better definition of a choice. In a deterministic Universe becomes glaringly obvious that all the framework of free will and choice is just an abstraction, that abstract away things that are not really needed to make a decision. Moreover I think I can hint how to deal with it: relativity. Different observers cannot agree if an observed agent has free will or not. Accept it fundamentally, like relativity accepts that the universal time doesn't exist, and all the logical paradoxes will go away.
  - chriswarbo 7mo ago
    > I believe, that if your definition of a choice stop working if we assume a deterministic Universe, then you need a better definition of a choice. In a deterministic Universe becomes glaringly obvious that all the framework of free will and choice is just an abstraction, that abstract away things that are not really needed to make a decision. Indeed, I think of concepts like "agency", "choice", "free will", etc. as aspects of a particular sort of scientific model. That sort of model can make good predictions about people, organisations, etc. which would be intractable to many other approaches. It can also be useful in situations that we have more sophisticated models for, e.g. treating a physical system as "wanting" to minimise its energy can give a reasonable prediction of its behaviour very quickly. That sort of model has also been applied to systems where its predictive powers aren't very good; e.g. modelling weather, agriculture, etc. as being determined by some "will of the gods", and attempting to infer the desires of those gods based on their observed "choices". It baffles me that some people might think a model of this sort might have any relevance at a fundamental level.
  - vidarh 7mo ago
    This is a compatibilist view. However, we can tell that most people don't adhere to a compatibilist view of free will because it tends to make people very upset if you suggest they have no "genuine" free will or agency, and the moral implications behind the assumption of genuine agency are e.g. baked into everything from our welfare systems to our justice systems, that assumes people have an actual choice in what they do. For that reason I strongly disagree with the compatibilist view - language is defined by use, and most people act in ways that clearly signal a non-compatibilist view of free will.
jack_pp 7mo ago
There's rational and then there's common sense, if put in that situation who in their right mind would take even a 50% chance that the entity is wrong and greed it for 1000$. All I'd need to know is that it is far more likely I get the million if I go into the game thinking I'd only one-box
gegtik 7mo ago
In some ways it is an interesting problem about whether someone can engage a question about a hypothetic question -- and for the purpose of the exercise, assume the proposed parameters of the scenario.
vidarh 7mo ago
Assuming I have no way of testing the predictor, my decision would be to pick both boxes on the basis that $1000 is not a lot of money to me, but $1000000 is, and I wouldn't worry about the odds, because without knowing the nature of the specific predictor we're down to Pascal's Wager married to the Halting Problem: We don't know whether or how our actions and thought processes processes might affect the outcome, and so any speculation over odds is meaningless and devolves to making assumptions we can't test, without even knowing whether that speculation itself might alter the outcome, or how. But I don't need to speculate about the relative value of $1000 and $1000000 to me. Others might opt for the safe $1000 for the same reason.
- malfist 7mo ago
  Two boxes is the only choice that makes sense. It is always better than one box. No matter what you do after you enter the room, the predictor has already made their move, nothing you do now will change it. The only logical thing to do is to take both boxes because whatever the value in the second box is it will be added to the first box. If you only take the second box you are objectively always giving up $1,000 and getting no value in exchange for doing so (since not taking the first box doesn't change what's in the second)
  - Smaug123 7mo ago
    And for you, of course, that's true! Because you are the sort of being who two-boxes, and this fact is visible to the predictor. Other types of being can do better.
    - dalmo3 7mo ago
      This is the best reply in this thread, as it irrefutably demonstrates this so-called paradox is a religious question and has nothing to do with logic or probability. The question is do you believe in an omniscient god or not. The fact that they dress up god as a supercomputer and that attracts all sorts of math and tech nerds is hilarious.
  - OskarS 7mo ago
GaelFG 7mo ago
I don't get the 'choice' : the content of the box is aldready defined when you take your decision so taking it won't change the content of the black box and the open/transparent box have no drawback. What am I missing ?
- xigoi 7mo ago
  Assuming that the predictor is always right, there are only two possible scenarios: • You take one box and get $1000000 • You take two boxes and get $1000 The choice seems quite clear to me.
  - GaelFG 7mo ago
    Not from the article : Before you walk in, a supercomputer predicted which choice you'd make, and put $1000000 in the opaque box if it predicted you'd take just the one, or $0 if it predicted you'd take both. So the amount of money in the black box don't change whatever you REALLY pick. Either the predicator would have guessed you'd pick both and there is 0$ in black box, in that case you have interest to take both boxes and win $1000 which is better than zero. Or it predicted you would only take the black box, put $1000000 in it and then again you win more by taking the two boxes.
    - xigoi 7mo ago
      This is exactly what’s funny about the paradox – we both think that our choice is completely obvious. My argument is that since the predictor is always right, the situation where you choose two boxes and you get $1001000 simply cannot happen, because then the predictor would’ve predicted your choice and placed nothing in the variable box.
gradschool 7mo ago
I don't know about y'all, but this paradox was resolved to my complete satisfaction in a blog post some years ago, I believe by Scott Aaronson, though I can't find the link. If the predictor has such a good success rate, then it must be simulating people's brains, but since it's not always right, the simulation isn't perfect. The best strategy for playing this game therefore is to look for indications as to whether I'm the real me or the simulation when the question is posed to me, and choose accordingly. Am I floating in a sensory deprivation tank being asked my choice by a disembodied voice with no recollection of how I got there and no memory of my childhood? In that case maybe I'm the simulation, so my answer is that I'll choose just one box. Is it an ordinary day of my life and a plausible setting with all of my faculties and recollections intact? Then I'll assume simulated me had my back and take both boxes.
djoldman 7mo ago
For folks reasoning through the "paradox," this may be helpful: https://arxiv.org/pdf/0904.2540 https://arxiv.org/pdf/0904.2540 Abstract: > ...We show that the conflicting recommendations in Newcomb’s scenario use different Bayes nets to relate your choice and the algorithm’s prediction. These two Bayes nets are incompatible. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the specification of the underlying Bayes net is open to two, conflicting interpretations...
genshii 7mo ago
I've been presented with this thought experiment before and I always feel like I'm missing something when other people talk about it. Why would you ever take both boxes? The premise is that the predictor is always right. So whether you take one or both boxes, the predictor would have predicted that choice. We know from the setup that if the predictor said you would take the one box, it will have a million dollars. Therefore, if you take the one box it will have a million dollars in it (because whatever you choose is what the predictor predicted). As an aside, I think whatever this says about free will or if you're actually making a "choice" is irrelevant in regards to if the million dollars is in the box. The way I see both choices is this: You "decide" to take both boxes -> the perfect predictor predicted this -> the opaque box has zero dollars -> you get a thousand dollars You "decide" to take the opaque (one) box -> the perfect predictor predicted this -> the opaque box has a million dollars -> you get a million dollars If you want to consider the version of this where the predictor is almost perfect instead of truly perfect, I don't think that changes anything. Say it's 99% accurate or even 90% accurate. You take the opaque box -> the predictor has a 90% chance of predicting this -> it follows that there's a 90% chance that the box has a million dollars -> you have a 90% chance of getting a million dollars Had you picked both boxes, you have a 90% chance of not getting the million.
- mcphage 7mo ago
  > Why would you ever take both boxes? As near as I can tell, it boils down to this: no matter what the predictor has chosen, one you walk into that room, there's more money in both boxes, then there is in one box. But it feels like half an analysis—focusing solely on what you decide, while ignoring the fact that the other side is deciding based on what you think they'll decide. Maybe that's me being unfair, because I'm a solid one boxer. I also disagree with the linked article—I don't think it matters at all how the predictor makes their decision, because the outcome really doesn't matter if it's 100% accurate or 99% accurate. Or even like, 80% accurate. There's no magic required for the experiment to work.
  - vidarh 7mo ago
    Even if it's 50% accurate the benefit of picking both is marginal. If it's 50% accurate and you pick both boxes, 50% of the time you get nothing, 50% of the time you get 0.1% more. So unless you know that the predictor is worse than chance, you at worst suffer a meaningless loss if you pick one box.
imtringued 7mo ago
I can't get behind this paradox, because the setup is too contrived and complicated. I'd take the $1000 box without the second box just to mess with the computer. Free money scenarios are always suspect so why would you ever expect to get a million dollars out of one?
bennettnate5 7mo ago
Here's a potential winning strategy: take a coin out of your pocket and flip it 100 times. If it lands heads 51 or more times, take both boxes; otherwise, just take the one. Provided the computer had anticipated you being the kind of person that would do this, it would anticipate you are probabilistically more likely to take the single box exclusively and put the million dollars in it. Regardless of the outcome of the coin tosses, you get that million dollar box, and you still get the added $1000 in the first box 49% of the time.

15 points by sestep 7mo ago

The existence of a flawless predictor means that you do not have a choice after the predictor made its prediction, the decision must already be baked into the state of the universe accessible to the predictor. It also precludes that any true randomness is affecting the choice as that could not be predicted ahead of time. I do not think that allowing some prediction error fundamentally changes this, it only means that sometimes the choice may depend on unpredictable true randomness or sometimes the predictor does not measured the relevant state of the universe exactly enough or the prediction algorithm is not flawless. But if the predictor still arrives at the correct prediction most of the time, then most of the time you do not have a choice and most of the time the choice does not depend on true randomness. Which also renders the entire paradox somewhat moot because there is no choice for you to be made. The existence of a good predictor and the ability to make a choice after the prediction are incompatible. Up to wild time travel scenarios and thinks like that.

halfcat 7mo ago
A flawless predictor would indicate you’re in a simulation, but also we cannot even simulate multiple cells at the most fine-grained level of physics. But also you’re right that even a pretty good (but not perfect) predictor doesn’t change the scenario. What I find interesting is to change the amounts. If the open box has $0.01 instead of $1000, you’re not thinking ”at least I got something”, and you just one-box. But if both boxes contain equal amounts, or you swap the amounts in each box, two-boxing is always better. All that to say, the idea that the right strategy here is to ”be the kind of person who one-boxes” isn’t a universe virtue. If the amounts change, the virtues change.
- danbruc 7mo ago
  A flawless predictor would indicate you’re in a simulation [...] No, it does not. Replace the human with a computer entering the room, the predictor analyzes the computer and the software running on the computer when it enters. If the decision program does not query a hardware random source or some stray cosmic particle changes the choice, the predictor could perfectly predict the choice just by accurately enough emulating the computer. If the program makes any use of external inputs, say the image from an attached webcam, the predictor also needs to know those inputs well enough. The same could, at least in principle, work for humans.
  - vidarh 7mo ago
    I agree with you that it doesn't require that you are in a simulation, but a flawless predictor would be a strong indication that a simulation is possible, and that should raise our assumed probability that we're in a simulation.
    - arethuza 7mo ago
      I would think that the existence of a flawless predictor is probably more likely to indicate that memories of predictions, and any associated records, have been modified to make the predictor appear flawless.
      - vidarh 7mo ago
        I would say that if we presume memories of everyone involved have been modified, that is an equally strong predictor that we are in a simulation.
        danbruc 7mo ago
        Where does this obsession with the simulation hypothesis come from, it has been so widespread in the last years? It is more or less pointless to think about it, it will not get you anywhere. You only know this universe, to some extend, but you have no idea what a real universe looks like and you have no idea what a simulated universe looks like, so you will never be able to tell which kind our universe is. But what if we discover that our universe is made from tiny voxels or something like that, that will be undeniable evidence, right? Wrong! Who says that real universes are not made of tiny voxels? It could be [1] the other way around, maybe real universes are discrete but their universe simulations are continuous, in which case the lack of tiny voxels in our universe would be the smoking gun evidence for being in a simulation. [1] This is meant as an example, I have no idea if one can actually come up with a discrete universe that admits continuous simulations, which probably should also be efficient in some sense.
ordu 7mo ago
> Which also renders the entire paradox somewhat moot because there is no choice for you to be made. Not quite. You did choose your decision making methods at some point in your life, and you could change them multiple times till you came to the setup of Newcomb's paradox. If we look at your past life as a variable in the problem, then changing this variable changes the outcome, it changes the prediction made by the predictor. > The existence of a flawless predictor means that you do not have a choice after the predictor made its prediction I believe, that if your definition of a choice stop working if we assume a deterministic Universe, then you need a better definition of a choice. In a deterministic Universe becomes glaringly obvious that all the framework of free will and choice is just an abstraction, that abstract away things that are not really needed to make a decision. Moreover I think I can hint how to deal with it: relativity. Different observers cannot agree if an observed agent has free will or not. Accept it fundamentally, like relativity accepts that the universal time doesn't exist, and all the logical paradoxes will go away.
- chriswarbo 7mo ago
  > I believe, that if your definition of a choice stop working if we assume a deterministic Universe, then you need a better definition of a choice. In a deterministic Universe becomes glaringly obvious that all the framework of free will and choice is just an abstraction, that abstract away things that are not really needed to make a decision. Indeed, I think of concepts like "agency", "choice", "free will", etc. as aspects of a particular sort of scientific model. That sort of model can make good predictions about people, organisations, etc. which would be intractable to many other approaches. It can also be useful in situations that we have more sophisticated models for, e.g. treating a physical system as "wanting" to minimise its energy can give a reasonable prediction of its behaviour very quickly. That sort of model has also been applied to systems where its predictive powers aren't very good; e.g. modelling weather, agriculture, etc. as being determined by some "will of the gods", and attempting to infer the desires of those gods based on their observed "choices". It baffles me that some people might think a model of this sort might have any relevance at a fundamental level.
- vidarh 7mo ago
  This is a compatibilist view. However, we can tell that most people don't adhere to a compatibilist view of free will because it tends to make people very upset if you suggest they have no "genuine" free will or agency, and the moral implications behind the assumption of genuine agency are e.g. baked into everything from our welfare systems to our justice systems, that assumes people have an actual choice in what they do. For that reason I strongly disagree with the compatibilist view - language is defined by use, and most people act in ways that clearly signal a non-compatibilist view of free will.

jack_pp 7mo ago

There's rational and then there's common sense, if put in that situation who in their right mind would take even a 50% chance that the entity is wrong and greed it for 1000$. All I'd need to know is that it is far more likely I get the million if I go into the game thinking I'd only one-box

gegtik 7mo ago

In some ways it is an interesting problem about whether someone can engage a question about a hypothetic question -- and for the purpose of the exercise, assume the proposed parameters of the scenario.

vidarh 7mo ago

Assuming I have no way of testing the predictor, my decision would be to pick both boxes on the basis that $1000 is not a lot of money to me, but $1000000 is, and I wouldn't worry about the odds, because without knowing the nature of the specific predictor we're down to Pascal's Wager married to the Halting Problem: We don't know whether or how our actions and thought processes processes might affect the outcome, and so any speculation over odds is meaningless and devolves to making assumptions we can't test, without even knowing whether that speculation itself might alter the outcome, or how. But I don't need to speculate about the relative value of $1000 and $1000000 to me. Others might opt for the safe $1000 for the same reason.

malfist 7mo ago
Two boxes is the only choice that makes sense. It is always better than one box. No matter what you do after you enter the room, the predictor has already made their move, nothing you do now will change it. The only logical thing to do is to take both boxes because whatever the value in the second box is it will be added to the first box. If you only take the second box you are objectively always giving up $1,000 and getting no value in exchange for doing so (since not taking the first box doesn't change what's in the second)
- Smaug123 7mo ago
  And for you, of course, that's true! Because you are the sort of being who two-boxes, and this fact is visible to the predictor. Other types of being can do better.
  - dalmo3 7mo ago
    This is the best reply in this thread, as it irrefutably demonstrates this so-called paradox is a religious question and has nothing to do with logic or probability. The question is do you believe in an omniscient god or not. The fact that they dress up god as a supercomputer and that attracts all sorts of math and tech nerds is hilarious.
- OskarS 7mo ago

GaelFG 7mo ago

I don't get the 'choice' : the content of the box is aldready defined when you take your decision so taking it won't change the content of the black box and the open/transparent box have no drawback. What am I missing ?

xigoi 7mo ago
Assuming that the predictor is always right, there are only two possible scenarios: • You take one box and get $1000000 • You take two boxes and get $1000 The choice seems quite clear to me.
- GaelFG 7mo ago
  Not from the article : Before you walk in, a supercomputer predicted which choice you'd make, and put $1000000 in the opaque box if it predicted you'd take just the one, or $0 if it predicted you'd take both. So the amount of money in the black box don't change whatever you REALLY pick. Either the predicator would have guessed you'd pick both and there is 0$ in black box, in that case you have interest to take both boxes and win $1000 which is better than zero. Or it predicted you would only take the black box, put $1000000 in it and then again you win more by taking the two boxes.
  - xigoi 7mo ago
    This is exactly what’s funny about the paradox – we both think that our choice is completely obvious. My argument is that since the predictor is always right, the situation where you choose two boxes and you get $1001000 simply cannot happen, because then the predictor would’ve predicted your choice and placed nothing in the variable box.

gradschool 7mo ago

I don't know about y'all, but this paradox was resolved to my complete satisfaction in a blog post some years ago, I believe by Scott Aaronson, though I can't find the link. If the predictor has such a good success rate, then it must be simulating people's brains, but since it's not always right, the simulation isn't perfect. The best strategy for playing this game therefore is to look for indications as to whether I'm the real me or the simulation when the question is posed to me, and choose accordingly. Am I floating in a sensory deprivation tank being asked my choice by a disembodied voice with no recollection of how I got there and no memory of my childhood? In that case maybe I'm the simulation, so my answer is that I'll choose just one box. Is it an ordinary day of my life and a plausible setting with all of my faculties and recollections intact? Then I'll assume simulated me had my back and take both boxes.

djoldman 7mo ago

For folks reasoning through the "paradox," this may be helpful: https://arxiv.org/pdf/0904.2540 https://arxiv.org/pdf/0904.2540 Abstract: > ...We show that the conflicting recommendations in Newcomb’s scenario use different Bayes nets to relate your choice and the algorithm’s prediction. These two Bayes nets are incompatible. This resolves the paradox: the reason there appears to be two conflicting recommendations is that the specification of the underlying Bayes net is open to two, conflicting interpretations...

genshii 7mo ago

I've been presented with this thought experiment before and I always feel like I'm missing something when other people talk about it. Why would you ever take both boxes? The premise is that the predictor is always right. So whether you take one or both boxes, the predictor would have predicted that choice. We know from the setup that if the predictor said you would take the one box, it will have a million dollars. Therefore, if you take the one box it will have a million dollars in it (because whatever you choose is what the predictor predicted). As an aside, I think whatever this says about free will or if you're actually making a "choice" is irrelevant in regards to if the million dollars is in the box. The way I see both choices is this: You "decide" to take both boxes -> the perfect predictor predicted this -> the opaque box has zero dollars -> you get a thousand dollars You "decide" to take the opaque (one) box -> the perfect predictor predicted this -> the opaque box has a million dollars -> you get a million dollars If you want to consider the version of this where the predictor is almost perfect instead of truly perfect, I don't think that changes anything. Say it's 99% accurate or even 90% accurate. You take the opaque box -> the predictor has a 90% chance of predicting this -> it follows that there's a 90% chance that the box has a million dollars -> you have a 90% chance of getting a million dollars Had you picked both boxes, you have a 90% chance of not getting the million.

mcphage 7mo ago
> Why would you ever take both boxes? As near as I can tell, it boils down to this: no matter what the predictor has chosen, one you walk into that room, there's more money in both boxes, then there is in one box. But it feels like half an analysis—focusing solely on what you decide, while ignoring the fact that the other side is deciding based on what you think they'll decide. Maybe that's me being unfair, because I'm a solid one boxer. I also disagree with the linked article—I don't think it matters at all how the predictor makes their decision, because the outcome really doesn't matter if it's 100% accurate or 99% accurate. Or even like, 80% accurate. There's no magic required for the experiment to work.
- vidarh 7mo ago
  Even if it's 50% accurate the benefit of picking both is marginal. If it's 50% accurate and you pick both boxes, 50% of the time you get nothing, 50% of the time you get 0.1% more. So unless you know that the predictor is worse than chance, you at worst suffer a meaningless loss if you pick one box.

imtringued 7mo ago

I can't get behind this paradox, because the setup is too contrived and complicated. I'd take the $1000 box without the second box just to mess with the computer. Free money scenarios are always suspect so why would you ever expect to get a million dollars out of one?

bennettnate5 7mo ago

Here's a potential winning strategy: take a coin out of your pocket and flip it 100 times. If it lands heads 51 or more times, take both boxes; otherwise, just take the one. Provided the computer had anticipated you being the kind of person that would do this, it would anticipate you are probabilistically more likely to take the single box exclusively and put the million dollars in it. Regardless of the outcome of the coin tosses, you get that million dollar box, and you still get the added $1000 in the first box 49% of the time.