Newcomb's Paradox Needs a Demon | Hacker News Reader

Newcomb's Paradox Needs a Demon

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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.

> 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.

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.

(To two-boxers) it's not half an analysis because once you walk into the room your choice is causally independent of the demon/AI/alien prediction.

There's something vaguely similar to the fallacy of proposed (Cooperate,Cooperate) solutions to the Prisoner's Dilemma. The arguments go as follows: (1) if we're both rational agents and we have the same information and same payoffs, we will make the same choice; (2) therefore, (Cooperate,Defect) and (Defect,Cooperate) are out of the question; (3) therefore, the only options are (Defect,Defect) and (Cooperate,Cooperate); (4) so I should Cooperate since it gives the better payoff. It seems to follow logically but (1) and (2) are problematic because you can't assume symmetrical solutions and thus eliminate asymmetrical outcomes, because that is essentially the same as saying "what I choose causally affects what my opponent chooses".

In the same way, one-boxing is irrational (for this argument, anyway; I'm undecided myself) because the prediction has already been made, and so your choice to one-box or two-box cannot have any causal relevance to the contents of the boxes. Even a perfect predictor cannot invert the flow of causality.

> that is essentially the same as saying "what I choose causally affects what my opponent chooses".

No, it’s the same as saying “what my opponent thinks I will choose causally affects what my opponent chooses”, which is obviously true. Also, “what my opponent thinks I will choose is positively correlated with what I do choose”, unless my opponent isn’t very good.

The thing is, you can not chose once you are in the room. The fact that an [almost] perfect predictor exists implies that your choice must already be fixed at the point in time the predictor makes its prediction. Or the other way around, if you could still choose both options once you are in the room, say by basing your choice on some truly random and therefore unpredictable event like a radioactive decay - at least as far as we know truly unpredictable - then the predictor could not [almost] perfectly predict your choice, i.e. an [almost] perfect predictor can not exist.

So what you really want is to be in a state that will make you chose one box and you want to already be in that state at the time the predictor makes its predictions because the predictor will see this and place the million dollars into the second box. And as we have already said, you can not chose to take two boxes afterwards as that would contradict the existence of the predictor.

> So what you really want is to be in a state that will make you chose one box and you want to already be in that state at the time the predictor makes its predictions because the predictor will see this and place the million dollars into the second box.

Here’s the thing: no, I don’t. I’d much rather walk away with the easy million instead of risking it all for an extra thousand.

You can only get a thousand - take both boxes - or a million - take only the second box, zero and one million one thousand are not possible - or at least unlikely - because that would require a misprediction by the predictor but we assume an [almost] perfect predictor.

Then I for one choose the million.

As a one boxer myself this is the way I see it. The problem is presented as a value proposition, how do I walk out of this room with the most money? This typically prompts people to think of this as a statistics problem, and you genuinely can use statistics to 'solve' this, but that has nothing to do with what seems to be the problems underlying premise. Which is, do you actually believe that the predictor can even make that prediction? I think most people who take things logically at face value (like Veritasium watchers) would accept the premise as it's set up. I think for the two boxers there's some doubt they have about the predictors actual abilities, or they think they can 'outsmart' the predictor. The problem is setup in such a way however that it's fundamentally impossible to outsmart, which is I think what makes this problem so interesting.

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.

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.

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.

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.

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.

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.

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.

> 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.

> 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.

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.

I personally don't see any problems with this. For example, in most cases we can agree if someone had free will or no when they committed a crime. Even if I prefer compatibilist view and you are not, we'll agree in the most cases. In the cases when we may not agree the reasons of disagreement will not stem from this fundamental disagreements, but from things like should we treat state of affect as a state when a human has no free will.

So, a compatibilist view is not incompatible with the world we live in, but moreover, it is needed to keep our world functioning. The world we live in is mostly artificially constructed. Welfare and justice systems are not "genuine", they are artificial constructs. They play a role in our society and the ideas of "free will" and "guilt" are constructed also, and they are tweaked to make our systems to work better. If you assume that free will and guilt are "genuine" or God given, then you can't tune them to better match their purposes. You are losing agency this way, losing part of your free will, you can't consciously and reasonably discuss if state of affect should be an exception from the rule "any person has a free will". You'll be forced either to skip the discussion, or to resort to some kind of theological arguments.

But if you accept, that "free will" is a social construct, then you can easily identify the affected variables: it is all about punishment for crimes or awarding people for their pro-social deeds. You can think of how "state of affect inhibits free will" can influence all these goals, you can think of the possibility of people simulating state of affect (or even nurturing their personal traits that increase the probability of entering state of affect) to avoid a punishment. You can think rationally, logically and to pick a solution that benefits the society the best. Those very society with baked in idea of free will. Or you can choose to believe "free will" is God given, because of an irrelevant linguistic argument, and lose the ability to make our world better.

> most people act in ways that clearly signal a non-compatibilist view of free will.

Of course, we are not living in quantum mechanics we live in a world that is constructed by people. I mean, all this is built on top of QM, but QM laws do not manifest themselves directly for us. We have other explanatory structures to deal with everyday physics. But even physics doesn't matter that much: I turn the switch and voila I have light, and the heck with conservation of energy. I can talk to you, despite we are residing on different continents, 1000s of km don't matter. If I want to eat I do not try to kill some animal to eat it nor do I gather seeds and roots in a wild to eat them. I go to work and do something, get my salary and buy food in a local store. We are living in an artificial world with artificial rules. Free will is part of this world. Of course we talk about it like it exists. We talk about it like it is a universal truth. Relativity I mentioned above doesn't show itself most of the time, because the world is constructed in a way, when we can agree about someone having it. Situations when this is not the case are very strange and can be even punished: manipulation (which is come close to taking people's agency away from them) is deemed amoral.

The world constructed so we can ignore that free will is just an illusion, moreover it is constructed to think about it in terms of free will, so you'll have issues thinking about it in other terms. Like you'll have a lot of issues trying to calculate aerodynamic of a plane relying on equations of quantum mechanics.

A compatibilist view, to me, is usually immoral, because it seems to maintain the pretence of agency while admitting it's an illusion, and so persist in accepting treating people as if they have agency.

People who at least genuinely believe in free will and agency has an excuse if they e.g. support punishment that is not strictly aimed at minimising harm including to the perpetrator. A compatibilist has no excuse.

It is of course possible to hold a compatibilist view and still argue we should restructure society to treat people as if they do not have agency, but then the point on holding onto the illusion drops to near zero.

> A compatibilist view, to me, is usually immoral, because it seems to maintain the pretence of agency while admitting it's an illusion, and so persist in accepting treating people as if they have agency.

Is thermodynamics immoral? You see, there is nothing fundamental about pressure or temperature, they are just statistical averages, they are all in imagination, it is an illusion. But we still pretend that pressure and temperature exist.

Or what about biological species? If you look into it, you'll see that there is no clear way to define what species are, all the definitions are imperfect projections of our high-level illusions onto the underlying biology and biochemistry. But we (and biologists also, who much more aware of the issues) still pretend that species exist. Are biologists immoral?

Nothing wrong with it. Nothing immoral, it is just a regular mental tool. You see, the question is what does it mean for thing to exist. Some things are easy: like there is a car, we can see it, we can touch it, we can drive it, therefore we agree that the car exists. But some things are not so easy, especially when we talk about immaterial things. But to make things even more interesting, some things seem to exist on some level, and do not exist on other levels. Like life for example. There is no life in an atom of carbon or hydrogen or nitrogen, but the bunch of such atoms connected just right can be alive. And it normally don't make people jumpy. At the some time some people have issues with the idea that free will exists on some levels but not others.

> People who at least genuinely believe in free will and agency has an excuse if they e.g. support punishment that is not strictly aimed at minimising harm including to the perpetrator. A compatibilist has no excuse.

Yea. I don't believe in free will and agency "genuinely", so I have no excuse. But I believe that any such excuses are borderline immoral. If anyone allows their emotions and animal instincts to take over them and act against the greater good of a society, it is immoral. I mean, if they do it for their own gain, it may be not immoral, there is a tradeoff between interests of a society and interests of an individual, and sometimes we should prefer the former and sometimes the latter. So going against the society interests is not inherently bad. But doing it because of uncontrollable emotions and animal instincts is bad. It still counts as an excuse, but I'm not sure if it is a good thing. I should believe that this is a good thing, because I don't know how to test it experimentally without risking to harm people even more. But still while I can accepts excuses of others, I don't accept such excuses from me. I just don't let myself to let emotions drive without any oversight from me (whatever this "me" is: this is one more interesting question without any good answers).

The point is: my "non-genuine" belief in free will make me much more free willed than a genuine belief. If I succumbed to my emotions and didn't control myself for three seconds, I'd see it as my personal failure. In my head I'm in control, not someone or something else.

> It is of course possible to hold a compatibilist view and still argue we should restructure society to treat people as if they do not have agency

No point in it. It is like arguing "lets forget thermodynamics and resort to pure QM because it is closer to fundamental laws of the Universe". We need the idea of free will, even if it doesn't hold on fundamental level.

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.

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

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.

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)

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.

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.

> Two boxes is the only choice that makes sense. It is always better than one box.

Congratulations on your $1,000. I'll use some of my $1,000,000 I got by nonsensically picking one box to toast in your honor and dedication to logic.

Or your zero dollars if your predictor wasn't quiet as perfect as billed.

But the predictor would need to be almost as bad as pure chance for the odds to tilt away from one box. Unless you think it is materially worse than chance, it's a bad bet.

Too late to edit my original comment now, but my intent was actually to make the argument for picking one, hence my comment on not caring much about the $1000.

If the predictor is indeed flawless, or almost flawless, if I were to be the type of person likely to pick both boxes, the opaque box would almost certainly be empty. So the winning strategy is not just picking the opaque box, but being the kind of person likely to pick the opaque box only.

You're right that what I do after I enter the room is irrelevant if it is somehow independent of what I have done before. But it can't be independent of what I did before if the predictor is flawless. If the predictor is flawless, then either my actions needs to be deterministic so that it can in fact know what I will do when in the room, or the predictor is supernatural and can know or cause me to act in a certain way for that reason.

Either way, giving any indication that you'd pick both boxes would be a bad idea (so I guess my typo above might screw me over if ever presented with this choice).

For folks reasoning through the "paradox," this may be helpful:

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...

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.

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 ?

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.

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.

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.

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?

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.

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