Newcomb's Paradox Needs a Demon(samestep.com) |
Newcomb's Paradox Needs a Demon(samestep.com) |
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.
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.
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.
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.
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.
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.
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)
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...
• You take one box and get $1000000
• You take two boxes and get $1000
The choice seems quite clear to me.
So the amount of money in the black box don't change whatever you REALLY pick. Either the predicator would have guessed you'd pick both and there is 0$ 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.
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?
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.
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.
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.
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.
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.
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).
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.
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.
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.
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.
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.
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.
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.
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.
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.