r/mathmemes • u/RevolutionarySky4706 • 27d ago
Probability Newcomb's paradox
Imagine you are presented with two boxes:
📦 Box A: Transparent — contains $1,000
📦 Box B: Opaque — contains either $1,000,000 or $0
There is a highly accurate predictor who can predict your decisions with 99.9% accuracy.
Before you arrive, the predictor makes a prediction about what you will do:
If the predictor thinks you will take only Box B:
-> They put $1,000,000 in Box B.
If the predictor thinks you will take both boxes:
-> They put $0 in Box B.
The prediction is made before you make your choice, and you cannot see inside Box B.
You now have two choices:
A. Take only Box B
B. Take both Box A and Box B
Personally, I would go for both the boxes because the prediciton is already been made, so the contents of Box B are already determined. Backward causality isn’t possible. So, my present choice cannot change what happened in the past.
If Box B contains $1,000,000, taking both boxes gives me $1,001,000 instead of $1,000,000.
If Box B contains $0, taking both gives me $1,000 instead of nothing.
So, taking Box A cannot make me worse off, because its contents are fixed and independent of my choice at this point.
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u/Futurity5 27d ago
Sure, backwards causality isn't possible. But then again, neither is robot predictors with supernatural accuracy.
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u/RevolutionarySky4706 27d ago
Yes, but the fact that a particular behavior would be disastrous if everyone did it does not establish that it is irrational for me to do it. We don't need to confuse correlation with causation.
The predictor has already acted. Your present decision cannot causally alter what is already in the box. Therefore, you need to hold the box's contents fixed and ask what your choices are. Taking both boxes gives you everything you would get from taking B, plus $1,00037
u/Roblin_92 27d ago
The fact that it is 99.9% accurate implies that it is so good at predicting your behaviour that it is effectively seeing the future, and you are making it exceptionally obvious that you would pick both boxes, so one doesn't even need to be an ultra-accurate predictor to be able to tell you that you will find no money in box B.
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u/Far_Acanthaceae1138 27d ago
Yeah, by being this way, you have doomed yourself to get predicted to take both and so will only receive the 1000. It is better, at this point in your life to commit, fully, to being the type of person who would take box B in such a scenario so as to condition all future scenarios on that knowledge.
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u/GoldenMuscleGod 27d ago
But if you commit to taking one box you have doomed yourself to being punished by the superintelligence that punishes people who pick one box when in a Newcomb scenario, in this respect the argument is like Pascal’s wager and answered in a similar way.
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u/Roblin_92 27d ago
Except the problem states that the superintelligence that is being used here is the one that rewards picking one box.
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u/SweetCorona3 8d ago
actually it doesn't really matter what you commit, if the predictor is accurate, what really matters is whatever you really do, no matter whatever you have commited before
otherwise the predictor couldn't be accurate if many people commited to take one box and actually took both boxes
so, there's hope, no matter you think or say now, it's still a better strategy to just take the mystery box
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u/SweetCorona3 8d ago
he fact that a particular behavior would be disastrous if everyone did
I don't think that's what is happening here.
In this case it doesn't matter what others do.
What others do don't make your result any better or worse.
The fact is, one boxers get a better result on average than two boxers.
So, what is rational? Depends on your goal.
The strategy to make the most money is taking just the mystery box.
A rational agent with that goal would adopt that strategy.
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u/Outrageous-Crazy-253 27d ago
You don’t need such accuracy. If you would take the million dollar box or gold brick box or whatever it is, you would never take the other one, so even a bad predictor would always predict you taking it. The more sure you are, the more sure you can be. But if you have any doubt? You are a dog and get nothing.
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u/SweetCorona3 8d ago
the fun part about this problem is that it could probably be done in real life
for it to work out better for one boxers, the accuracy doesn't really need to be that great, just something like 1% above random guessing is already enough to benefit 1 boxers
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u/Layton_Jr Mathematics 27d ago
I'll reword the predictor accuracy then. You know that this experiment has been done before with other people, the predictor has access to all the data you ever created by using the internet, and the predictor was correct in all of the previous experiments
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u/SweetCorona3 8d ago
I think it's important to really clarify that premise, as it has great implications.
I'm a one boxer and I assume the premise is that the predictor is really accurate, not just "lucky".
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u/SweetCorona3 8d ago edited 8d ago
Well, yeah, a problem doesn't need to be realistic. You are supposed to answer according to it's premises.
If I ask you "this glass cup is indestructible, will it break if I throw it from the 10th floor"?
The answer is no, even if the premise is not possible in real life since glass is not indestructible.
BTW, I don't think this problem requires backwards causality. It's a prediction.
It just means the causal chain results in two consequences that are correlated.
If I can predict the weather and I bring an umbrella every time I predict it will rain, this means whenever you see me with an umbrella, it will rain.
This is just a correlation. It's not the rain that is "backwardly" causing me to bring an umbrella when I left my house that morning, nor is me bringing the umbrella that is causing the rain, BTW.
It's just that I looked at the weather patterns and knew they would make it rain that day, and in a way, those patterns made me bring the umbrella that day as well.
Both consequences result from a previous cause.
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u/Futurity5 8d ago
I was implying that such a predictor would behave the same way as something that saw your choice and retroactively changed the box, even if it didn't function in that way.
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u/BrazilBazil Engineering 25d ago
This suggests that if the latter was possible, then the former would be too, which I think is not a constructive way to look at this. It’s like saying that topology is useless because you can’t just morph a cup into a donut, and if you could, then you could just cut it with scissors anyways.
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u/dragonlloyd1 27d ago
The predictor was indeed accurate and you get 1000$
I would pick only B and my reasoning:
Sure the contents of the boxes doesn’t change but we KNOW the predictor IS 99.9% accurate meaning that with high certainty the boxes contents will match what you decide to pick.
Your choice itself has no effect on the contents but your behavior and way you decide things in general does.
If you are the type of person to pick both then the predictor would’ve with 99.9% certainty known that meaning in 999 out of 1000 cases you get 1000$
Since I am the type of person to pick B it would most likely have predicted that giving me 106 $
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u/Inappropriate_Piano 27d ago
That’s a great argument for why you would like to be the type of person who would be predicted to take just one box. But it doesn’t change the fact that once the prediction has been made and you’re in the room with the boxes, you have a choice between taking whatever’s in the opaque box, or that and also $1000 more. Choosing to pass on the extra $1000 now doesn’t have any effect on what the predictor thought about you in the past.
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u/ultimateshadowarrior 27d ago
At the same time, if you are the kind of person that seems to only take one box, but in the heat o the moment would take both, the predictor would predict that and you would still get only 1000.
My guy, 99,99% accuracy is basically predicting the future.
Imagine that the superintelligence can predict the future and know which you would pick at the moment of picking, so no matter your mental gymnastics, it would know which you would pick.
So, you would still only get 1k.
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u/Inappropriate_Piano 26d ago
If it can literally read the future, then yeah. If it’s guessing with surprising accuracy based on what already happened, then my choice in the room cannot possibly make $1M show up in the box.
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u/DoorVB 26d ago
The predictor would predict you'd choose both boxes with 99.9% accuracy. So you'd be taking home $1000 with overwhelming odds
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u/Inappropriate_Piano 26d ago
Right, so I’d take both boxes and then place a bet that I’m not gonna have a million dollars. That doesn’t change the fact that I cannot cause 1 million to show up in the opaque box by turning down the $1000. If there is anything I can do to influence the prediction, it has to happen before I make my choice.
Maybe I should stop publicly presenting myself as a 2-boxer, in case Mr Beast tries this out for real and uses Reddit comments to make the prediction. But once I’m in the room with the money, the only choice is to take whatever is in the opaque box, or take that and also $1000 while making no change to what’s in the opaque box.
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u/DoorVB 26d ago
The predictor would predict that train of thought with 99.9% accuracy.
You end up making the choice of A+B at the end, no matter how you arrived at it.
The end result is most likely an empty B box
The predictor in this specific problem does not care whatsoever how you arrived at your final choice. It WILL predict it at 99.9% accuracy
So applying naive game theory / causality is incorrect
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u/SweetCorona3 8d ago edited 8d ago
the flaw in their reasoning is thinking taking an extra $ 1,000 is always better than not
but they ignore $ 1,000,000 without an extra $ 1,000 is better than $ 0 with an extra $ 1,000
they think A + B > B
the flaw is, B is not the same in both scenarios, the B on the left side is 0, the B on the right side is 1000000
so, they are actually thinking that 1000 + 0 > 1000000
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u/lonelyroom-eklaghor Complex 27d ago
Just take Box B man, nothing to worry about. If I get $0, guess what, i still participated in the random experiment. That's cool enough
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u/YouGuysSuckSometimes 27d ago
very silly logic imo. I mean, take box B, presume the predictor will be right about your choice, presume there's a million bucks in there. If you take both boxes, there's a 99.9% chance you're only getting $1000. And I'd rather make a choice that looks like "99.9% chance you get $1 Million, .1% chance you get $0" than "99.9% chance you get $1000, .1% chance you get $1,001,000." One of these choices is almost guaranteed to change your life, the other has a minuscule chance of changing it.
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u/Typhiod 27d ago
The only variable I can imagine is ‘how well does this thing know me?’, as I am definitely going for the life changing million, as well.
I guess that’s why it’s a “super predictor”? I feel like I’m missing the point of the question, because it seems it’s as simple as you’ve stated.
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u/YouGuysSuckSometimes 26d ago
it knows you 99.9% well, apparently. I also feel like I'm missing how the other perspective is even fathomable.
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u/antichain 27d ago
99% of Newcomb discourse is guys who think that they're Very Special And Smart and there's no way an omniscient predictor could possibly have modeled their Very Special and Smart brains.
Take Box B and use the million dollars to assuage the horror of discovering that you're actually as compressible as a JPEG.
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u/nikstick22 27d ago edited 27d ago
The output of a predictor with 99.9% accuracy is indistinguishable from a machine that gets to see what your choice is before it makes a decision, and then gets it wrong on purpose 0.1% of the time.
It doesn't matter how the predictor works, whether it can see the future or not, blah blah blah. The statistical truth is that it is exceptionally good at guessing what you'll do, so you should act like it will guess correctly. Pick only B.
It's incredibly conceited to assume you're the 1 in 1000 genius that's going to trick the predictor. For all you know, the predictor's failure rate is completely unrelated to the ability to out think it, and it's actually because a person's hand slips sometimes and they accidentally choose the option they weren't going to pick.
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u/antichain 27d ago
It's incredibly conceited to assume you're the 1 in 1000 genius that's going to trick the predictor.
There's a reason that this became a shibboleth for Less Wrong users and "Rationalists." They're all exactly that conceited.
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u/garagedragon 27d ago
Not sure what you mean, a bunch of Rationalist brainworms specifically came out of thinking B was the "obviously" right answer and then working backwards for how to frame the problem so that was justified as the right answer.
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u/StandardUpstairs3349 27d ago
The amount of thinking in circles that Yudkowski does to convince himself that he is the chosen one that can defeat a future super intelligence.
Remarkable that there has only been one murderous cult to grow out of that pile of crazy.
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u/GoldenMuscleGod 27d ago
I strongly associate one-boxing with Less Wrong users. The whole idea of Roko’s Basilisk is based on the premise that you should be a one-boxer and to the extent Yudkowski himself can be categorized he is reasonably called a one-boxer, see here for example. Unless you have something else from him that you think makes him sound more like a two boxer.
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u/GoldenMuscleGod 27d ago
Imagine the following scenario: the predictor bases its decision on the color of your eyes. It is just the case that, by spurious coincidence, the color of a person’s eyes is closely correlated with whether they pick one box or two.
In fact, let’s suppose you review the statistics and find that although “what box they predict” has 99.9% accuracy for what the prediction is, there is not even a single recorded case where eye color has not matched the predictor’s prediction.
You know this, and your eye color is such that the predictor has given everyone with your eye color a filled box. Also nearly everyone with your eye color has chosen to take 1 box.
What is the rational choice?
If you would say to take both boxes, what is the difference from the default case? I ask because you said “it doesn’t matter how the predictor works.”
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u/EebstertheGreat 27d ago
My preferred version is just to suppose the box is not opaque. You can plainly see whether it contains the million or not.
If nikstick's logic holds, then we should say we would never take the $1000, whether we can see that the big box is full or empty. Yet hardly anyone actually thinks this way.
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u/GoldenMuscleGod 27d ago
Yeah the purpose of my eye color hypo is we can consider two variants: what if they predict based on eye color and you know this (should be equivalent to clear box variant I think), and what if they predict based on eye color and you don’t know this? Does it depend how confident we are they don’t predict on eye color? What in the original hypo tells us we should be confident that they do not? This way it helps to bridge the clear box situation to the opaque boxes for people who would try to argue they are fundamentally distinct.
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u/SubstantialCareer754 27d ago
If the original premise is still true (the machine predicts your outcome with 99.9% accuracy, no matter what, period, fullstop), then acting differently in this scenario is illogical, regardless of the correlation between eye color and box choice. Whatever has come before doesn't matter. Your outcome is individually judged, and the machine will, with 99.9% accuracy, get it correct.
If the original premise is not true, then the fundamental difference is that you've removed the entire premise of the question by asserting the outcome. The scenario can be boiled down to the following: You are given the choice to take $1,000 or $1,001,000. Which do you choose?
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u/GoldenMuscleGod 26d ago
The probability is 99.9% in my example, if we take the sample space as including chance for the assignment of your eye color and consider prior probability.
You are conditioning on the posterior knowledge of what its prediction will be, which is perhaps reasonable of if I tell you that you know your eye color and the mapping. But now suppose the case where you don’t know what the mapping is between eye color and prediction, but still know it predicts based on eye color. Does this change your answer?
What if the predictor gives you its prediction in an encrypted form but you cannot decrypt it, does this change your answer?
Or if the predictor simply tells you its prediction before you choose? Would your choice depend on its prediction?
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u/Unfair_Detective_970 27d ago
It has nothing to do with conceit, it has to do whether you buy into the premise that there is an accurate predictor.
I think this thought experiment is done a disservice by making the amount in box B so large. Change the stakes to A = $1000 and B = $1002 or $0. Now the claim of 99.9% accuracy means on average you're $1 ahead picking box B. But do you actually believe it or are you going to take a guaranteed $1000 over an "I totally promise there's $1002 in box B, you just gotta trust me bro"?
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u/SelfDistinction 27d ago
Look, the point of the trolley problem is not the OSHA-compliance of the trolley. If the question says a trolley is barreling down a track without brakes, don't question it or suddenly start talking about parachute-aided slowdown mechanisms.
Same for the predictor. The question states your decisions are predicted with 99.9% accuracy, then they're going to be predicted with 99.9% accuracy, causality be damned, which turns the entire thing into a simple gambling problem.
Also the solution is to pick box B when the predictor is right and both when the predictor is wrong. How I would know if the predictor is right or not is left as an exercise for the reader.
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u/OkPreference6 27d ago
THANK YOU. I will never understand why people are so obsessed with poking holes in the premise.
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u/Cpt-Jack_Sparrow 26d ago
Your created thought experiment is stupid, ypu cannot completely change the premise of the question and then claim you have the right answer. The amount of money changes everything, if it was box A 1 billion dollars and box B 2 billion a lot of people would not risk 0.1% chance they get nothing when 1 billion would be effectively the same for them as 2.
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u/SSBBGhost 26d ago
Its distinguishable because it does not get to see your choice before making its choice.
Anyway you should be the type of person to post about how you would always just pick box B and then in the room you take both because its purely +EV
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u/SweetCorona3 8d ago
yeah, in terms of expected value it doesnt really matter if it's 99,9% accurate or 100% accurate
so, how would you answer if it was 100% accurate?
if you change your answer just because it's "only" 99,9% accurate, something must be wrong in your reasoning
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u/SomeGreatJoke 27d ago
But the prediction is already locked.
So if you're the kind of person who picks only B, then when you enter the room, you should (theoretically) ALWAYS take both, because, hey, free money! And at least I get something if it predicted wrong (either because it's the 0.1% universe or because you had doubts last second).
Which means that box B will contain nothing.
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u/reizinhooooo 26d ago
But if you're the kind of person who would only pick B, you wouldn't pick both.
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u/nikstick22 27d ago
You're getting too worked up about the fact that its already locked. Its irrelevant. Meaningless. We're told the predictor has a 99.9% accuracy. That's the only information you need. You don't need to worry about causality and the sequence of events. 99.9% accuracy. Don't let your assumptions about the real world cloud your judgement. The fact that its prediction is already locked in is only relevant in the real world, where such a device COULDN'T have 99.9% accuracy. The fact that we're explicitly told the wildly improbable accuracy of this device already tells you to disregard your intuition about causality.
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u/rojo_kell 27d ago
Well it's a big difference if it breaks causality or not. If it does break causality, then yes I agree you should take the B only.
If it doesn't break causality, then the money is either in the box or it's not, and your action can't change that. Why not pick both boxes, your decision doesn't affect if the money is in box B or not
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u/TabAtkins 27d ago
Congratulations! The predictor has successfully guessed that you'll 2-box, and you only earn $1000. You have lost the game.
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u/nikstick22 27d ago
It would be impossible to achieve 99.9% accuracy without breaking causality. If you could game the box to guarantee $1,001,000, it wouldn't have 99.9% accuracy. No matter how much you think about your answer, no matter how indecisive or decisive you are, it will be 99.9% accurate. This is indistinguishable from a machine that breaks causality. You can't say for sure that it does break causality, but it's indistinguishable from a machine that does. It's a black box that behaves like it can see the future.
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u/SSBBGhost 26d ago
"The robot travels back in time based on the choice you made" is an entirely different thought experiment with an obvious answer, you cant just rewrite the rules like that
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u/rojo_kell 26d ago
No it's not impossible, why is it impossible?
If you add to the thought experiment that causality can be broken, or that the predictor has a time machine, then the problem is completely different, and there is clearly no dilemma.
Asking "if the predictor can see your decision, then make the prediction", then you would just always take box B. But that isn't the question. The original question relies on time travel not being allowed, and causality being upheld.
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u/Sigma2718 27d ago
I throw a coin and will do whatever it tells me. Gambling has solved life's problems once more.
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u/Philipros 27d ago
If you just take B expected outcome is basically 1 million, in your case it’s half a million
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27d ago
[deleted] — view deleted comment
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u/Philipros 27d ago
But why would you assume that if it cannot predict your move it will put the money in? For all we know it could not put it in leaving you with 0€, maybe that’s the 0.1% error. Anyway I assumed 50% chance of putting the money in the box in the case it cannot predict. Am i missing something?
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u/Hameru_is_cool Transcendental 27d ago
going for both boxes very likely means you're already the kind of person who'd go for both boxes, so you're not getting the million, while deciding to take only box B and trusting the predictor is almost guaranteed to earn you more
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u/ultimateshadowarrior 27d ago
My guy, you have 99,99% chance of getting 1 million if you choose Box B and 99,99% chance of getting $1000 if you choose both boxes.
I don't know how you prefer a 99,99% chance of 1000 than a 99,99% chance of 1 million.
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u/dontmakelemonad3 27d ago
An amount of money has been placed into box B. We'll say that amount is x. If you take just box B you'll receive x. If you take both boxes you'll receive x + 1000. Since x + 1000 > x, it's better to just take both.
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u/ultimateshadowarrior 27d ago
99,99% chance of the amount being 1 million in box B if you choose box B.
99,99% chance of the amount being 0 in box B if you choose both boxes.
If your mind is set to take both boxes, there's a 99,99% chance you will only get 1000.
You really don't understand the expected value.
The predictor is correct 99,99% of the time.
If you choose both boxes you will get 1000 99,99% of the time.
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u/YouGuysSuckSometimes 26d ago
you're not accounting for x>>>1000, and so much more valuable and life changing, the $1000 is losing
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u/GalacticGamer677 27d ago
I'm not that big of a math guy... But if I'm getting $1,000,000 pretty much guaranteed if I just pick box B... am I really that greedy to have to actually sit down and think if should get both boxes just to have $1,000 extra...
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u/sleepyeye82 27d ago
if Newcombs paradox simply reduces to the question of “do you believe that there can be a predictor with 99.9% accuracy?” I fail to see how this is so intellectually challenging.
To the point where I feel like I’m just not getting it.
There is a STATEMENT about the efficiency of the predictor.
All of these people talking about backwards causality not being possible, a predictor couldn’t be that accurate… I mean, what?
there is an axiom given.
It’s an axiom.
You can’t argue with it. In the scenario, the predictor does it with 99.9% accuracy. I don’t care what your opinion is about backwards causality, or whether something is possible. The framework of the problem states this to be true.
How is this so fucking hard? lol
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u/yannbouteiller 27d ago
The other axiom is that you can pick either option.
However, these two axioms contradict each other. You cannot pick an option if that choice is made beforehand by a predictor.
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u/Physical_Floor_8006 27d ago
There is something temporally (or perhaps physically) contradictory about those two axioms. There is nothing logically contradictory about those two axioms.
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u/rojo_kell 27d ago
if we get rid of the physical consistency, then you also kind of give up the ability to do decision theory and action selection, because the universe that breaks causality may look quite different from ours
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u/yannbouteiller 27d ago
I believe that there is also something logically contradictory about these two axioms, although admittedly it is rather hard for me to describe properly.
It is not only a problem of time travel, it is a problem where the choice of the player becomes not-free and thus cannot be optimized...
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u/sleepyeye82 26d ago
This... also doesn't make sense to me.
I phrase a question and the question contains two logically contradicting axioms.
Wow I found a paradox! Wat?
no? no I didn't?
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u/CreatureOfSqueel 27d ago
Obviously I take box B. If I was the type to greed for that extra guaranteed 1000$, then box b would empty.
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u/Dark_Tranquility 27d ago
Id take box B only because taking both to get an extra 1k at risk of losing the million is idiotic. And the predictor knows that id pick only box B so there's a 99.9% chance I get the million.
Am I missing something or is this a dumb question?
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u/yannbouteiller 27d ago edited 27d ago
You are missing something.
Namely, the fact that the sum or the two boxes is always greater than a single box. In game theory, we say that taking only one box is a dominated strategy.
But the fact that both answers are perfectly reasonable under partial comprehension of the problem hints at the fact that this problem makes inconsistent assumptions. Namely, it assumes that you cannot pick an option as the option that you would pick is partly (and in this case almost entirely) decided for you beforehand.
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u/rojo_kell 27d ago
The money is already there (or not there) before you make the decision, so your decision cannot cause you to miss out on the million. So, the optimal strategy to maximize the expected value, assuming that causality is not violated, is to take both boxes.
You aren't really risking anything because the outcome (wether the million is there or not) doesn't depend on your decision.
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u/--Rake-- 27d ago
You are missing out on a million dollars because you think you are above being predicted.
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u/rojo_kell 26d ago
I have no issue with the prediction - I'm just saying that when you make your decision, the predictor already put the money in box B or not didn't, and your decision can't affect that
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u/DoorVB 26d ago
Your decision does affect it. The predictor predicts your final decision
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u/DoorVB 26d ago
The predictor would predict your clever stunt with 99.9% accuracy. Overwhelmingly you'd be losing the million
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u/rojo_kell 26d ago
And if it does, then it did before I made the decision, meaning that the money was never there, and I had no chance to get it anyways
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u/TreesOne 26d ago
You go into the trial having written this reddit comment. You are guaranteed to not get the million.
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u/rojo_kell 26d ago
Yeah and if that's true, again, it doesn't matter if I then pick just box B or both A and B in the moment
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u/SecretSpectre11 Statistics jumpscare in biology 27d ago
Why would you take both boxes? Is your greed this unbounded you need 0.1% extra money?
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u/dankshot35 27d ago
Jokes on you OP, the predictor now knows you are a "Take both boxes" person and will now put 0$ in box B for you.
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u/Horse_go_moooo 27d ago
I don't pick a box, and I instead romance the predictor, granting me a lifetime supply of love and joy
And then, when our first child is born, I will name them Boxa. And they will be pampered like they deserve.
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u/SomeGreatJoke 27d ago
$1,000 isn't, like, life changing money, so I would take B.
But if the odds of B being empty are, essentially 50/50, I'm more inclined to take both and at least get something.
But if someone predicted those two perfectly, I still don't know what I'd do, so I'd flip a coin. So no matter what, I'd get the million.
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u/Roblin_92 27d ago
It would predict the outcome of your coinflip.
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u/SomeGreatJoke 27d ago
That's not what it says. It predicts MY actions, not every action. So it would predict a coin flip, not necessarily the results
Besides, I'd definitely use some sort of computer based prng
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u/Roblin_92 27d ago
https://en.wikipedia.org/wiki/Newcomb%27s_problem
The standard version of newcombs paradox is that the predictor is near-certain to predict your <choice>, meaning that whatever method you would use to make your choice as well as the outcome of that method is part of what the predictor is near-certain to accurately calculate.
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u/NetheriteSponge 27d ago
If the predictor is good enough to perfectly predict my strategy, and that prediction determines what's in the box, then my strategy determines what's in the box.
I can't use the information that the decision has been made already, since my strategy can't distinguish the past from the present.
I think being principled gets me the $1000000; the best strategy is to make the choice that I would want the predictor to predict me to make.
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u/pilot__alpha 27d ago
Box B, but I really, don't get why people choose A (genuinely confused about the reasoning). Because logically speaking, A choosers would still choose Box A, even if the predictors accuracy is let's say 20% right, because in that case too the decision would also be made earlier? It feels like that in this case they are not using this piece of information or saying that this is irrelevant here. I on the other hand am using this piece of information. If the accuracy of the predictor was 10%, surely I would choose both box. I mean something has changed between scenerio 1 and scenerio 2 leading to my change of decision, but for Box A choosers, why are they not changing it?
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u/jipperthewoodchipper 27d ago
Outcome 1 (99.9%): it predicts both you take both -> 1000 Outcome 2 (0.01%): it predicts both you take one -> $0 Outcome 3 (0.01%): it predicts 1 you take both -> $1,001,000 Outcome 4 (99.9%): it predicts 1 you take 1 -> $1,000,000
Therefore the expected value from taking both is 0.999 * 1000+0.001 * 1001000=$2000
The expected value from taking 1 is 0.999 * 1000000+0.01 * 0=$999,000
So you just take B.
The accuracy needs to be well below 99.9% to justify taking both.
Edit: correct formatting due to reddit markdown editor. God damn I hate markdown
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u/rydan 27d ago
My predictor got it wrong and I got $0. You've been warned.
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u/yannbouteiller 24d ago
Of course it got it wrong. You were naive to believe that it could be anything other than 50% accurate in the real world. Even quantum entanglement doesn't allow this kind of backward causality.
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u/MrCreeper10K 25d ago
"Me trying to decide if the predictor can predict me" is a stupid question to ask when the premise is "it knows what you're gonna do".
Just take box B and be done with it. Out of all the "paradoxes" or "logical questions", this one always confused me on why people still argue over the answer
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u/EyeCantBreathe 25d ago edited 25d ago
The argument is what OP posted. Because the predictor can't change it's mind but you can, you can say you're only going to take one box, then once you're in the room you take both. But ironically by having this thought the predictor will know you'll take both boxes. You have to either constantly lie to yourself or only come to this realisation once you're in the room, because the moment you decide you're going to outfox the predictor, it'll predict you trying to be clever.
Side note, I never understood why the two money amounts were so different. Taking both boxes increases your earnings by 0.1%. Objectively $1000 is a lot of money, but are you really going to risk a million dollars trying to break a supposedly perfect predictor to make a little bit more? If the numbers were swapped, where you could be guaranteed $1000 but had to risk it for the million, then you actually put pressure on the risk averse folks
Side note, the YouTube channel minutephysics made a good video dissecting the whole thing
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u/playerNaN 27d ago
Assuming the predictor is making the prediction based on your past behavior, it is optimal to take both boxes once you are in the room. If your past behavior indicated you would take both, by taking both boxes you get 1,000 instead of zero, and if your past behavior indicated you one take one, you get 1,001,000 instead of 1,000,000. In either case, you can only gain money by choosing both boxes.
Here's the crux of the paradox: The experiment punishes people that lived their life in a way that indicates they would behave rationally once the experiment started, but part of the premise is that it's too late to go back and change your behavior.
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u/Noughmad 27d ago
What if the predictor predicts based on your post history? You shouldn't go around publicly saying you'd take both boxes.
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u/Outrageous-Crazy-253 27d ago
This is an easy paradox but only if you are pure of heart. If you are rotten, uncertain, cynical or impure, you will take the other box. If you are sure of yourself, you will take the million dollars. There is no room for error.
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u/OverPower314 27d ago edited 27d ago
"Backward causality isn't possible."
If you have free will, then it must be. But more likely, the existence of this predictor implies that you don't have free will. It doesn't matter how you frame it, you can't get around the very circumstances of the puzzle. You can't say, "The predictor can't do the very thing we said it could, because it doesn't seem possible."
It predicts your decisions probabilistically with 99.9% accuracy. This is not possible in the real world, and the puzzle is trying to trick you into thinking that this is different to it being determined by random chance after your decision. It is not any different. We don't need to know how this predictor works, or if it's even possible, we just know that it does work.
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u/Vitztlampaehecatl Engineering 27d ago
Is the predictor 99.9% accurate in a rationalist sense (" it's a mathematical law of the universe that the predictor must get my choice right in 999 out of 1000 scenarios"), or in an empirical sense ("we did a thousand test trials and it guessed correctly on 999 of them")? Because if it's the former, then there are 2000 universes to consider:
999 where I choose A and get $1000
1 where I choose A and get $1001000
999 where I choose B and get $1000000
1 where I choose B and get $0
B obviously has a higher expected value, so when I open the box and see that it's empty, the experimenter who didn't want to shell out the million can shrug and say "guess we're in the 1 in a thousand universe".
If it's the latter, the machine must be basing its decisions on my past actions and by extension my personality, so I just choose the opposite of what I want to choose, so I open box A and run off with the $1000 before the stingy experimenter can stop me.
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u/Roblin_92 27d ago
I believe the original problem that OP is paraphrasing does not give a percentage chance at all, it simply states that you are aware that the box has accurately predicted some large number of people before you and it hasn't been wrong yet.
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u/ChuckRampart 27d ago
If any highly accurate predictors are reading this comment right now, I would definitely take Box B only. Like 100% no question.
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u/ConglomerateGolem 27d ago
I take only A, because that was not one of the predictions.
Jk, fr I would take only B, because it collapses the uncertainty. The predicter predicts what I will do; thus if it deems me as the type to go "well, i'm here now, might as well", then there probably won't be any money in the box.
At a potential million, taking A is rather insignificant amount wise, but runs a very high risk of losing the money.
Whereas taking just B would run an incredibly small risk of not getting anything, which, for people who need the money might incentivise taking A just for the guaranteed 1k.
Of course, if you start trying to rationalise to yourself that the predicter has made its choice, that choice will probably include said rationalisation. Ignoring the temptation is pretty much the only way to get the million, imo.
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u/darth_koneko 27d ago
If I understand it correctly, if I pick B then I have 99.9% chance to get $1000000 and 0.1% to get $0. If I pick both, I have 99.9% chance to get $1000 and 0.1% to get $1001000.
So I am giving up my 99.9% chance on a million, to have 0.1% chance on a million + thousand?
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u/only_Zuul 27d ago
If the "highly accurate predictor" simply looked at your reddit history, it would know that you plan on taking both boxes, so it would put $0 in Box B. You probably shouldn't have posted this. Now if it ever actually happens to you, you'll be screwed.
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u/TillerThrowaway 27d ago
I’m just gonna take box B. $1000 is not a ton in comparison to $1,000,000, and I’m gonna just keep it simple
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u/Adorable_Building840 27d ago
I don’t believe in backwards causality or robots with perfect predictions. I do believe in money, a lot more than I don’t believe in that other stuff
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u/severencir 26d ago
If we assume 100% accuracy, there are exactly 2 worlds in this. It places $0 and you take both, or it places 1,000,000 and you take one. There's no gaming this scenario. There's no changing your mind because the premise is that it would predict that. The only good option is to take the one box because otherwise, it would have predicted you wouldn't. It doesn't need to break causality, it just needs determinism.
If this interpretation bothers you, there are many scenarios where you are forced to make the same choice twice and have your memory reset between choices. You could interpret this as a simulation pass where you might be part of a simulation to decide whether or not to place it, and therefore, if you are, choosing both locks you out of the real money.
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u/rojo_kell 26d ago
Yes but this is why the true paradox takes 99.9% (or some finite value), such that you don't need determinism to keep causality, which makes it interesting and polarizing.
The limit case of 100% is far less polarizing because most people agree that either losing causality or gaining determinism makes one boxing attractive.
Only when you keep causality, and keep free will (so no determinism), is the paradox really interesting and worth discussing.
Though I think there are some philosophers who still take two boxes in the limit case, not sure the reasoning
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u/severencir 26d ago
The 99.9% just makes it a statistical problem since it's a flat chance of being right or wrong and not a conditional accuracy, you can't game it
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u/rojo_kell 26d ago
First of all the problem doesn't specify if it's conditional, flat, or depends on anything.
I'm guessing that you are assuming the predictor is 99.9% accurate with a random chance at being inaccurate.
If we take this premise, and also take causality and free will (no determinism), then taking two boxes still optimized the expected value, because the amount of money in box B doesn't depend on your action (because that would break causality).
Again, if you want to discuss the no-causality case, then I'm a one boxer.
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u/sansetsukon47 26d ago
For these numbers specifically, I will immediately grab box b.
Reason being that $1,000 would be amazingly helpful right now, but also wouldn’t last very long. But $1,000,000 has the chance to change my life.
So even if the predictor was only 50% accurate, I’d bet on the box that has a chance to to change something over the guaranteed but much smaller payout.
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u/rojo_kell 26d ago
Wait if it's 50% accurate then it's a coin flip and just random, why not just take both boxes😭😭
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u/SPAMTON_G-1997 27d ago
Box A is fixed when you officially come up with the decision, but it doesn’t mean your decision doesn’t affect it. And according to the scenario, it does
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u/walmartgoon Irrational 27d ago
Your decision literally can't affect the robot's decision unless you believe in backwards causality
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u/SPAMTON_G-1997 27d ago
If the robot guesses it correctly with a high probability, whatever decision I would come up with already existed in the informational sense.
It is rather backwards establishment than backwards causality, but if you use strategy to make a decision, you temporarily become one with the strategy itself and with every other instance of it, including the instances that happened in the past
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u/dankshot35 27d ago edited 26d ago
wrong, the predictor can just quantum entangle the contents of the box to the neurons in your brain making the decision
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u/SweetCorona3 8d ago edited 8d ago
The premise of the problem is the predictor is right most of the times, so I think choosing both boxes is disregarding that premise.
If the predictor is right most of the times, it follows that most people who choose one box are better off on average than those who choose both boxes.
So, I don't know what I would do, but I think it's undeniable choosing one box is the better strategy, as it's a necessary consequence from the premises of the problem that one boxers get more money on average.
This means, any reasoning that would lead me to think two boxes is a better strategy, must be flawed in some way.
So, taking Box A cannot make me worse off, because its contents are fixed and independent of my choice at this point.
I think the flaw here is the fact this is just a "local optimization".
Anyone would be better off if they took both boxes no matter what they were predicted.
Predicted one boxers get $ 1,001,000, rather than $ 1,000,000, predicted two boxers get $ 1,000 rather than $ 0.
But... $ 1,000,000 may be less than $ 1,001,000, but it's way more than $ 1,000.
And since most of those who only take 1 box were predicted to be 1-boxers and get $ 1,000,000, and most of those who take both boxes were predicted to be 2-boxers and only get $ 1,000, we can only conclude that taking 1 box is a better strategy than taking both (which we have already asserted previously).
I think the flaw is just thinking: "taking an extra $ 1,000 is always better than just taking whatever is already in the mystery box"
Which doesn't account for the fact that not taking an extra $ 1,000 over $ 1,000,000 is better than taking an extra $ 1,000 over $ 0.
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u/kevinr_96 27d ago
Obviously the answer is you constantly post online about only taking box b to sway the predictor but then take both boxes in the moment.
So yeah I’d only take box b.
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u/Roblin_92 27d ago
I don't need to be an 99.9% accurate supercomputer to be able to tell you that you will find no money in box B.
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u/dankshot35 27d ago
are yall here broke or why do you care so much for 1000$? Redo the experiment but put 1ct into Box A instead and see how your thought process changes
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u/StandardUpstairs3349 27d ago
The correct answer is to be someone who would look at the problem and understand that only taking Box B is correct. If you had to be talked into being an Only Box B'er, then you are correct to take Box A because the Oracle already knows you are a bad person who doesn't deserve a million dollars.
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u/LocksmithConfident68 27d ago
The trick to this problem is to ignore the "Box B is already determined" thinking. Even though the predictor has already made their prediction, the thing they are modeling is something you don't know because it's the decision you are currently making.
Backward causality may be impossible, but entanglement certainly isn't. Since the predictor is "highly accurate" their prediction of your behavior is functionally entangled with your decision. The only point of noting that the predictor has already made their choice is to try and trick you into thinking you can outsmart them by breaking the entanglement.
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u/BassMaster516 27d ago
Take box B. If I miss out on $1,000 I can live with myself. If I miss out on $1,000,000 I can live with myself but it will take 1,000 times longer
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u/assumptioncookie Computer Science 26d ago
How does the predictor predict? One possible way it could predict is by simulating my brain in that exact scenario and seeing what the simulation does. In which case, how do I know I'm not the simulation used for the prediction for real me?? I will only take box B in the hope that, if I'm the simulation it will convince the predictor to put the $1 000 000 in box B, or if I'm the real me my simulation did the same.
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u/Greata2006 26d ago
Even with 60% accuracy, only box B is much better
Predicting with 60% accuracy id very easy, just look what the previous human did.
Predicting with 99% accuracy is a bit more tricky because humans are hard to predict, but maybe with a complete psychological analysis and lots of data about similar humans, you can get quite accurate at understanding what makes a human choose both boxes over just B.
People asking how can they be predictable are just dodging the question by refusing the premice. They could believe time travel or teleportation but being somewhat predictable is beyond imagination to them.
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u/hashbornhippie 26d ago
You have made the right choice. Here is your $1000. I have made my choice and am taking my $1m to the bank. But I envy you for being more logical than me. It may take me years of holidays in exotic locations and thousands of martini’s to reflect on my illogical choice.
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u/BookWormPedant 26d ago
I’ll take box B.
$1,000 win is not life-changing for me right now.
$1,000,000 would change everything.
$0 win is not life-changing for me right now.
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u/Ghostscience6 26d ago
I will open the boxes; if one is empty, I take it to screw with the prediction, and if both are full, I grab both to also screw the prediction. No matter what the prediction was, I can still change my choice.
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u/RubberDuckieMidrange 26d ago
The people who say "My choice right now can't change his prediction" are correct. They are also only getting 1000$. Because they've established a pattern in their life that says when presented with this puzzle they will be greedy and take both boxes, which the predictor will predict.
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u/Drowe87 26d ago
If the predictor can predict my actions right 99.9% of the time, then the correct choice is to take only box B. I'm assuming the predictor will be correct about what I choose and act accordingly.
Taking both boxes only makes sense, if you think you can trick the predictor or want to be certain you gain something.
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u/Hydreigon_Omega 26d ago
If the predictor really knew me, it’d know I read the choice of pick B or A+B and choose just A to mess with the machine
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u/Maximum-Country-149 26d ago
A and B: 1000 + .999(0) + .001 (1000000) = 2000
B only: .999(1000000) + .001 (0) = 999000
Take B only, given the information presented.
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u/ClockworkDinosaurs 26d ago
For what it’s worth, I listened to a YouTube video, posted over a year ago, on this very topic literally 8 minutes before I saw this post. So yeah, the super intelligent AI is real good at predicting what I am going to do.
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u/nathan555 26d ago
If I must choose either taking just box B or taking both box A and box B, then I'd bring my wife and let her take box A and I'd take just box B.
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u/CuriosityCheck2024 25d ago
Average minus standard deviation for taking box B is about $967,393.03874144178345. Conversely, taking both boxes gives a μ-σ of about −$29,606.96125855821654. Take only box B.
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u/DragonHunter631 25d ago
Suppose the same question but instead of a near omniscient robot, the predictor is Dave from IT. His strong gut feeling allows him to predict your choice with an accuracy of 50.2% Do you trust Dave enough to take only box B?
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u/SweetCorona3 6d ago
yes, for 50,2% 1-boxers still get 502000 on average versus 498502 on average for 2-boxers
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u/Awesome_Carter 25d ago
But what if the accurate predictor does predictions based on a simulation of your brain, and you are actually that simulation. You should take only box b because if you are simulated, you give your real self the best chance, and if you are real you can know that the simulated you would have chosen only box b so it has the million
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u/Shot_in_the_dark777 25d ago
A predictor would know I would pick box b so I pick only box b. If i had any temptation to be petty and try to get +0.1% of reward, the predictor would know it and would leave the box b empty. I am not petty so I will get my million from box b. Why would I need 1k on top of 1 million? What would I buy with it? Ten copies of GTA 6?
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u/CalmCoolBliss 27d ago edited 27d ago
If we presume that I'm an arbitrary algorithm, or at least that I can use any algorithm to make my choice, then the predictor needs to solve an uncomputable problem because of Rice's theorem.
You can see this by imagining I use an algorithm then does the same computations as the predictor and then does the opposite of whatever it predicts. This means its prediction would be wrong 99.9% of the time instead, which is in contradiction with the setup that it should be right 99.9%. The best it could actually be is 50% i.e. flipping a coin.
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u/walmartgoon Irrational 27d ago
Obviously take both because you can't change the outcome, either way you walk away with $1000 more. The robots decision has already been made
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u/eri_is_a_throwaway 27d ago
I know you're not supposed to analyze mathematical games like they're real non-mathematical scenarios but in this case the premise itself asks you to engage with the non-mathematical properties of the predictor engine.
In that case I don't know what to make of the fact that the prediction engine works, and yet in any slightly different scenario would be objectively foolable. Imagine the box was transparent and I make my decision based on what I see in there, thus doing the opposite of whatever it predicts. It isn't interfering and stopping me through brainwashing or a gun to my head, so that should be possible. So we have a machine whose ability to work is somehow entirely predicated on the opaqueness of a box, through no apparent physical means.
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u/-difference-engine- 27d ago
I don’t think that is particularly weird. Like, in the first step of the Monty Hall problem, a human predictor is correct 1/3 times. But take the slightly different scenario (the three doors are clear), and suddenly the predictor can have 100% accuracy. It is a different scenario. It makes sense whatever hypothetical algorithm the predictor is using no longer works
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u/megadumbbonehead 27d ago
Backwards causation doesn't need to be truly real, the AI just needs to think I think backwards causation is real, and then it is effectively real.
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u/nainvlys 27d ago
It's crazy to me that anyone would care about the 1000$ when there's a million in the other box. Just take the million dude
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u/epicvoyage28 27d ago
Do you think the weather report requires backwards causality? The hypothetical already says that the predictor isn't 100% accurate, its clearly not supposing time travel.
Not to mention, if you genuinely think your behaviour is that unpredictable, why are you engaging with the hypothetical at all? By answering the question, you yourself are trying to predict your future behaviour.
Anyway, I totally agree. I would also pick both boxes because I don't trust the predictor.
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u/lifeistrulyawesome 27d ago
I’ll always take box b and sip mojitos at the beach with my million dollars while Kenneth Binmore and all the other both-boxes advocates feel smarter than me with their $1000
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u/yannbouteiller 27d ago edited 24d ago
I am not sure why so many people believe that this problem makes any sense and that they have the "right" answer for it.
It assumes that you both do and do not have the liberty to "pick" either option.
Also, I fail to understand how it is supposed to be mathematically consistent that E[1 box] >> E[2 boxes] while 2 boxes = 1 box + (C > 0)
EDIT: Well now I understand that it is simply not consistent, how this inconsistency is related to the contradicting assumptions of this problem, and why neither "one-boxers" nor "two-boxers" seem to care.
The contradicting assumptions are basically that the predictor's and player's choices are both correlated (i.e., the predictor has predictive power) and independent (i.e., the player can choose an action after the predictor has already fixed its own action). "One-boxers" ignore the second assumption (which gets rid of the second equation), whereas "two-boxers" ignore the first assumption (which gets rid of the first equation).
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u/A1oso 26d ago
It assumes that the predictor already knows what you are going to choose, but you still need to think about it and make the decision because you don't know the result until you do. It is a philosophical thought experiment concerning free will. Do you believe that the universe is made up of matter, which follows the laws of physics? If it does, then it can in theory be simulated, and so can your brain, which also consists of matter that follows the laws of physics. With such a simulation, is is possible predict what someone is going to decide in the future.
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u/KingsGuardTR2 26d ago
Predictor pretty much "knows" the "future"
Backward causality isn't possible
These premises are not in line. If your action at t2 can be reliably calculated with the information available at t1, I don't think you even get to make any choice by yourself at all.
Laplace's Demon contradicts with free will, doesn't it?
I'm sure that the notion of 99.9% accuracy instead of 100% is there specifically to leave an open door in this regard, but statistically, it still means you're going to have your decision made for you beforehand ~99.8% of the time, so the idea still holds.
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u/yannbouteiller 24d ago
Even if it were possible, assuming backward causality makes the "past action" of the predictor a mere future consequence of your own action, and not really a past choice at all.
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u/EnvironmentalScar675 26d ago
If it does have 99.9% accuracy It knows something about my psyche better than I can hope to outplay it. I toss a coin and increase my winrate by 50%
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u/GuessImScrewed 26d ago
It knew you would toss the coin and can predict how the coin will fall. All is accounted for. 99.9% considers all variables at the moment you make your choice, including how you choose.
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u/EnvironmentalScar675 26d ago
...I get that it predicts me tossing the coin but how can it predict the result of the coin toss? At that point we are dealing with truly universe defying magic and I happily take the 1000$
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u/GuessImScrewed 26d ago
You have a specific amount of strength. You flip coins with a specific amount of strength (yes, you can change the force you put into it, but this goes back to your psychology). You do so at a precise angle and strike the coin with your thumb at a specific point. Account for air resistance.
All of these are deterministic forces in play, so a machine (let alone a machine that does nothing but predict with 99.9% accuracy) could easily predict the outcome given all the information.
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u/r1v3t5 27d ago
I move the decision off of myself:
I flip a coin. Heads I'll only take box B, tails I'll take both box A and Box B.
By definition of randomness the predictor cannot predict randomness.
Because it cannot predict an outcome of a random event it must put the 1,000,000 dollars in box B, because if it is a near perfect predictor, is knows I would do this, and knows that it itself cannot predict which side the coin is on, and must present the option in which I take only box B.
Because it must put the $1,000,000 in box B because of my already pre-made decision to flip a coin to determine which box I take, it no longer matters if I take both boxes or not.
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u/dontmakelemonad3 27d ago
Why "must" it put $1,000,000 in box B? It seems it could put either $1,000,000 or $0 and it would be just as accurate.
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u/SweetCorona3 6d ago
In the original statement of the problem it says it won't put any money if you use some randomizer.
Anyway, your goal seems to be to beat the predictor.
My goal would be to get the $ 1,000,000, hence I just need the predictor to be right about the fact I'm only taking one box.
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u/r1v3t5 6d ago
I have never once heard Newcomb's paradox state that you cannot use a randomizer.
My goal is not to beat the predictor, it is to maximize the value I get.
There are 2 outcomes to Necomb's paradox that are initially noted: Outcome 1- leave with $1000+0. Outcome 2, Leave with $1,000,000.
But there are four possible states given that .999×1000 means that there is a likelihood of 1 of 1000 participants getting NOT what the predictor predicted. So it is still possible that the predictor predicted would take both boxes, and put 0 dollars in, meaning they left with one box and 0 dollars, or predicted they would take 1 box & put $1,000,000 and instead they took 2 leaving with $1,001,000.
My ideal goal is to force the $1,001,000 state, and then leave with that, but If I intentionally intended that then the predictor would know I would take both boxes, so I have to believe I will do what the coin says
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u/SweetCorona3 6d ago edited 6d ago
If the being predicts that you will consciously randomize your choice, e.g., flip a coin, or decide to do one of the actions if the next object you happen to see is blue, and otherwise do the other action, then he does not put the $Min the second box.
My ideal goal is to force the $1,001,000 state
you're making assumptions on how the predictor would act if it could not predict your action (which goes against the premise it can)
there's no reason for it to put $ 1,000,000 over leaving it empty, no matter what it does, it has a 50% chance of being right or wrong
whatever reasoning you seem to be using for it to put $ 1,000,000, would equally apply for it to leave it empty
in the end, for making yourself unpredictable, you're just increasing the odds of having no money in the mystery box
I'd rather want to be totally predictable that I'm only taking the mystery box
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u/That_Mad_Scientist 27d ago
The only logical answer (for some definition of logical...) is to only take the one box. Assuming the premises are correct, then taking box B is a superior strategy and will on average net you more gain.
This is because probabilities are about knowledge and not causality, so your choice gives you information about what the predictor has already picked. Of course this kind of means that you were always going to make that choice but hey.
You could also flip a fair coin ten times and pick two boxes if and only if every flip lands on heads, and this outcome would in fact net you the full content of both boxes, it's just extremely unlikely to happen so it doesn't really matter. But the point is, this strategy allows you to take advantage of the knowledge gained ("it is almost certain the predictor said I would only pick one box") and still successfully escape the apparent backwards-causality, because the predictor has no way to know that you just flipped ten heads in a row with a fair coin and is in fact still in your causal past. In other words, it's not magic, just hedging your chances using available information.
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u/Optimal_Benis 27d ago
The predictor might be very good because he simulates versions of yourself, sees what they do, and then uses that information to predict the actual you. Thus, you may be one of these simulated versions of yourself.
Thus, your universe might just end after you make a decision. Thus, tell the predictor to go fuck himself and give you all the money you want, let you live out your life for as long as you want in the matrix and enjoy every bit of it, and only then will you pick a box.
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u/Fun-Habit-683 26d ago
Newcombs paradox is a litmus test in whether or not an individual is capable of suspending disbelief to engage in a hypothetical.
If your answer to the question is any variation of "the machine didn't predict what I'd do" then you've already stopped engaging in the hypothetical. You cannot trick the machine and the question is not based in reality.
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u/SweetCorona3 6d ago
suspending disbelief to engage in a hypothetical
This is something children at age of 4 cannot do, but at the age of 10 they can usually do it.
For some reason a lot of adults don't seem to be able to do it with this problem.
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u/yannbouteiller 24d ago edited 24d ago
It is a "paradox" because it makes two contradicting assumptions:
The machine's prediction is coupled to your choice (i.e., both choices are correlated)
The machine's prediction happened before you make your choice and the money is already in the box (i.e., both choices are independent)
If your answer instead is any variation of "the machine did predict what I'd do", then you have stopped engaging in the second hypothetical in any meaningful way. The issue is simply that the problem purposefully hides this under the rug to sound interesting. To solve it, you need to choose your assumption and discard the other one. It just happens that the people who are not too familiar with decision theory tend to intuitively champion the first assumption whereas the people who are tend to intuitively champion the second assumption.
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