Philosophers working in decision theory are drastically worse at Newcomb
Listen, this is like someone who believes the Axiom of Choice saying “constructivist mathematicians are drastically worse at set theory” (because they reject Choice). Newcomb is all about how you view free will. This is not a settled question yet.
Why does ‘free will’ make any difference? If Omega can only predict you with e.g. 60% accuracy, that’s still enough to generate the problem.
I’m not saying the right answer, i.e., the right decision theory, is a settled question. I’m just saying they lose. This matters. If their family members’ or friends’ welfare were on the line, as opposed to some spare cash, I strongly suspect philosophers would be less blasé about privileging their pet formal decision-making theory over actually making the world a better place. The units of value don’t matter; what matters is that causal decision theory loses, and loses by arbitrarily large amounts.
I once took a martial arts class (taught by a guy who once appeared on the “ninja episode” of Mythbusters, where they tried to figure out if a human can catch an arrow out of the air). He knew this trick called “choshi dori” (I think it roughly means ‘attention/initiative grabbing’). How exactly this trick works is a long story, but it has to do with “hacking the lower brain” of the opponent in various ways. One of the things he could do was have a guy punch him in the face and have the punch instead land on empty air, completely contrary to the volition of the puncher. Note: it would work even if he told you exactly what he was doing.
He could do this because of the way punch targeting works (the largely subconscious system responsible has certain rules it follows that could be influenced in a way that causes you to miss).
There are various ways to defeat “choshi dori,” although the gentleman in question could certainly get the vast majority of randomly chosen people to fall for it. Whatever “free will” is, its probably more complicated than just taking Omega at its word. Perhaps Omega achieved his accuracy by a similar defeatable hack. Omega claims to “open up the agent,” and my response is to try to “open up Omega,” to see what’s behind his prediction %.
I don’t see why it would be at all difficult or mysterious for Omega to predict that I one-box. I mean, it’s not like my thought processes there are at all difficult to understand or predict.
My point is exactly that it is not mysterious. Omega used some concrete method to win his game, much in the same way that the fellow in question uses a particular method to win the punching game. The interesting question in the Newcomb problem is (a) what is the method, and (b) is the method defeatable. The punching game is defeatable. Giving up too early on the punching game is a missed chance to learn something about volition.
The right response to a “magic trick” is to try to learn how the trick works, not go around for the rest of one’s life assuming strangers can always pick out the ace of spades.
Omega’s not dumb. As soon as Omega knows you’re trying to “come up with a method to defeat him”, Omega knows your conclusion—coming to it by some clever line of reasoning isn’t going to change anything. The trick can’t be defeated by some future insight because there’s nothing mysterious about it.
Free-will-based causal decision theory: The simultaneous belief that two-boxing is the massively obvious, overdetermined answer output by a simple decision theory that everyone should adopt for reasons which seem super clear to you, and that Omega isn’t allowed to predict how many boxes you’re going to take by looking at you.
I am not saying anything weird, merely that the statements of the Newcomb’s problem I heard do not specify how Omega wins the game, merely that it wins a high percentage (all?) of the previous attempts. The same can be said for the punching game, played by a human (who, while quite smart about the volition of punching, is still defeatable).
There are algorithms that Omega could follow that are not defeatable (people like to discuss simulating players, and some others are possible too). Others might be defeatable. The correct decision theory in the punching game would learn how to defeat the punching game and walk away with $$$. The right decision theory in the Newcomb’s problem ought to first try to figure out if Omega is using a defeatable algorithm, and only one box if it is not, or if it is not possible to figure this out.
Okay, let’s try and defeat Omega. The goal is to do better than Eliezer Yudkowsky, which seems to be trustworthy about doing what he publicly says all over the place. Omega will definitely predict that Eliezer will one-box, and Eliezer will get the million.
The only way to do better is to two-box while making Omega believe that we will one-box, so we can get the $1001000 with more than 99.9% certainty. And of course,
Omega has access to our brain schematics
We don’t have access to Omega’s schematics. (optional)
Omega has way more processing power than we do.
Err, short of building an AI to beat the crap out of Omega, that looks pretty impossible. $1000 is not enough to make me do the impossible.
Omega used some concrete method to win his game, much in the same way that the fellow in question uses a particular method to win the punching game.
A crucial difference is that the punching game is real, while Newcomb’s problem is fiction, a thought experiment.
In the punching game, you can try to learn how the trick is done and how to defeat the opponent, and you are still engaged in the punching game.
In Newcomb’s problem, Omega is not a real thing that you could discover something about, in the way that there is something to discover about a real choshi dori master. There is no such thing as what Omega is really doing. If you think up different things that an Omega-like entity might be doing, and how these might be defeated to win $1,001,000, then you are no longer thinking about Newcomb’s problem, but about a different thought experiment in some class of Newcomb-like problems. I expect a lot of such thinking goes on at MIRI, and is more useful than endlessly debating the original problem, but it is not the sort of thing that you are doing to defeat choshi dori.
The right response to a “magic trick” is to try to learn how the trick works, not go around for the rest of one’s life assuming strangers can always pick out the ace of spades.
Here is a trivial model of the “trick” being fool-proof (and I do mean “fool” literally), which I believe has been discussed here a time or ten. Omega runs a perfect simulation of you, terminates it right after you make your selection or if you refuse to choose (he is a mean one), checks what it outputs, uses it to place money in the boxes. Omega won’t even offer the real you the game if you are one of those stubborn non-choosers. The termination clause is to prevent you from enjoying the spoils in case YOU are that simulation, so only the “real you” will know if he won or not. And to avoid any basilisk-like acausal trade. He is not that mean.
EDIT: if you think that the termination is a cruel cold-blooded murder, note that you do that all the time when evaluating what other people would do, then stop thinking about it, once you have your answer. The only difference is the fidelity level. If you don’t require 100% accuracy, you don’t need a perfect simulation.
Do you think that gets rid of the problem? ‘It might be possible to outsmart Omega’ strikes me as fairly irrelevant. As long as it’s logically possible that you don’t successfully outsmart Omega, the original problem can still be posed. You still have to make a decision, in those cases where you don’t catch Omega in a net.
I am not saying there isn’t a problem, I am saying the problem is about clarifying volition (in a way not too dissimilar to the “choshi dori” trick in my anecdote). Punching empty air is “losing.” Does this then mean we should abstain from punching? Seems a bit drastic.
Many problems/paradoxes are about clarification. For example the Simpson’s paradox is about clarifying causal vs statistical intuitions.
More specifically, what I am saying is that depending on what commitments you want to make about volition, you would either want to one box, or two box in such a way that Omega can be defeated. The problem is “non-identified” as stated. This is equivalent to choosing axioms in set theory. You don’t get to say someone fails set theory if they don’t like Choice.
1 - Supposing I have no philosophical views at all about volition, I would be rationally obliged to one-box. In a state of ignorance, the choice is clear simply provided that I value whatever is being offered. Why should I then take the time to form a theory of volition, if you’re right and at most it can only make me lose more often?
We don’t know what the right answer to Newcomb-like problems will look like, but we do know what the wrong answers will look like.
2 - Supposing I do have a view about volition that makes me think I should two-box, I’ll still be rationally obliged to one-box in any case where my confidence in that view is low enough relative to the difference between the options’ expected values.
For instance, if we assign to two-boxing the value ‘every human being except you gets their skin ripped off and is then executed, plus you get $10’ and assign to one-boxing the value ‘nobody gets tortured or killed, but you miss out on the $10’, no sane and reasonable person would choose to two-box, no matter how confident they (realistically) thought they were that they have a clever impossibility proof. But if two-boxing is the right answer sometimes, then, pace Nozick, it should always be the right answer, at least in cases where the difference between the 2B and 1B outcomes is dramatic enough to even register as a significant decision. Every single one of the arguments for two-boxing generalize to the skin-ripping-off case, e.g., ‘I can’t help being (causal-decision-theory-)rational!’ and ‘it’s unfair to punish me for liking CDT; I protest by continuing to employ CDT’.
3 - You seem to be under the impression that there’s something implausible or far-fetched about the premise of Newcomb’s Problem. There isn’t. If you can’t understand a 100% success rate on Omega’s part, then imagine a 99% success rate, or a 50% one. The problem isn’t altered in substance by this.
Edit: and come to think of it I am somewhat less sure about the lower success rates in general. If I can roughly estimate Omega’s prediction about me that would seem to screen off any timeless effect. Like, you could probably pretty reliably predict how someone would answer this question based on variables like Less Wrong participation and having a Phd in philosophy. Using this information, I could conclude that an Omega with 60% accuracy is probably going to classify me as a one-boxer no matter what I decide… and in that case why not two box?
Sorry, by a 50% success rate I meant that Omega correctly predicts your action 50% of the time, and the other half of the time just guesses. Guessing can also yield the right answer, so this isn’t equivalent to a 50% success rate in the sense you meant, which was simply ‘Does Omega put the money in the box he would have wished to?’
If you know that Omega will take into account that you’re a LessWronger, but also know that he won’t take into account any other information about you (including not taking into account the fact that you know that he knows you’re a LessWronger!), then yes, you should two-box. But that’s quite different from merely knowing that Omega has a certain success rate. Let’s suppose we know that 60% of the time Omega makes the decision it would have wished were it omniscient. Then we get:
If I one-box: 60% chance of $1,000,000, 40% chance of $1000.
If I two-box: 60% chance of $1000, 40% chance of $1,001,000.
Then the expected value of one-boxing is $600,400. Expected value of two-boxing is $401,000. So you should one-box in this situation.
You are not listening to me. Suppose this fellow comes by and offers to play a game with you. He asks you to punch him in the face, where he is not allowed to dodge or push your hand. If you hit him, he gives you 1000 dollars, if you miss, you give him 1000 dollars. He also informs you that he has a success rate of over 90% playing this game with randomly sampled strangers. He can show you videos of previous games, etc.
This game is not a philosophical contrivance. There are people who can do this here in physical reality where we both live.
Now, what is the right reaction here? My point is that if your right reaction is to not play then you are giving up too soon. The reaction to not play is to assume a certain model of the situation and leave it there. In fact, all models are wrong, and there is much to be learned about e.g. how punching works in digging deeper into how this fellow wins this game. To not play and leave it at that is incurious.
Certainly the success rate this fellow has with the punching game has nothing to do with any grand philosophical statement about the lack of physical volition by humans.
Learning about how punching works, rather than winning 1000 dollars, is the entire point of this game.
My answer to Newcomb’s problem is to one-box if and only if Omega is not defeatable and two-box in a way that defeats Omega otherwise. Omega can be non-defeatable only if certain things hold. For example if it is possible to fully simulate in physical reality a given human’s decision process at a particular point in time, and have this simulation be “referentially transparent.”
My answer to Newcomb’s problem is to one-box if and only if Omega is not defeatable and two-box in a way that defeats Omega otherwise
But now you’ve laid out your decision-making process, so all Omega needs to do now is to predict whether you think he’s defeatable. ;-)
In general, I expect Omega could actually be implemented just by being able to tell whether somebody is likely to overthink the problem, and if so, predict they will two-box. That might be sufficient to get better-than-chance predictions.
To put it yet another way: if you’re trying to outsmart Omega, that means you’re trying to figure out a rationalization that will let you two-box… which means Omega should predict you’ll two-box. ;-)
There are various ways to defeat “choshi dori,” although the gentleman in question could certainly get the vast majority of randomly chosen people to fall for it. Whatever “free will” is, its probably more complicated than just taking Omega at its word. Perhaps Omega achieved his accuracy by a similar defeatable hack.
Omega claims to “open up the agent,” and my response is to try to “open up Omega,” to see what’s behind his prediction %.
Let’s try using your martial arts analogy. Consider the following:
You find yourself in a real world physical confrontation with a ninja who demands your wallet. You have seen this ninja fight several other ninjas, a pirate and a Jedi in turn and each time he used “choshi dori” upon them then proceeded to break both of their legs and take their wallet. What do you do?
Punch the ninja in the face.
Shout “I have free will!” and punch the ninja in the face.
Think “I want to open up the ninja and see how his choshi dori works” then try to punch the ninja in the face.
Toss your wallet to the ninja and then run away.
This isn’t a trick question. All the answers that either punch the ninja in the face or take two boxes are wrong. They leave you with two broken legs or an otherwise less desirable outcome.
Sometimes people fight a hypothetical because the hypothetical is problematic. I lean toward two-boxing in Newcomb’s problem, basically because I can’t not fight this hypothetical. My reasoning is more or less as follows. If the being claiming to be Omega actually exists and can in fact instantly model my mental processes, then I’m almost certainly a simulation. One-boxing would reveal that I know that and risk getting me turned off, making the money in the box rather beside the point, so I two-box. If I’m not a simulation, I don’t accept the possibility of Omega existing in the first place, so I two-box. Basically, I think Newcomb’s problem is not a particularly useful hypothetical, because I don’t see it as predictive of decision-making in other circumstances.
One-boxing would reveal that I know that and risk getting me turned off, making the money in the box rather beside the point, so I two-box.
It seems to me that if Omega concludes that you are aware that you are in a simulation based on the fact that you take one box then Omega is systematically wrong when reasoning about a broad class of agents that happens to include all the rational agents (and some others). This is rather a significant flaw in an Omega implementation.
Basically, I think Newcomb’s problem is not a particularly useful hypothetical, because I don’t see it as predictive of decision-making in other circumstances.
For agents with coherent decision making procedures it is equivalent to playing a Prisoner’s Dilemma against a clone of yourself. That is something that feels closer to a real world scenario for some people. It is similarly equivalent to Parfit’s Hitch-hiker when said hitch-hiker is at the ATM.
That’s why I don’t like Newcomb’s problem. In a prisoner’s dilemma with myself, I’d cooperate (I trust me to cooperate with myself). Throwing Omega in confuses this pointlessly. I suspect if people substituted “God” for “Omega” I’d get more sympathy on this.
Are you suggesting that if you are a simulation, two-boxing reduces your risk of being turned off? If not, I don’t understand your reasoning at all. If so, I guess I understand your reasoning from that point on (presumably you feel no particular loyalty to the entity you’re simulating?), but I don’t understand how you arrive at that point.
At a minimum, I can’t see how two-boxing could be worse in terms of risk of being turned off. I suppose Omega could think I was trying to be tricky by two-boxing specifically to avoid giving my awareness that I’m being simulated away, but at that point the psychology becomes infinitely recursive. I’ll take my chances while the simulator puzzles that out.
I’m not sure I understand your parenthetical. Does the existence of a simulation imply the existence of an outside entity being simulated?
can’t see how two-boxing could be worse in terms of risk of being turned off.
Neither can I. Nor can I see how it could be better. In fact, I see no likely correlation between one/two-boxing and likelihood of being turned off at all. But if my chances of being turned off aren’t affected by my one/two-box choice, then “One-boxing would [..] risk getting me turned off [..] so I two-box” doesn’t make much sense.
You clearly have a scenario in mind wherein I get turned off if my simulator is aware that I’m aware that I’m being simulated and not otherwise, but I don’t understand why I should expect that.
Does the existence of a simulation imply the existence of an outside entity being simulated?
To be honest, I’ve never quite understood what the difference is supposed to be between the phrases “existing in a simulation” and “existing”.
But regardless, my understanding of “If the being claiming to be Omega actually exists and can in fact instantly model my mental processes, then I’m almost certainly a simulation” had initially been something like “If Omega can perfectly model Dave’s mental processes in order to determine Dave’s likely actions, then Omega will probably create lots of simulated Daves in the process. Since those simulated Daves will think they are Dave, and there are many more of them than there are of Dave, and I think I’m Dave, the odds are (if Omega exists and can do this stuff) that I’m in a simulation.”
All of which also implies that there’s an outside entity being simulated in this scenario, in which case if I feel loyalty to that entity (or otherwise have some basis for caring about how my choices affect it) then whether I get turned off or not isn’t my only concern anyway..
I infer from your question that I misunderstood you in the first place, though, in which case you can probably ignore my parenthetical. Let me back up and ask, instead, why if the being claiming to be Omega actually exists and can in fact instantly model my mental processes, then I’m almost certainly a simulation?
My thinking here is that if a being suddenly shows up and can perfectly model me, despite not having scanned my neural pathways, taken any tissue samples, observed my life history, or gathered any other data whatsoever, then it’s cheating somehow—i.e. I’m a simulation and it has my source code.
This doesn’t require there to be a more real Prismattic one turtle down, as it were. I could be a simulation created to test a set of parameters, not necessarily a model of another entity.
In general, you can’t make people miss or fall over without touching them unless they know you can make them miss or fall over when touching is allowed.
I don’t think controversies over the Axiom of Choice are similar in the right ways to controversies over Newcomb’s Problem. In pragmatic terms, we know that true two-boxers will willingly take on arbitrarily large disutility (or give up arbitrarily large utility), inasmuch as they’re confident that two-boxing is the right answer. The point can even be put psychologically: To the extent that it’s a psychological fact that humans don’t assign infinite value to being Causal Decision Theorists, the utility (relative to people’s actual values) of following CDT can’t outweigh the bad consequences of consistently two-boxing.
I know of no correspondingly strong demonstration that weakening Choice or eliminating LEM leads demonstrably to irrationality (relative to how the world actually is and, in particular, what preferences people actually have).
In pragmatic terms, we know that true two-boxers will willingly take on arbitrarily large disutility
This is only the case in a world-view that accepts that Omega cannot be tricked. How do you know Omega cannot be tricked? This view corresponds to a certain view of how choices get made, how the choice making algorithm is simulated, and various properties of this simulation as embodied in physical reality. Absent an actual proof, this view is just that—a view.
Two-boxers aren’t (necessarily!) stupid, they simply adhere to commitments that make it possible to fool Omega.
Two-boxers aren’t (necessarily!) stupid, they simply adhere to commitments that make it possible to fool Omega.
No, they don’t. You seem to be confused not just about Newcomb’s Problem but also about why the (somewhat educated subset of) people who Two-Box make that choice. They emphatically do not do it because they believe they are able to fool Omega. They expect to lose (ie. not get the $1,000,000).
This is only the case in a world-view that accepts that Omega cannot be tricked. How do you know Omega cannot be tricked?
By hypothesis, this is how it works. Omega can predict your choice with >0.5 accuracy (strictly more than half the time). Regardless of Free Will or Word of God or trickery or Magic.
The whole point of the thought experiment is to analyze a choice under some circumstances where the choice causes the outcomes to have been laid out differently.
If you fight the hypothesis by asserting that some other worldviews grant players Magical Powers From The Beyond to deceive Omega (who is just a mental tool for the thought experiment), then I can freely assert that Omega has Magical Powers From The Outer Further Away Beyond that can neutralize those lesser powers or predict them altogether. Or maybe Omega just has a time machine. Or maybe Omega just fucking can, don’t fight the premises damnit!
And as wedrifid pointed out, this is not even the main reason why the smarter two-boxers two-box. It’s certainly one of the common reasons why the less-smart ones do though, in my experience. (Since they never read the Sequences, aren’t scientists, and never learned to not fight the premises! Ahem.)
I think the ease with which this community adopts one boxing has to do with us having internalized a computationalist view of the mind and the person. This has a lot in common with the psychological view of person-hood. Basically, we treat agents as decision algorithms which makes it much easier to see how decisions could have non-causal properties.
This is, incidentally, related to my platonism you asked me about. Computationalism leads to a Platonic view of personhood (where who you are is basically an algorithm that can have multiple instantiations). One-boxing falls right out of this theory. The decision you make in Newcombs problem is determined by your decision algorithm. You decision algorithm can be wholly or partly instantiated by Omega and that’s what allows Omega to predict your behavior.
My problem with thinking of Newcomb’s paradox this way is that it is possible that my decision algorithm will be “try to predict what Omega does, and....” For Omega to predict my behavior by running through my algorithm will involve a self-reference paradox; it may be literally impossible, even in principle, for Omega to predict what I do.
Of course, you can always say “well, maybe you can’t predict what Omega does”, but the problem as normally posed implies that there’s an algorithm for producing the optimal result and that I am capable of running such an algorithm; if there are some algorithms I can’t run, I may be incapable of properly choosing whether to one-box or two-box at all.
Your prediction of what Omega does is just as recursive as as Omega’s prediction. But if you actually make a decision at some point that means that your decision algorithm has an escape clause (ow! my brain hurts!) which means that Omega can predict what you’re going to do (by modelling the all the recursions you did).
but the problem as normally posed implies that there’s an algorithm for producing the optimal result and that I am capable of running such an algorithm
It doesn’t actually. The optimal result is two boxing when Omega thinks you are going to one box. But since Omega is a God-like super computer and you aren’t that isn’t going to happen. If you happen to have more information about Omega than it has about you and the hardware to run a simulation of Omega then you can win like this. But that isn’t the thought experiment.
My point (or the second part of it) is that simply by asking “what should you do to achieve an optimal result”, the question assumes that your reasoning capacity is good enough to compute the optimal result. If computing the optimal result requires being able to simulate Omega, then the original question implicitly assumes that you are able to simulate Omega.
Where does the question assume that you can compute the optimal result? Newcomb’s Problem simply poses a hypothetical and asks ‘What would you do?‘. Some people think they’ve gotten the right answer; others are less confident. But no answer should need to presuppose at the outset that we can arrive at the very best answer no matter what; if it did, that would show the impossibility of getting the right answer, not the trustworthiness of the ‘I can optimally answer this question’ postulate.
I once had a man walk up to me and ask me if I had the correct time. I looked at my watch and told him the time. But it seemed a little odd that he asked for the correct time. Did he think that if he didn’t specify the qualifier “correct”, I might be uncertain whether I should give him the correct or incorrect time?
I think that asking what you would do, in the context of a reasoning problem, carries the implication “figure out the correct choice” even if you are not being explicitly asked what is correct. Besides, the problem is seldom worded exactly the same way each time and some formulations of it do ask for the correct answer.
For the record, I would one-box, but I don’t actually think that finding the correct answer requires simulating Omega. But I can think of variations of the problem where finding the correct answer does require being able to simulate Omega (or worse yet, produces a self-reference paradox without anyone having to simulate Omega.)
When you suggest someone read three full length posts in response to a single sentence some context is helpful, especially if they weren’t upvoted. Maybe summarize their point or something.
If it was easy to summarize, it wouldn’t have required a three parter sequence. :-)
However, perhaps one relevant point from it is:
For the purposes of Newcomb’s problem, and the rationality of Fred’s decisions, it doesn’t matter how close to that level of power Omega actually is. What matters, in terms of rationality, is the evidence available to Fred about how close Omega is to having to that level of power; or, more precisely, the evidence available to Fred relevant to Fred making predictions about Omega’s performance in this particular game.
Since this is a key factor in Fred’s decision, we ought to be cautious. Rather than specify when setting up the problem that Fred knows with a certainty of 1 that Omega does have that power, it is better to specify a concrete level of evidence that would lead Fred to assign a probability of (1 - δ) to Omega having that power, then examine the effect upon which option to the box problem it is rational for Fred to pick, as δ tends towards 0.
Listen, this is like someone who believes the Axiom of Choice saying “constructivist mathematicians are drastically worse at set theory” (because they reject Choice). Newcomb is all about how you view free will. This is not a settled question yet.
To the extent that Newcomb’s Problem is ‘about how you view free will’ people who two box on Newcomb’s Problem are confused about free will.
This isn’t like constructivist mathematicians being worse at set theory because they reject choice. It’s closer to a kindergarten child scribbling in crayon on a Math exam then insisting “other people are bad at Math too therefore you should give me full marks anyway”.
To the extent that Newcomb’s Problem is ‘about how you view free will’ people who two box on Newcomb’s Problem are confused about free will.
I don’t think that’s fair (though I also don’t think Newcomb’s problem has anything to do with free will either). The question is whether one-boxing or two-boxing is rational. It’s not fair to respond simply with ‘One-boxing is rational because you get more money’, because two-boxers know one-boxing yields more money. They still say it’s irrational. It would be question begging to try to dismiss this view because rationality is just whatever gets you more money, since that’s exactly what the argument is about.
To the extent that Newcomb’s Problem is ‘about how you view free will’ people who two box on Newcomb’s
Problem are confused about free will.
If you say so. If I learn enough about “choshi dori” to fool the punch-avoiding algorithm and win 1000 dollars, and you don’t play, who is confused? Rationalists are supposed to win, remember, not stick to a particular view of a problem.
If you say so. If I learn enough about “choshi dori” to fool the punch-avoiding algorithm and win 1000 dollars, and you don’t play, who is confused? Rationalists are supposed to win, remember, not stick to a particular view of a problem.
Rational agents who play Newcomb’s Problem one box. Rational agents who are in entirely different circumstances make entirely different decisions as determined by said circumstances. They also tend to have a rudimentary capability of noticing the difference between problems.
(a) You are being a dick. I certainly did not insult anyone in this thread.
(b) The isomorphism is exact. The point is granularity. If the guy can avoid the punch 90% of the time (or more precisely guess what your punch decision algorithm will do in response to some inputs 90% of the time), and Omega guesses what you will do correctly 90% of the time, that ought to be sufficient to do the math on expected values, if you want to leave it there.
Or, alternatively, you can try to “open up the agent you are playing against” and try to trick it. It’s certainly possible in the punching game. It may or may not be possible in the game with Omega—the problem doesn’t specify.
If you say “well, rational people do X and not Y, end of story” that’s fine. I am going to make my updates on you and move on.
A typical example of irrational behavior is intransitive preference. As the money pump thread shows people often don’t actually fall for money pumping, even if they have intransitive preferences. In other words, the map doesn’t fully reflect the territory of what people actually do.
Another example is gwern’s example with correlation and causation. Correlation does not imply causation, says gwern, but if we knew how often it does imply it, we may well be rational to conclude the latter from the former if the odds are good enough. He’s right—but no one does this (I don’t think!).
I used the example of the punching game on purpose—it makes the theoretical situation with Omega practical, as in you can go and try this game if you wanted. My response to trying the game was to learn how it works, rather than give up playing it. This is what people actually do. If your model doesn’t capture it, it’s not a good model.
A broader comment: I do math for a living. The issues of applicability of math to practical problems, and changing math models around is something I think about quite a bit.
It took a non-trivial exertion in the direction of politeness to refrain from answering the rhetorical question “who is confused?” with a literal answer.
I certainly did not insult anyone in this thread.
Arguable. I would concede at least that you did not say anything insulting that you do not sincerely believe is warranted.
(b) The isomorphism is exact. The point is granularity. If the guy can avoid the punch 90% of the time (or more precisely guess what your punch decision algorithm will do in response to some inputs 90% of the time), and Omega guesses what you will do correctly 90% of the time, that ought to be sufficient to do the math on expected values, if you want to leave it there.
Doing expected value calculations on probabilistic variants of newcomb’s problem is also old news. And results in one boxing unless the probability gets quite close to random guessing. Once again, if you choose a sufficiently different problem than Newcomb’s (such as by choosing an accuracy sufficiently close to 0.5, reducing the payoff ratio or by positing that you are in fact more intelligent than Omega) then you have failed to respond to a relevant question (or an interesting question, for that matter).
If you say “well, rational people do X and not Y, end of story” that’s fine. I am going to make my updates on you and move on.
Please do. I have likewise updated. Evidence suggests you are ill suited to considering counterfactual problems and unlikely to learn. My only recourse here is to minimize the damage you can do to the local sanity waterline. I’ll leave further attempts at verbal interaction to the half a dozen others who have been attempting to educate you, assuming they have more patience than I.
A broader comment: I do math for a living. The issues of applicability of math to practical problems, and changing math models around is something I think about quite a bit.
I would be interested in seeing how philosophers do on tests of analytical versus intuitive reasoning (I forget the name of the test normally used for gauging this) and ability to narrow down hypotheses when the answers are known and easily verifiable.
I would be interested in seeing how philosophers do on tests of analytical versus intuitive reasoning (I forget the name of the test normally used for gauging this)
Listen, this is like someone who believes the Axiom of Choice saying “constructivist mathematicians are drastically worse at set theory” (because they reject Choice). Newcomb is all about how you view free will. This is not a settled question yet.
Why does ‘free will’ make any difference? If Omega can only predict you with e.g. 60% accuracy, that’s still enough to generate the problem.
I’m not saying the right answer, i.e., the right decision theory, is a settled question. I’m just saying they lose. This matters. If their family members’ or friends’ welfare were on the line, as opposed to some spare cash, I strongly suspect philosophers would be less blasé about privileging their pet formal decision-making theory over actually making the world a better place. The units of value don’t matter; what matters is that causal decision theory loses, and loses by arbitrarily large amounts.
I once took a martial arts class (taught by a guy who once appeared on the “ninja episode” of Mythbusters, where they tried to figure out if a human can catch an arrow out of the air). He knew this trick called “choshi dori” (I think it roughly means ‘attention/initiative grabbing’). How exactly this trick works is a long story, but it has to do with “hacking the lower brain” of the opponent in various ways. One of the things he could do was have a guy punch him in the face and have the punch instead land on empty air, completely contrary to the volition of the puncher. Note: it would work even if he told you exactly what he was doing.
He could do this because of the way punch targeting works (the largely subconscious system responsible has certain rules it follows that could be influenced in a way that causes you to miss).
There are various ways to defeat “choshi dori,” although the gentleman in question could certainly get the vast majority of randomly chosen people to fall for it. Whatever “free will” is, its probably more complicated than just taking Omega at its word. Perhaps Omega achieved his accuracy by a similar defeatable hack. Omega claims to “open up the agent,” and my response is to try to “open up Omega,” to see what’s behind his prediction %.
I don’t see why it would be at all difficult or mysterious for Omega to predict that I one-box. I mean, it’s not like my thought processes there are at all difficult to understand or predict.
My point is exactly that it is not mysterious. Omega used some concrete method to win his game, much in the same way that the fellow in question uses a particular method to win the punching game. The interesting question in the Newcomb problem is (a) what is the method, and (b) is the method defeatable. The punching game is defeatable. Giving up too early on the punching game is a missed chance to learn something about volition.
The right response to a “magic trick” is to try to learn how the trick works, not go around for the rest of one’s life assuming strangers can always pick out the ace of spades.
Omega’s not dumb. As soon as Omega knows you’re trying to “come up with a method to defeat him”, Omega knows your conclusion—coming to it by some clever line of reasoning isn’t going to change anything. The trick can’t be defeated by some future insight because there’s nothing mysterious about it.
Free-will-based causal decision theory: The simultaneous belief that two-boxing is the massively obvious, overdetermined answer output by a simple decision theory that everyone should adopt for reasons which seem super clear to you, and that Omega isn’t allowed to predict how many boxes you’re going to take by looking at you.
I am not saying anything weird, merely that the statements of the Newcomb’s problem I heard do not specify how Omega wins the game, merely that it wins a high percentage (all?) of the previous attempts. The same can be said for the punching game, played by a human (who, while quite smart about the volition of punching, is still defeatable).
There are algorithms that Omega could follow that are not defeatable (people like to discuss simulating players, and some others are possible too). Others might be defeatable. The correct decision theory in the punching game would learn how to defeat the punching game and walk away with $$$. The right decision theory in the Newcomb’s problem ought to first try to figure out if Omega is using a defeatable algorithm, and only one box if it is not, or if it is not possible to figure this out.
Okay, let’s try and defeat Omega. The goal is to do better than Eliezer Yudkowsky, which seems to be trustworthy about doing what he publicly says all over the place. Omega will definitely predict that Eliezer will one-box, and Eliezer will get the million.
The only way to do better is to two-box while making Omega believe that we will one-box, so we can get the $1001000 with more than 99.9% certainty. And of course,
Omega has access to our brain schematics
We don’t have access to Omega’s schematics. (optional)
Omega has way more processing power than we do.
Err, short of building an AI to beat the crap out of Omega, that looks pretty impossible. $1000 is not enough to make me do the impossible.
A crucial difference is that the punching game is real, while Newcomb’s problem is fiction, a thought experiment.
In the punching game, you can try to learn how the trick is done and how to defeat the opponent, and you are still engaged in the punching game.
In Newcomb’s problem, Omega is not a real thing that you could discover something about, in the way that there is something to discover about a real choshi dori master. There is no such thing as what Omega is really doing. If you think up different things that an Omega-like entity might be doing, and how these might be defeated to win $1,001,000, then you are no longer thinking about Newcomb’s problem, but about a different thought experiment in some class of Newcomb-like problems. I expect a lot of such thinking goes on at MIRI, and is more useful than endlessly debating the original problem, but it is not the sort of thing that you are doing to defeat choshi dori.
Here is a trivial model of the “trick” being fool-proof (and I do mean “fool” literally), which I believe has been discussed here a time or ten. Omega runs a perfect simulation of you, terminates it right after you make your selection or if you refuse to choose (he is a mean one), checks what it outputs, uses it to place money in the boxes. Omega won’t even offer the real you the game if you are one of those stubborn non-choosers. The termination clause is to prevent you from enjoying the spoils in case YOU are that simulation, so only the “real you” will know if he won or not. And to avoid any basilisk-like acausal trade. He is not that mean.
EDIT: if you think that the termination is a cruel cold-blooded murder, note that you do that all the time when evaluating what other people would do, then stop thinking about it, once you have your answer. The only difference is the fidelity level. If you don’t require 100% accuracy, you don’t need a perfect simulation.
Do you think that gets rid of the problem? ‘It might be possible to outsmart Omega’ strikes me as fairly irrelevant. As long as it’s logically possible that you don’t successfully outsmart Omega, the original problem can still be posed. You still have to make a decision, in those cases where you don’t catch Omega in a net.
I am not saying there isn’t a problem, I am saying the problem is about clarifying volition (in a way not too dissimilar to the “choshi dori” trick in my anecdote). Punching empty air is “losing.” Does this then mean we should abstain from punching? Seems a bit drastic.
Many problems/paradoxes are about clarification. For example the Simpson’s paradox is about clarifying causal vs statistical intuitions.
More specifically, what I am saying is that depending on what commitments you want to make about volition, you would either want to one box, or two box in such a way that Omega can be defeated. The problem is “non-identified” as stated. This is equivalent to choosing axioms in set theory. You don’t get to say someone fails set theory if they don’t like Choice.
1 - Supposing I have no philosophical views at all about volition, I would be rationally obliged to one-box. In a state of ignorance, the choice is clear simply provided that I value whatever is being offered. Why should I then take the time to form a theory of volition, if you’re right and at most it can only make me lose more often?
We don’t know what the right answer to Newcomb-like problems will look like, but we do know what the wrong answers will look like.
2 - Supposing I do have a view about volition that makes me think I should two-box, I’ll still be rationally obliged to one-box in any case where my confidence in that view is low enough relative to the difference between the options’ expected values.
For instance, if we assign to two-boxing the value ‘every human being except you gets their skin ripped off and is then executed, plus you get $10’ and assign to one-boxing the value ‘nobody gets tortured or killed, but you miss out on the $10’, no sane and reasonable person would choose to two-box, no matter how confident they (realistically) thought they were that they have a clever impossibility proof. But if two-boxing is the right answer sometimes, then, pace Nozick, it should always be the right answer, at least in cases where the difference between the 2B and 1B outcomes is dramatic enough to even register as a significant decision. Every single one of the arguments for two-boxing generalize to the skin-ripping-off case, e.g., ‘I can’t help being (causal-decision-theory-)rational!’ and ‘it’s unfair to punish me for liking CDT; I protest by continuing to employ CDT’.
3 - You seem to be under the impression that there’s something implausible or far-fetched about the premise of Newcomb’s Problem. There isn’t. If you can’t understand a 100% success rate on Omega’s part, then imagine a 99% success rate, or a 50% one. The problem isn’t altered in substance by this.
A 50% success rate would recommend two boxing.
Edit: and come to think of it I am somewhat less sure about the lower success rates in general. If I can roughly estimate Omega’s prediction about me that would seem to screen off any timeless effect. Like, you could probably pretty reliably predict how someone would answer this question based on variables like Less Wrong participation and having a Phd in philosophy. Using this information, I could conclude that an Omega with 60% accuracy is probably going to classify me as a one-boxer no matter what I decide… and in that case why not two box?
Sorry, by a 50% success rate I meant that Omega correctly predicts your action 50% of the time, and the other half of the time just guesses. Guessing can also yield the right answer, so this isn’t equivalent to a 50% success rate in the sense you meant, which was simply ‘Does Omega put the money in the box he would have wished to?’
If you know that Omega will take into account that you’re a LessWronger, but also know that he won’t take into account any other information about you (including not taking into account the fact that you know that he knows you’re a LessWronger!), then yes, you should two-box. But that’s quite different from merely knowing that Omega has a certain success rate. Let’s suppose we know that 60% of the time Omega makes the decision it would have wished were it omniscient. Then we get:
If I one-box: 60% chance of $1,000,000, 40% chance of $1000.
If I two-box: 60% chance of $1000, 40% chance of $1,001,000.
Then the expected value of one-boxing is $600,400. Expected value of two-boxing is $401,000. So you should one-box in this situation.
This makes sense.
You are not listening to me. Suppose this fellow comes by and offers to play a game with you. He asks you to punch him in the face, where he is not allowed to dodge or push your hand. If you hit him, he gives you 1000 dollars, if you miss, you give him 1000 dollars. He also informs you that he has a success rate of over 90% playing this game with randomly sampled strangers. He can show you videos of previous games, etc.
This game is not a philosophical contrivance. There are people who can do this here in physical reality where we both live.
Now, what is the right reaction here? My point is that if your right reaction is to not play then you are giving up too soon. The reaction to not play is to assume a certain model of the situation and leave it there. In fact, all models are wrong, and there is much to be learned about e.g. how punching works in digging deeper into how this fellow wins this game. To not play and leave it at that is incurious.
Certainly the success rate this fellow has with the punching game has nothing to do with any grand philosophical statement about the lack of physical volition by humans.
Learning about how punching works, rather than winning 1000 dollars, is the entire point of this game.
My answer to Newcomb’s problem is to one-box if and only if Omega is not defeatable and two-box in a way that defeats Omega otherwise. Omega can be non-defeatable only if certain things hold. For example if it is possible to fully simulate in physical reality a given human’s decision process at a particular point in time, and have this simulation be “referentially transparent.”
edit: fixed a typo.
There is a typo here.
But now you’ve laid out your decision-making process, so all Omega needs to do now is to predict whether you think he’s defeatable. ;-)
In general, I expect Omega could actually be implemented just by being able to tell whether somebody is likely to overthink the problem, and if so, predict they will two-box. That might be sufficient to get better-than-chance predictions.
To put it yet another way: if you’re trying to outsmart Omega, that means you’re trying to figure out a rationalization that will let you two-box… which means Omega should predict you’ll two-box. ;-)
You are (merely) fighting the hypothetical.
Let’s try using your martial arts analogy. Consider the following:
You find yourself in a real world physical confrontation with a ninja who demands your wallet. You have seen this ninja fight several other ninjas, a pirate and a Jedi in turn and each time he used “choshi dori” upon them then proceeded to break both of their legs and take their wallet. What do you do?
Punch the ninja in the face.
Shout “I have free will!” and punch the ninja in the face.
Think “I want to open up the ninja and see how his choshi dori works” then try to punch the ninja in the face.
Toss your wallet to the ninja and then run away.
This isn’t a trick question. All the answers that either punch the ninja in the face or take two boxes are wrong. They leave you with two broken legs or an otherwise less desirable outcome.
Sometimes people fight a hypothetical because the hypothetical is problematic. I lean toward two-boxing in Newcomb’s problem, basically because I can’t not fight this hypothetical. My reasoning is more or less as follows. If the being claiming to be Omega actually exists and can in fact instantly model my mental processes, then I’m almost certainly a simulation. One-boxing would reveal that I know that and risk getting me turned off, making the money in the box rather beside the point, so I two-box. If I’m not a simulation, I don’t accept the possibility of Omega existing in the first place, so I two-box. Basically, I think Newcomb’s problem is not a particularly useful hypothetical, because I don’t see it as predictive of decision-making in other circumstances.
It seems to me that if Omega concludes that you are aware that you are in a simulation based on the fact that you take one box then Omega is systematically wrong when reasoning about a broad class of agents that happens to include all the rational agents (and some others). This is rather a significant flaw in an Omega implementation.
For agents with coherent decision making procedures it is equivalent to playing a Prisoner’s Dilemma against a clone of yourself. That is something that feels closer to a real world scenario for some people. It is similarly equivalent to Parfit’s Hitch-hiker when said hitch-hiker is at the ATM.
That’s why I don’t like Newcomb’s problem. In a prisoner’s dilemma with myself, I’d cooperate (I trust me to cooperate with myself). Throwing Omega in confuses this pointlessly. I suspect if people substituted “God” for “Omega” I’d get more sympathy on this.
Are you suggesting that if you are a simulation, two-boxing reduces your risk of being turned off?
If not, I don’t understand your reasoning at all.
If so, I guess I understand your reasoning from that point on (presumably you feel no particular loyalty to the entity you’re simulating?), but I don’t understand how you arrive at that point.
At a minimum, I can’t see how two-boxing could be worse in terms of risk of being turned off. I suppose Omega could think I was trying to be tricky by two-boxing specifically to avoid giving my awareness that I’m being simulated away, but at that point the psychology becomes infinitely recursive. I’ll take my chances while the simulator puzzles that out.
I’m not sure I understand your parenthetical. Does the existence of a simulation imply the existence of an outside entity being simulated?
Neither can I. Nor can I see how it could be better. In fact, I see no likely correlation between one/two-boxing and likelihood of being turned off at all. But if my chances of being turned off aren’t affected by my one/two-box choice, then “One-boxing would [..] risk getting me turned off [..] so I two-box” doesn’t make much sense.
You clearly have a scenario in mind wherein I get turned off if my simulator is aware that I’m aware that I’m being simulated and not otherwise, but I don’t understand why I should expect that.
To be honest, I’ve never quite understood what the difference is supposed to be between the phrases “existing in a simulation” and “existing”.
But regardless, my understanding of “If the being claiming to be Omega actually exists and can in fact instantly model my mental processes, then I’m almost certainly a simulation” had initially been something like “If Omega can perfectly model Dave’s mental processes in order to determine Dave’s likely actions, then Omega will probably create lots of simulated Daves in the process. Since those simulated Daves will think they are Dave, and there are many more of them than there are of Dave, and I think I’m Dave, the odds are (if Omega exists and can do this stuff) that I’m in a simulation.”
All of which also implies that there’s an outside entity being simulated in this scenario, in which case if I feel loyalty to that entity (or otherwise have some basis for caring about how my choices affect it) then whether I get turned off or not isn’t my only concern anyway..
I infer from your question that I misunderstood you in the first place, though, in which case you can probably ignore my parenthetical. Let me back up and ask, instead, why if the being claiming to be Omega actually exists and can in fact instantly model my mental processes, then I’m almost certainly a simulation?
My thinking here is that if a being suddenly shows up and can perfectly model me, despite not having scanned my neural pathways, taken any tissue samples, observed my life history, or gathered any other data whatsoever, then it’s cheating somehow—i.e. I’m a simulation and it has my source code.
This doesn’t require there to be a more real Prismattic one turtle down, as it were. I could be a simulation created to test a set of parameters, not necessarily a model of another entity.
Ah, I see.
OK, thanks for clarifying.
I would like to know more about this “choshi dori”. Do you know of videos or useful write-ups of the technique?
Discussion from a ninjutsu (Bujinkan) forum
Discussion from a general martial arts forum
A fat Russian guy demonstrating the same thing, from a different system.
In general, you can’t make people miss or fall over without touching them unless they know you can make them miss or fall over when touching is allowed.
I don’t think controversies over the Axiom of Choice are similar in the right ways to controversies over Newcomb’s Problem. In pragmatic terms, we know that true two-boxers will willingly take on arbitrarily large disutility (or give up arbitrarily large utility), inasmuch as they’re confident that two-boxing is the right answer. The point can even be put psychologically: To the extent that it’s a psychological fact that humans don’t assign infinite value to being Causal Decision Theorists, the utility (relative to people’s actual values) of following CDT can’t outweigh the bad consequences of consistently two-boxing.
I know of no correspondingly strong demonstration that weakening Choice or eliminating LEM leads demonstrably to irrationality (relative to how the world actually is and, in particular, what preferences people actually have).
This is only the case in a world-view that accepts that Omega cannot be tricked. How do you know Omega cannot be tricked? This view corresponds to a certain view of how choices get made, how the choice making algorithm is simulated, and various properties of this simulation as embodied in physical reality. Absent an actual proof, this view is just that—a view.
Two-boxers aren’t (necessarily!) stupid, they simply adhere to commitments that make it possible to fool Omega.
No, they don’t. You seem to be confused not just about Newcomb’s Problem but also about why the (somewhat educated subset of) people who Two-Box make that choice. They emphatically do not do it because they believe they are able to fool Omega. They expect to lose (ie. not get the $1,000,000).
By hypothesis, this is how it works. Omega can predict your choice with >0.5 accuracy (strictly more than half the time). Regardless of Free Will or Word of God or trickery or Magic.
The whole point of the thought experiment is to analyze a choice under some circumstances where the choice causes the outcomes to have been laid out differently.
If you fight the hypothesis by asserting that some other worldviews grant players Magical Powers From The Beyond to deceive Omega (who is just a mental tool for the thought experiment), then I can freely assert that Omega has Magical Powers From The Outer Further Away Beyond that can neutralize those lesser powers or predict them altogether. Or maybe Omega just has a time machine. Or maybe Omega just fucking can, don’t fight the premises damnit!
And as wedrifid pointed out, this is not even the main reason why the smarter two-boxers two-box. It’s certainly one of the common reasons why the less-smart ones do though, in my experience. (Since they never read the Sequences, aren’t scientists, and never learned to not fight the premises! Ahem.)
I would say Newcomb is all about how you view personal identity. But I’m not sure why this comment was directed at me.
Why would you say personal identity is relevant?
I think the ease with which this community adopts one boxing has to do with us having internalized a computationalist view of the mind and the person. This has a lot in common with the psychological view of person-hood. Basically, we treat agents as decision algorithms which makes it much easier to see how decisions could have non-causal properties.
This is, incidentally, related to my platonism you asked me about. Computationalism leads to a Platonic view of personhood (where who you are is basically an algorithm that can have multiple instantiations). One-boxing falls right out of this theory. The decision you make in Newcombs problem is determined by your decision algorithm. You decision algorithm can be wholly or partly instantiated by Omega and that’s what allows Omega to predict your behavior.
My problem with thinking of Newcomb’s paradox this way is that it is possible that my decision algorithm will be “try to predict what Omega does, and....” For Omega to predict my behavior by running through my algorithm will involve a self-reference paradox; it may be literally impossible, even in principle, for Omega to predict what I do.
Of course, you can always say “well, maybe you can’t predict what Omega does”, but the problem as normally posed implies that there’s an algorithm for producing the optimal result and that I am capable of running such an algorithm; if there are some algorithms I can’t run, I may be incapable of properly choosing whether to one-box or two-box at all.
Your prediction of what Omega does is just as recursive as as Omega’s prediction. But if you actually make a decision at some point that means that your decision algorithm has an escape clause (ow! my brain hurts!) which means that Omega can predict what you’re going to do (by modelling the all the recursions you did).
It doesn’t actually. The optimal result is two boxing when Omega thinks you are going to one box. But since Omega is a God-like super computer and you aren’t that isn’t going to happen. If you happen to have more information about Omega than it has about you and the hardware to run a simulation of Omega then you can win like this. But that isn’t the thought experiment.
My point (or the second part of it) is that simply by asking “what should you do to achieve an optimal result”, the question assumes that your reasoning capacity is good enough to compute the optimal result. If computing the optimal result requires being able to simulate Omega, then the original question implicitly assumes that you are able to simulate Omega.
Right, I just don’t agree that the question assumes that.
Where does the question assume that you can compute the optimal result? Newcomb’s Problem simply poses a hypothetical and asks ‘What would you do?‘. Some people think they’ve gotten the right answer; others are less confident. But no answer should need to presuppose at the outset that we can arrive at the very best answer no matter what; if it did, that would show the impossibility of getting the right answer, not the trustworthiness of the ‘I can optimally answer this question’ postulate.
I once had a man walk up to me and ask me if I had the correct time. I looked at my watch and told him the time. But it seemed a little odd that he asked for the correct time. Did he think that if he didn’t specify the qualifier “correct”, I might be uncertain whether I should give him the correct or incorrect time?
I think that asking what you would do, in the context of a reasoning problem, carries the implication “figure out the correct choice” even if you are not being explicitly asked what is correct. Besides, the problem is seldom worded exactly the same way each time and some formulations of it do ask for the correct answer.
For the record, I would one-box, but I don’t actually think that finding the correct answer requires simulating Omega. But I can think of variations of the problem where finding the correct answer does require being able to simulate Omega (or worse yet, produces a self-reference paradox without anyone having to simulate Omega.)
See the sequence:
A solvable Newcomb-like problem—part 1 of 3
A solvable Newcomb-like problem—part 2 of 3
A solvable Newcomb-like problem—part 3 of 3
When you suggest someone read three full length posts in response to a single sentence some context is helpful, especially if they weren’t upvoted. Maybe summarize their point or something.
If it was easy to summarize, it wouldn’t have required a three parter sequence. :-)
However, perhaps one relevant point from it is:
For the purposes of Newcomb’s problem, and the rationality of Fred’s decisions, it doesn’t matter how close to that level of power Omega actually is. What matters, in terms of rationality, is the evidence available to Fred about how close Omega is to having to that level of power; or, more precisely, the evidence available to Fred relevant to Fred making predictions about Omega’s performance in this particular game.
Since this is a key factor in Fred’s decision, we ought to be cautious. Rather than specify when setting up the problem that Fred knows with a certainty of 1 that Omega does have that power, it is better to specify a concrete level of evidence that would lead Fred to assign a probability of (1 - δ) to Omega having that power, then examine the effect upon which option to the box problem it is rational for Fred to pick, as δ tends towards 0.
To the extent that Newcomb’s Problem is ‘about how you view free will’ people who two box on Newcomb’s Problem are confused about free will.
This isn’t like constructivist mathematicians being worse at set theory because they reject choice. It’s closer to a kindergarten child scribbling in crayon on a Math exam then insisting “other people are bad at Math too therefore you should give me full marks anyway”.
I don’t think that’s fair (though I also don’t think Newcomb’s problem has anything to do with free will either). The question is whether one-boxing or two-boxing is rational. It’s not fair to respond simply with ‘One-boxing is rational because you get more money’, because two-boxers know one-boxing yields more money. They still say it’s irrational. It would be question begging to try to dismiss this view because rationality is just whatever gets you more money, since that’s exactly what the argument is about.
If you say so. If I learn enough about “choshi dori” to fool the punch-avoiding algorithm and win 1000 dollars, and you don’t play, who is confused? Rationalists are supposed to win, remember, not stick to a particular view of a problem.
Rational agents who play Newcomb’s Problem one box. Rational agents who are in entirely different circumstances make entirely different decisions as determined by said circumstances. They also tend to have a rudimentary capability of noticing the difference between problems.
(a) You are being a dick. I certainly did not insult anyone in this thread.
(b) The isomorphism is exact. The point is granularity. If the guy can avoid the punch 90% of the time (or more precisely guess what your punch decision algorithm will do in response to some inputs 90% of the time), and Omega guesses what you will do correctly 90% of the time, that ought to be sufficient to do the math on expected values, if you want to leave it there.
Or, alternatively, you can try to “open up the agent you are playing against” and try to trick it. It’s certainly possible in the punching game. It may or may not be possible in the game with Omega—the problem doesn’t specify.
If you say “well, rational people do X and not Y, end of story” that’s fine. I am going to make my updates on you and move on.
A typical example of irrational behavior is intransitive preference. As the money pump thread shows people often don’t actually fall for money pumping, even if they have intransitive preferences. In other words, the map doesn’t fully reflect the territory of what people actually do.
Another example is gwern’s example with correlation and causation. Correlation does not imply causation, says gwern, but if we knew how often it does imply it, we may well be rational to conclude the latter from the former if the odds are good enough. He’s right—but no one does this (I don’t think!).
I used the example of the punching game on purpose—it makes the theoretical situation with Omega practical, as in you can go and try this game if you wanted. My response to trying the game was to learn how it works, rather than give up playing it. This is what people actually do. If your model doesn’t capture it, it’s not a good model.
A broader comment: I do math for a living. The issues of applicability of math to practical problems, and changing math models around is something I think about quite a bit.
It took a non-trivial exertion in the direction of politeness to refrain from answering the rhetorical question “who is confused?” with a literal answer.
Arguable. I would concede at least that you did not say anything insulting that you do not sincerely believe is warranted.
Doing expected value calculations on probabilistic variants of newcomb’s problem is also old news. And results in one boxing unless the probability gets quite close to random guessing. Once again, if you choose a sufficiently different problem than Newcomb’s (such as by choosing an accuracy sufficiently close to 0.5, reducing the payoff ratio or by positing that you are in fact more intelligent than Omega) then you have failed to respond to a relevant question (or an interesting question, for that matter).
Please do. I have likewise updated. Evidence suggests you are ill suited to considering counterfactual problems and unlikely to learn. My only recourse here is to minimize the damage you can do to the local sanity waterline. I’ll leave further attempts at verbal interaction to the half a dozen others who have been attempting to educate you, assuming they have more patience than I.
See.
I would be interested in seeing how philosophers do on tests of analytical versus intuitive reasoning (I forget the name of the test normally used for gauging this) and ability to narrow down hypotheses when the answers are known and easily verifiable.
Cognitive Reflection Test?
That was the one, thanks.
We do pretty well, actually (pdf). (Though I think this is a selection effect, not a positive effect of training.)
Upvoted for understatement.