Max Weber’s Newcomb problem

Schroedinger’s cat does morality?

Look, I am not by most standards a stupid person, and your description of the Newcomb problem makes no sense to me. “A sign that you are in that world is that you are disposed…” sounds immediately like theology. Forget about analogies to Calvin. It’s a sign, not evidence. My arbitrary initial disposition about an issue on which I can have no experience can’t be evidence. From the sound of this, I might as well be listening to voices out of whirlwinds. What’s the point of describing that in terms normally used for rational decisions?

I know, I must be missing something, I should google, I should go away and think about it for a while. I will. But if you start getting a lot of nonsensical comments that don’t even address the issue, the explanation of the Newcomb problem might be one of the causes.

But if the being in the Newcomb problem is a time traveler, then it is your choice that is determining what is in the boxes, and then there is no paradox at all, just take box A.

Do Calvinists believe that your status as damned or elect is independent of your actions, or simply determined by them in a non-temporal manner by a timeless God?

I don’t know about all Calvinists, but at least some important ones (Johnathan Edwards, in the US) believed, as far as I could tell, that God’s choice of who to save or damn was essentially arbitrary, at least as far as we could tell. That’s in a strong sense, too- if it’s intelligible in any way, it’s not in a way that beings like us can make any sense of at all. It’s certainly not determined by our actions in any way at all. Plus, all of us are equally revolting to God- he looks upon us as we look upon the most loathsome spider, if I recall the formulation correctly. (Perhaps that’s part of the reason Edwards thought the main pleasure of heaven was watching those in hell suffer, though perhaps he just thought that was intrinsically fun.) The basic and quite common Christian idea of salvation by grace provides the essentials for this view (no one could deserve to be saved, so being saved is a capriciously given benefit) but the Calvinist view, especially in the form pushed by Edwards in the US, just takes this a bit further.

I don’t see the parallels. The way you have described the first scenario the only goal is getting the biggest reward. In the second scenario the issue is that the process leading up to the reward has itself different values. Put it this way: it’s not like I would enjoy opening both boxes.

Why would you open both boxes if you KNOW that in that case there is only 1000$? If you are under the impression the thing is random that makes sense, but know as described, unless the problem is “how will people take a decision if I tell them the situation is different from what really is”, in which case it is kind of trivial (“I lied and they fell for it”)

It’s much more complicated than that. Consider a variant in which your best friend gets to peek in the boxes before your selection. He can’t tell you whether the $1 million is there or not, but he can suggest which choice you should make. He will, invariably, suggest that you take both boxes.

My knowledge of Calvinism is very limited (actually almost nonexistent), but I always believed that the causation ran in the other direction:
Some people are born “pure”, and will be saved at the end; some other are not pure and will not be saved.
The people who are pure have not wordly desires (since they are pure), and as a consequence they will live a pure life; but the pure life is a consequence of the pure soul, not the other way around, hence the parallel breaks down.

Writing this, I realize that I’m attributing to Calvin a worldview that is very similar to that of the Catars and of ancient Gnostics. Can someone knowledgeable of Calvinist theology tell me if this is right?

OK, more seriously, it depends on how much you need that $1000. If you have a secure job, an inheritance, some wealth, the answer is clear.

If you say that “the being always guesses right,” the being is not guessing. The being knows what you are going to do, which means that your sense that you are making a choice is an illusion arising from your limited powers of perception. The future is already determined, and your belief that you can change what will occur is an error on the level of believing that you can alter the landscape over the hill ahead of you simply because you cannot see it yet.

So it makes no sense to analyze what you “should” do. You are not in control of what you will do; you are merely along for the ride.

This is the conceit of Slaughterhouse-Five, IIRC.

Similarly, the Calvinist knows that he cannot influence whether he is saved or damned. But he believes that the elect, as they say, have certain characteristics in this life, and he sees that he has them. That is, he trusts in God, works hard and saves, and avoids sin. These are signs that he and others like him are saved. There is no voluntary causal relationship – he cannot choose to behave in a way that will bring about his salvation, any more than an ugly person can choose to be an attractive person. His behavior is merely an indication that he is among the elect.

If it’s merely an indication, who does it indicate to? Presumably the elect themselves–in which case it’s a nice confidence boost, I guess–and to other humans, in which case it’s status signalling. But surely no true elect would behave so vulgarly.

And has Newcomb’s being read Brennan’s paper? Because if so, it’s pretty clear there won’t be a million dollars in Brennan’s box.

Bloix: It doesn’t necessarily have to be deterministic. If the being can predict your actions with merely very high probability, then there’s still a pretty plausible argument for the one box option, as long as you adjust the payoffs such that the possibility of the being guessing wrongly and putting a million dollars in the box when you pick two is inconsequential enough to not throw off the overall calculation.

But even if it is deterministic, I don’t think you’re right anyway. After all, we can ask “should Napoleon have invaded Russia?” even though it’s already set that he did. Similarly, we can ask how a person in a Newcomb problem should act, even if it’s already set how they will act. It’s just comparing the apparent options. (Yes, there’s a distinction between “should” and “should have” but I think it’s largely grammatical.) Or, to phrase it another way, we could ask how an “ideal person” would act if posed with such a problem, since how a person should act and how an ideal person would act seems logically equivalent.

Seems to me the answer depends in part on whether the being is really another player in b’s own right. Given the grid, if the game is against another player, the answer is always take both. But the feedback loop, in effect, means you’re almost playing against yourself. So you can choose the world where the choices are all >=$1mil, and you take only one box. (Instead of asking (see), do I want 1&3 or 2&4, ask do I want 1&2 or 3&4.)

But that assumes something about the being. If you know nothing about the being, and don’t know whether b will expect you to mechanistically apply an inappropriate strategy, or whether b will predict “greedy and greed=2 instead of 1,” or whether b will predict “greedy and greed=world where all choices >=$1mil,” or what b’s criteria are going to be at all, there’s a good chance (even if you think you’re going to choose one box) that b will say you were going to choose two boxes. You’re basically playing against an ordinary opponent who might take either branch. Then you should take both boxes.

Or, obviously, if you think the being is probably God, and you know what God would say, then you should decide accordingly.

UserGoogol’s explanation is interesting, but seems to imply that someone playing a game like this can plausibly decide to do one thing and really do a different thing. (I mean, last night I decided to wash clothes in cold water but washed them in warm water instead, which presumably makes me not-elect, but I haven’t worked out whether this fits the problem.)

I don’t think even the Swiss believe in predestination anymore. The tendency among Calvinists everywhere since the 18th c. was to move toward Unitarianism.

While Resnik doesn’t mention anyone for his citation of the Calvinism example, I just checked Richard Jeffrey’s The Logic of Decision, and Jeffrey mentions Jonathan Edwards’ grappling with predestination as a theological version of Newcomb’s paradox.

See, this is the kind of thing that gives theology and certain flavours of philosophy a bad rap. To take this serious to the point of publishing a whole book about it when there is no evidence whatsoever that “God” or “salvation” is a more coherent concept than “zargleblorf” is just silly.

@Ethan 17
Thanks for the answer.
However while I understand that nobody really deserves salvation in the strict sense, the formulation of other commenters (such as Bloix @20 for example) are similar enough to my understanding that I will assume I was more or less right (although “pure” was an excessive word).

IIRC Martin Gardner in Mathematical Games in Scientific American sometime in the 1960’s quoted Isaac Asimov as saying he’d choose only box b so as to completely fool the omniscient being.

If you believe the being can violate causality, you should choose only box A. If you believe the being can’t violate causality, you should choose both boxes. Because for your choice to affect the being’s choice would violate causality — it’s part of the setup of the paradox that the being has already chosen and filled the boxes. The core question is whether you believe the being’s predictive powers are *literally* supernatural — so that the decision you *actually* make (as opposed to just the decision more consistent with your overall personality) affects the being’s choice.

Suppose the being knows that I’m a skeptic — that isn’t so hard to know. So he leaves box A empty. What good would it do me to play against type and pick only box A? Sure, I’d prove the being’s fallibility, but if I care more about that than $1000, then I’m not really playing Newcomb’s paradox, I’m playing some kind of variant with a different payoff matrix.

On the other hand, if my alternate universe twin is a man of faith and the being knows *that*, then my twin will presumably talk himself into taking only box A — but I can see that he’s giving up an easy extra $1000 by doing so.

What makes it seem paradoxical is that my rationality appears self-defeating — but really it isn’t. My twin doesn’t benefit from his *actual* irrationality — in fact, it costs him $1000. What he benefits from is his *reputation* for irrationality (in the eyes of the being). But that just makes Newcomb’s Paradox a game where a reputation for irrationality can be an asset — that’s not so unusual. Chicken has the same property.

P.S. If I estimated a substantial probability of someday being faced with an actual Newcomb’s Paradox, would it be rational to cultivate a public persona of faith in uncanny powers like the being’s? Does the effort and cost involved in doing that outweigh the benefit of having the being fall for the persona if I actually do encounter it? Of course, I’d have to consider the possibility that my ruse might fail, making it pointless to have ever attempted it.

Calvinist theology can be thought of more simply as sort of reverse thinking: Sick people take drugs. If I don’t take drugs, I’m not sick. The Calvinists thought: Those graced by God are often rewarded in this life. If I acquire that which makes it seem as if I have been rewarded, then God has graced me.

The Cavlinist example is a standard Newcomb example used in decision theory texts such as Resnik’s book (widely used by philosophers, at any rate), Choices. I don’t know if he cites anyone for the example, but his book is from the 1987, and the example is on p. 111. So it predates Norkas by quite a bit.

Following up, Jean-Pierre Dupuy (currently at Stanford, I guess) made more or less his entire career arguing that in fact the parallelism you point out is a direct causality: he argues that the doctrine of Protestant predestination, and the Newcomb-like reversal of causality it allows, was directly instrumental in the formulation of the doctrine of liberal rational choice by Scottish enlightenment philosophers. His thesis has a great deal of empirical support, I think (note for instance that the one influential liberal French-speaking philosopher, Benjamin Constant, grew up in Switzerland in a Huguenot family). His most relevant work would probably be Le sacrifice et l’envie, whose title already hints at the ensuing argument (what is the link between rational optimization, especially delayed gratification, and religious sentiment?).

BTW, do you have full access to Norkas’ article? If he doesn’t quote Dupuy extensively, this looks like a massive failure of scholarship at best.

chris: It doesn’t violate causality, it probably violates (libertarian) free will, but not causality. Your actions are caused by your psychological properties, the prediction is caused by your psychological properties, so all the causation is pointing forward.

If you assume no free will, the “paradox” is even less interesting: the being does what he is doomed to do, and I do what I am doomed to do. There is no game — in fact, games in general are impossible. The only paradox is that this kind of strong determinism violates the intuition that people do make choices about their actions.

Therefore, for Newcomb’s paradox to be at all interesting, you have to assume that some form of free will is real. I thought that went without saying.

Under that assumption, my psychological properties can’t be absolute, or I don’t even have a choice about which box(es) to take in the first place. (The theological version of this is even worse: people who do evil literally can’t choose otherwise, but get punished for it anyway, and we are supposed to call this justice? At least Newcomb’s being isn’t threatening to torture anyone for eternity.)

The paradox, since it relies on something that’s a logical impossibility, is rather uninteresting. It’s a bit like the Shape-Sorting Puzzle. Say you have the job of sorting different-shaped pieces of card. They all get put into different bins depending on how many sides they have. So triangles go into bin 3, squares and rectangles and parallelograms go into bin 4 and so on. But what if you get a shape that is a triangle that has four sides? Aha! Paradox!

ajay, the premise isn’t impossible here. Suppose there are two deterministic computer programs, one of which accesses the first value in an array and then the second value; the other of which accesses only the first value. The array itself is provided by the operating system. Whenever one of these programs runs, the operating system analyzes the program, and assigns the values to the array based on what the program will access.

Here are the programs:
void main(int argc, char **argv) { printf(“%d, %d\n”, argv[1], argv[2]); }
void main(int argc, char **argv) { printf(“%d!\n”, argv[1]); }

Running the first program prints “0, 1000”. Running the second program prints “1000000!”.

No logical impossibility there. Although one might argue that such an OS defies reasonable programmer expectations.

On the Newcomb problem, what is the deal with the two-boxers? It seems like faced with a situation where very likely we don’t know exactly what is going on, they appear to insist that we do know what is going on and that this powerful being is just getting very lucky. The actual stated defense of the two-box position appears to consist of the whine that the powerful being is rewarding irrationality. The problem with that whine is that it implies that the being is able to violate causality in the way we normally understand it, but if that’s true, it is no longer irrational to one-box. The two-box position is just to confuse the general concept of rationality with a specific concept of rationality within a universe that follows a specific set of rules that we assume our universe follows until informed otherwise. Well, this game provides evidence otherwise.

There are several mechanisms by which the being could be performing it’s tricks. Does it go back in time, is our mind state fully simulatable? Or perhaps it just has the ability to transport $1M bucks into the box in the instant before we select. Does it matter? The only question here is how we weight the probability that the being is simply very lucky against our priors that this being has some power that we can’t explain. This depends on some priors about your worldview and detailed observation of what exactly is going on in this game. But a person should probably be more willing to believe that they don’t have a full picture of physics (or that they can be fooled) than the likelihood that a person can correctly predict 100 truly random coin flips in a row. It’s kind of arrogant to assume otherwise.

mpowell, the being can’t be performing tricks. The premise states that the being knows what you will do before you even have to decide. By premise, it isn’t doing some kind of confidence game, swapping the boxes around. That might be the only realistic explanation of the described behavior, but this isn’t an observed phenomenon; this is a hypothetical.

This is really a ruinous premise in any strategic situation. Imagine you’re playing poker against a Newcomb being that always magically knows what you’re going to bet, in every round, before you even look at your cards. (And he’s playing to win.) Suppose the Newcomb being raises. How do you decide whether to fold? He wouldn’t have raised if your decision wasn’t wrong. So if you fold, you’re being bluffed out; wrong move. But if you call or raise, you’ve fallen into his trap; wrong move. By premise, all your moves are wrong. How can you decide what to do?

mpowell, the being can’t be performing tricks. The premise states that the being knows what you will do before you even have to decide. By premise, it isn’t doing some kind of confidence game, swapping the boxes around. That might be the only realistic explanation of the described behavior, but this isn’t an observed phenomenon; this is a hypothetical.

Sorry, that’s just invalid. If we are talking about game theory a hypothetical is a set of observations an actor has regarding the game. That can be a claimed description of the rules and the actor’s observation of what has happened. It’s common for game theorists to ignore this restriction, but frankly, that’s crap and it leads to fallacious and confusing results. The only way to evaluate how I should play a game is based on things I can observe and verify.

bianca@61:

As I mentioned in my follow up, the purpose of game theory is to figure out what you should do in a given situation. There terms of that situation can only be described by the things a person in the situation can observe or verify. Therfore, any hypothetical which insists such things as “this being is omniscient” or “nobody is playing tricks on you” are fundamentally ill posed hypotheticals. A hypothetical Newcomb problem cannot simply skirt this issue.

@mpowell
If you think it makes sense, when answering a problem in game theory, to think about what real-world situation from your own actual experience the problem probably corresponds to, and change the payoffs in your head to what you think corresponds to the real-world situation–which is what it sounds like you’re doing–then you’re either doing a different kind of math than I’ve ever heard of (one where there’s one perfect version of every problem and the person giving the problem might trick you about its details?), or you’re not doing math. (How many situations, outside of gambling or economics, are we ever in where we know the payoff matrix? If that’s close to 0, (under your assumptions) game theory would have to be a waste of time.) IMHO, of course.

I guess the definition of a game could be derived from real-world experience, but that doesn’t mean when you decide whether a result is correct you first list all the really possible real world outcomes.

mdc@64, It has always been a problem, and became acute after the discovery of America, with its vast population who had never heard of Christ. The Jesuit scholar A.H.T. Levi, who wrote about Erasmus, quotes Pico della Mirandola, who has God say to mankind: “Confined within no bounds, you shall fix the limits of your own nature according to the free choice in whose power I have placed you. We have made you neither mortal nor immortal, so that with freedom and honour you should be your own sculptor and maker, to fashion your form as you choose. You can fall away into the lower natures which are the animals. You can be reborn by the decision of your soul into the higher natures which are divine.” — Pico della Mirandola

According to Levi, “In the evangelical humanism that Erasmus inherited through [the French Humanist] Colet from Pico, not only was man’s perfection intrinsic to his moral achievement but, outside a formal theological context and the difficulties about Pelagianism [no need for God’s grace] it imposed, moral self determination was clearly put into man’s autonomous power. Erasmus never ceased to hold this view, and it explains his final rejection of Luther.” http://www.ourcivilisation.com/smartboard/shop/erasmus/intro/intro2.htm

Levi writes that “Both humanists and reformers wished to reject the Pelagianism of the scholastics and the deleterious religious extrinsicism [salvation by works] which it promoted. But while the humanists as such were dedicated to defending man’s intrinsic perfectibility in accordance with his self-determining moral choices, the reformers could find no logical answer to Pelagianism, short of denying to free will any power in the order of grace.
…
Levi goes on to say, “It is not difficult to see how this situation arose. If man’s `nature’ is capable even of accepting, to say nothing of meriting, grace, the result is at least semi-Pelagian theology and a religion of tension. If, however, it is not, man is necessarily deprived of any power of self-determination to a good which, on any theory, is supernatural, and he is incapable of influencing his own eternal fate. The dilemma is rigid. Erasmus’s treatise against Luther, the de libero arbitrio (On Free Will, 1524), accuses Luther of denying free will. Luther’s reply, the de servo arbitrio (On Unfree Will, 1525), accuses Erasmus unjustly of scepticism, but also of Pelagianism.”

About Roko’s Basilisk:

For those who don’t follow Less Wrong, this is something to do with the idea that a future super-powerful artificial intelligence, akin to Newcombe’s Omega, could make a simulated copy of you and do things to it in order to reward/punish the real you, and that you should care about this in some ways but not think too hard about it in other ways. I once promised not to reveal much more about it so that someone would explain it to me. I’m keeping that promise, but I can say that the full explanation is more bizarrely logical than you might think from that crazy intro. It’s almost convincing to me, on a logical level, even though on a common-sense level it has no appeal whatsoever.

Still, I reject the idea that it’s important. I’m only keeping the secret of Roko’s basilisk because I promised to, not because I think it’s worth keeping. My reason for rejecting it, though, is perhaps even crazier-sounding than the (vague outlines of) the idea itself. Basically, I (like most people on Less Wrong) accept the idea of quantum-mechanical “multiple universes”, superimposed in the universal wave function like the live and dead versions of Shrodinger’s cat. Thus it’s clear to me (unlike to those who fear Roko’s basilisk) that even if a hyper-powerful AI, able to simulate and predict (with high but not perfect certainty) human actions, will someday exist (an idea which I find unlikely but possible), it could not simulate all the myriad quantum branches, and thus my experience of being inside that simulation would be tiny compared to my experience in all the quantum branches of reality, so I should not worry about what happens in those simulations.

Sorry for all the parenthetical digressions, but otherwise it would take many paragraphs to say all that.

I haven’t actually met such a being yet, so, if I attached a 0.1 per cent probability that I ever would, it would be sensible for me to cultivate the disposition favored by such beings. That way, the being would correctly predict that I would take one box, I would take the box and get the million. Having thought about it that way, I conclude that
the probability of such a being is much smaller than 0.1 per cent, and the usefulness of the general principle “other things equal, more money is better than less”, so great, that I’m not going to cultivate the disposition. Should I meet the being, I’ll try to take the $1000 with as a good a grace as I can muster, and write a long blog post explaining that ex ante, I was still right.

Your description of Newcomb’s problem is logically inconsistent, especially in the phrases “always guesses right” and “choice”. Either he always knows (i.e. is perfectly prescient), in which case he does not guess and you don’t have a choice, or he guesses with some chance of being wrong, in which case he your choice should depend on your assessment as to what the being should be thinking about you. Therefore at least one part of the description of the rules must be wrong. Once you recognize this, it can be anything: either the being is not always right and you can cheat it, or perhaps the being can change the content of box A after your choice, or perhaps some other rule is not as it is described. So really the answer should depend on your assessment of the uncertainty in what the actual rules of the game are.

In a sense this is also true for protestantism. A lot of discussion has been going on as to what the exact rules are. A common believe is that you can loose your chance in heaven based on your life, basically saying that the being can empty box A. There is also a discussion on whether people are born sinners or innocents, which also basically implies that the content of box A is determined after you made your choice. And then there’s the inconsistency of saying that God is omni prescient, while acknowledging that you have a choice. Overall I do think that the protestant ethic is in the end based on the premise that you don’t really know how God decides (what the rules of the game are), so you better not take a chance of making the wrong choice.

bianca @ 64:

What I am pointing out is that the Newcomb problem only emerges as a paradox when you mix the two domains of perfect knowledge and actual player experience. If you want to specify that there is a being that can correctly perfectly predict your actions, then it doesn’t even make sense to ask the question of what you ought to do facing a Newcomb problem.

But if you want to ask, “what should I do facing a Newcomb problem?”, then you need to actually specify what is known by the person making the decision. This is perfectly consistent with the way game theory math works in that players must make decisions under uncertainty. To make the math easy, it is common to specify that the probability of various different possible outcomes is known precisely, but if you want to consider a game where the probability of various parameters of the game being a certain way are unknown, then you had better acknowledge that in your math.

I agree with Christiaan@72, except that the way I prefer to describe this is that the problem is ‘ill-posed’ instead of illogical. Once you specify the problem correctly, the paradox no longer appears.

Am I unique in having little patience with this sort of “problem” or “paradox”?

The argument seems to be, in a nutshell:
If we assume the impossible, then nonsense can occur.

While counter-factual arguments are useful, arguments based on impossibilities are not. It’s a general mathematical and logical result: if rubbish then anything.

As for the questions of God’s nature and Calvinism, I find those unconvincing for two reasons:
(1) a god that relies on philosophical or logical argument to be brought into existence (such as the ontological argument) is rather useless and can be ignored, certainly it is not worthy of worship;
(2) a god that is constrained by humans’ philosophical or logical arguments about its capabilities is also rather useless and can be ignored.

If a super-being has any interest in me understanding its nature, I expect it to communicate in flames stretching across the the sky announced by crashing thunderbolts, not from scholarly journals, random environmental occurrences (such as earthquakes or hurricanes), doorstep evangelists, Tom Cruise or David Icke.

As for the Newcomb argument, if I were forced into a response, and maybe I had missed someone suggesting it, but I’d consider tossing a coin. Or is that too Captain Kirkish?

That sounds like Antonioni’s Problem: what should I do when nothing I do makes any difference. Which is a subset of Becket’s Problem: what I should I do when nothing I do makes any difference even though I’m almost as smart as God and funnier.

re: 78

I think you’re confusing that with Bright’s Disease.

@77, 78
I thought Becket’s problem was Beckett’s problem.

Senate candidate Richard Mourdock:

“I struggled with it myself for a long time, but I came to realize life is that gift from God, and I think even when life begins in that horrible situation of rape, that it is something that God intended to happen.”

This is what Christians believe, okay? You have no control over your life. God wants you pregnant, he’s gonna get you pregnant. He wants you to pick a box with $1 million in it, you’ll pick the box. So stop trying to game the system.

And if this were Atrios’s blog, i cd add irrelevantly:
the electricity is still on here!
(though i don’t expect that to be the case v much longer)

68 “I once promised not to reveal much more about it so that someone would explain it to me.”

Why in rationality’s name would you not be able to explain it fully? Less Wrong is such a strange place.