Solving Newcomb’s problem with (possibly non) expected utility theory

by John Quiggin on December 1, 2016

The Grauniad has just resurrected Newcomb’s problem. I have a slightly special interest since the problem was popularized by one of my betes noires, Robert Nozick. So, in asserting that there’s a trivial solution, I have something of a bias.

Having read about the problem, it’s natural to consider the question: How likely is it that such a Superbeing exists? If the probability is high, say 1 in 10, my response is obvious. I should cultivate the kind of satisficing disposition that would lead me to pick only Box B. If the Being appears, and correctly predicts my action, I’m rewarded with a million currency units. My expected gain (ignoring the possibiity that the being makes an error) is 0.1*999000 or 99 000.

There are some wrinkles in decision theory here. A risk averse expected utility maximizer would value a .001 chance of a million units at less than the certainty of a thousand units. On the other hand, my academic fame, such as it is, rests on the idea that decisionmakers will overweight low-probability extreme events like this.

But this isn’t really a problem. The probability of such a Being is tiny (I’d happily take a million to one against, so overweighting doesn;t matter. And (as with Pascal’s wager) it’s just as likely that any Being who might present me with a problem is a Trump/Gekko believe in “Greed is Good”. So, I won’t bother cultivating a disposition. Should Newcomb’s Being appear, I’ll admit I bet wrong, take both boxes, and hope for the best.



Cyril Hédoin 12.01.16 at 8:11 am

I have explored this kind of reasoning about Newcomb’s problem on my blog some months ago:


Jim Buck 12.01.16 at 8:32 am

Dogs exist. Relative to a dog, I am a super intelligent being. I throw a stick, my dog runs after it. I predict that. Gods may or may not exist. Relative to myself though, there may be (evolved) super intelligent beings, to whom my behaviour is as predictable as a dog’s is to the likes of me.
Any road, I would pick Box B. I could get over losing a grand, fairly quickly. A million though…


J-D 12.01.16 at 8:40 am

If such a being exists, what is the probability that it is a malicious prankster motivated primarily by an arbitrary spiteful desire to make me the butt of its practical jokes?

Its pattern of behaviour, as described, does not resemble the behaviour of anybody I normally interact with. Its pattern of behaviour fits fairly well with the hypothesis that it is playing insidious mind games, and a good strategy for dealing with players of insidious mind games is avoidance.


Zamfir 12.01.16 at 8:56 am

This is one of those problems that’s hard in theory, but would be blindingly obvious in practice. By hypothesis, the being has an excellent track record by the time that you get to make the choice. I.e., there’s plenty of people before you who took 2 boxes and got a thousand, or who took 1 box and got a million. So you take 1 box, and philosophize about the paradox afterwards. If you’re the first person in the row, you take 2 boxes and lose out.

In fact, I don’t believe 2-boxers. Most of them would take 1 box as well, given a clear record of success. Faith and reason be damned.


Evan 12.01.16 at 9:25 am

I’ve always thought the problem is confused a bit by the amounts in question. The answer could depend on your level of wealth and the perspective it gives you on a thousand or a million dollars.

Essentially, if you take box B, you’re being asked to bet $1000 against the long-shot chance of a million. Well, I’m reasonably well-off, and I don’t really need $1000 today. I could make that bet, and not be particularly sad if I lost. If it paid off, the reward would be life-changing, so maybe I’d take box B.

On the other hand, if I were broke and starving, there’s no way I’d risk $1000 in the hand. I’d take both boxes in an instant. Or, if the amounts were a million and a billion, the ratios are the same and so the probability analysis ought to be the same, but I’d definitely take both boxes: I can get along fine without a billion, but I have immediate near-term uses for a million.

I kind of think this would be a better thought experiment if the size of my bank account didn’t factor into the analysis so much.


Z 12.01.16 at 9:49 am

Anybody who is educated enough to understand the setting of the puzzle is also educated enough to devise a mental pseudo-random generator so is able to constrain herself to choose randomly. So not only the probability of the existence of the predictive Being is tiny, but it would be almost impossible to sincerely believe in it outside of theistic belief. Hence, the premises of the puzzle are absurd, and there is little point in arguing starting from them. In the same vein, I think it is no accident that the original setting never explains what happens if the predictive Being gets it wrong when you choose to open only one the 10^6€ box: you open it and it is empty. I believe this is to maintain the fiction that we could believe in the existence of the Being, that is to say in the initial falsehood that makes all subsequent reasoning meaningless.


Collin Street 12.01.16 at 9:59 am

I’m not going to answer the question, for Roco’s Basilisk type reasons: a superhuman intelligence would be smart enough to…

Wait, no!

I would totes take box B only. For sure and certain, yes. Absolutely.


Asteele 12.01.16 at 10:01 am

I would only take B. A super being willing to give me a million pounds deserves to have me compliment it on being such a good predictor.


Manta 12.01.16 at 10:18 am

The super-intelligent being does exist: it is one of the books in the library of Babel.

Here is a simplified situation on how to find it.
Let’s say you toss 1000 coins.
Write a computer program, at each step produces 2 “super-intelligent beings”, one predicting tail and one head; then the program kills the being that predicted wrongly and keep the one that got it right, and iterate at the next step.

At the end, you will get 2 (super intelligent!) beings that predicted your 1000 coins toss correctly.
However, one will say that you will get tail at the 1001 toss and one will predict head…


reason 12.01.16 at 10:19 am

I’d wager that both boxes are always empty.


david 12.01.16 at 11:13 am

Seems subject to this attack, in any given probability of the Being existing – that is, the Being can weight the lottery so that the expected payoff is positive (for you). Hooray, an expected million currency units. But in normal, non-Nozickian experience, the payoff is negative.


Gabriel 12.01.16 at 11:39 am

Part of your response seems to violate the foundational notions of the thought experiment: that the creator is allowed to set up the world how he or she sees fit. One can attack those assumptions as being inconsistent, ungermane, unconnected to the ‘real world’, etc, but one cannot simply say ‘that’s not realistic!’. Well, yes, it isn’t, but that’s hardly the point.

Newcomb’s Problem very clearly states that such a being exists, and has been, up to this point, infallible.

Within the thought experiment, I think the clear answer is that, unless you have compelling enough evidence to believe that, in this one instant, unlike every time in the past, the SIB is wrong, you must take only B. The fact that the SIBs decision has already been made seems irrelevant, as we should then look to its prediction record, which is spotless. But many smart people seem to disagree with that conclusion.


Trader Joe 12.01.16 at 12:31 pm

Maybe the best answer is to just take box A and then imagine that Schrodinger’s cat is in the second box, and if its not dead it probably ate the $1 million check.

If the Superbeing had actually predicted that I’ll still be ahead and what could have been will never bother me.


Bob Zannelli 12.01.16 at 1:35 pm

Yahweh exists with equal probability as Zeus, Ah peku, Adonis, Allah, Enki, Inanna…… Thor. It’s all nonsense, not worth wasting time with.


mclaren 12.01.16 at 1:46 pm

A street-savvy young turk would demand to meet the Superbeing, since you weren’t born yesterday. Refusal means the offer is a scam. No Superbeing exists. Box B.

If, on the other hand, the ingtermediary making this spiffy offer ushers the Superbeing into your presence, you pistol-whip the Superbeing until s/he/it tells you the contents of the boxes.

Problem solved.


Jerry Vinokurov 12.01.16 at 1:57 pm

I think a more interesting question would be to ask what purpose “puzzles” like Newcomb’s Paradox (although where exactly the paradox lies is unclear) are supposed to serve. I for one am skeptical as to whether even contemplating questions like these has any philosophical utility whatsoever.


cs 12.01.16 at 2:01 pm

Part of your response seems to violate the foundational notions of the thought experiment: that the creator is allowed to set up the world how he or she sees fit.

But the problem with this thought experiment (it seems to me) is that the creator is being too coy about the details of the situation they created. If the superbeing is truly infallible, then it is equivalent to a situation where the money is placed in the box or not, depending on my choice, so I take box B. If the superbeing is fallible, then I might as well take both boxes. Not being given that information, my answer depends on how I interpret the scenario.


P.M.Lawrence 12.01.16 at 2:04 pm

It’s perfectly straightforward to run a real life experiment and see how people really would deal with this. Just set it up as a telephone Indian/inverted pyramid. Take a few thousand volunteers and put each of them alone in a room with the relevant boxes, separately, and let them run a few dry run iterations to confirm that the boxes have been set up as stipulated (discarding all the subjects who choose differently from the implied predictions), then let them have one try for real. Afterwards, debrief them to find out how they reasoned and why they made the real choice they did at the end.

It seems clear that this is only a paradox in the sense that it is counter-intuitive, not in the sense that it can’t happen – because clearly it can, in a sufficient proportion of cases.


faustusnotes 12.01.16 at 2:14 pm

Why is this even a thing? I can’t even!


MisterMr 12.01.16 at 2:33 pm

This is a time paradox, not a logical paradox.

For example: suppose I create a time machine and I travel 10 years in the future, where I discover that because of the time machine invention, humanity is doomed. Therefore I go back in time and I tell to past myself not to build the time machine. But if past myself actually doesn’t build the time machine I can’t go back in time to tell him not to, so…
Obviously this kind of “paradox” works because we are playing with the definition of “time” and “causality”, not with logic.

In “Newcomb’s problem”, the superbeing that can predict the future is just a narrative trick to make information go backwards in time, since he (?) can take info from the future to act in the past, just like my time machine.

An additional “paradox”: our superbeing A makes the same challenge, but then another superbeing B (who can see perfectly into the past) takes up the challenge. How can superbeing B pick the wrong decision if he can see perfectly into the past?
Solution: the day before the challenge starts, superbeing A takes the money and runs away in a tropical island, because he doesn’t want to lose the money.


Patrick 12.01.16 at 3:02 pm

This is the Calvinist predestination paradox. God has predestined you to either heaven as a member of the elect, or hell. His decision is absolute and will not change no matter how you live your life. There is also a perfect correlation between people who live as faithful Calvinists, and the people who turn out to have been chosen as the elect. How do you choose to live your life?

I found this momentarily diverting when I was in grade school and first learned about it. Then I decided that I shouldn’t be surprised if nonsense questions about nonsense ideas have nonsense answers. Garbage in garbage out applies to thought experiments as well as programs.

I decide that P(this is a scam and we just haven’t figured out the trick yet) is far greater than P(such a being exists). If the track record of the scam is verifiable I decide that the most likely explanation is that the contents of the boxes can be changed after the choice is made. This means that playing along with the scam likely yields the highest value. I do so if I need the money, otherwise I refuse to play.

If this is arguing with the hypothetical, so be it. The hypothetical asks for either guy instinct or logical analysis. Gut instinct is only meaningful in a world that follows the rules to which out gut instincts are adapted, and all I did was restore those rules. And logical analysis is already out the window if you’re presuming impossible things, like effectively omniscient entities that can perfectly predict our choices yet coexist with free will.


Mike Furlan 12.01.16 at 3:25 pm

I like the version with the trolley, and would add a fat guy.


Sky Masterson 12.01.16 at 3:27 pm

One of these days in your travels, a guy is going to show you a brand-new deck of cards on which the seal is not yet broken. Then this guy is going to offer to bet you that he can make the jack of spades jump out of this brand-new deck of cards and squirt cider in your ear. But, son, you do not accept this bet, because as sure as you stand there, you’re going to wind up with an ear full of cider.

Box B.


Dave Maier 12.01.16 at 3:46 pm

For Jerry @16 and others who think this is just stupid:

The way it was explained to me was this. In decision theory [they told me] there are two highly intuitive, generally accepted principles for determining the rationality of an action (that is, there are more than that but these are the two we are discussing today). Normally they go together (which is why they are both accepted). But clever Dr. Bob has come up with a situation in which they conflict. The point is not so much that the result will determine which one is right, but that there was any problem at all in the first place. It’s a paradox!

One principle is: maximize expected utility. Zamfir explains this idea well in #4: by hypothesis, people who choose one box only do better. End of story. (Only once probability comes into it, we may have to tweak the relative payoffs to make the numbers come out right.)

The other principle is domination (I think that’s what it’s called). If one action does better than another no matter how things turn out to be, then that’s what we should do (so it’s not surprising that in most cases the two principles tell us to do the same thing). I won’t draw the payoff matrix (it’s easier to see than to say), but the idea is this: no matter how much is in the one box, you surely do better in each case if you take not only that one but also the other one as well. In the context of the paradox, this takes some arguing (given the hypothesis, above), but it can be made fairly intuitive: surely, once you have picked the one box and are going out the door with it, and they say “are you sure you don’t want this one too?” it will at least occur to you that normally you would think it obvious that you should: two boxes “dominates” one box in that sense.

As someone not otherwise interested in decision theory, I think this paradox is at least interesting, and it’s fun to teach. (But if you must know, I’d just take the one box.)


William Berry 12.01.16 at 3:58 pm

What Evan said. It’s the view from the ground, regardless of what one thinks of the terms of the problem.

JQ’s solution strikes me as an unwarranted attempt to evade the strict terms of the problem. The existence of the super-intelligent doesn’t depend on what he thinks. It is stipulated.


William Berry 12.01.16 at 3:59 pm

[super-intelligent being] that is


MisterMr 12.01.16 at 4:38 pm

@Dave Maier 25

I understand your point, but it still is a fake paradox.

By introducing an entity that sees the future, we are meddling with the concept of causation (because the future action of the player causes the action of the superbeing).

If we ungarble the events following the logical causation scheme, we have:

1) the player makes his choice;
2) the superbeing “sees” the choice (from the past, hence the implied time travel);
3) the superbeing chooses what to put in the boxes (in the past).

from the logical point of view (ordering the events in terms of causation) we have 1, 2, 3; but with “conventional chronology” the order is 3, 1, 2. Conventional chronology is meaningless because we inserted time travel of some sorts in the hypothesis, so the actual order of the events is 1, 2, 3.

If you follow the order 1, 2, 3 the “dominance” strategy never enters into conflict with the maximizing strategy, because the superbeing is just cheating (he changes the content in the boxes “after” the choiche is made in the correct timeline), so in the end it’s just an apparent, fake paradox based on the not very original paradoxes of “time travel”.


CJColucci 12.01.16 at 4:42 pm

A super intelligent being, if truly super intelligent, would know that I deserve to get, and the world would be a better place if I did get, the maximum money, so it would put the million in Box B and leave it there so I would get it no matter what I chose.


Ben Alpers 12.01.16 at 4:49 pm

The other ridiculous thing stipulated is that we are in perfect communication with said superintelligent being.

Yes, if you take all the stipulations of the problem seriously it makes sense to choose one box. But the problem has nothing whatsoever to do with reality, precisely to the extent we take its stipulations seriously.

afaict, the function of the problem — which more or less “proves” that, if you assume the existence of an all-knowing creator that is in communication with us mortals, you should act as if there is an all-knowing creator that is on communication with us mortals — is to give the vague impression that you’ve proven the existence of an all-knowing creator who is in communication with us mortals.


lemmy caution 12.01.16 at 4:50 pm

If I take Box B and it is empty, then I have added to the knowledge concerning the super-human being. Otherwise, I am rich.


Glen Tomkins 12.01.16 at 5:23 pm

I really am jazzed by the concept of a deity who would eff with us as described in this paradox. That’s a God I can believe in!

In this universe, with this God, you’re going to get effed, so don’t bother making a choice. That’s my solution to the Newcomb problem.

Oh, and it ought to be called the Newcomb Paradox, not Problem. It sneaks in knowledge of the future under the guise of omniscience (perfect predictive power). Of course it results in all sorts of the same paradoxical impossibilities you introduce when you allow time travel in your story.


Jim Buck 12.01.16 at 5:29 pm

You keep the contents of the box/boxes you take, and your aim is to get the most money.

It has to be Box B; even if it does not contain the £million, my falsification of the super-intelligent being’s supposed powers of predication is likely to earn me more, on the after dinner speaking circuit , than the £thousand I lost.


Jerry Vinokurov 12.01.16 at 5:30 pm


The way it was explained to me was this. In decision theory [they told me] there are two highly intuitive, generally accepted principles for determining the rationality of an action (that is, there are more than that but these are the two we are discussing today). Normally they go together (which is why they are both accepted). But clever Dr. Bob has come up with a situation in which they conflict. The point is not so much that the result will determine which one is right, but that there was any problem at all in the first place. It’s a paradox!

I suppose I should have been clearer. I understand the decision-theoretic conflict that such things are intended to expose; I just think the conflict is false because it rests on magical assumptions. In the case of Newcomb’s problem, it seems to me that there is no real “choice” to be had at all. The superbeing has already predicted what I will do, and hence any “choice” that I might make isn’t really a choice at all, but only a fulfillment of the prediction that the superbeing has already made. I might as well pick box B, I guess, but it doesn’t really matter. But even if that were not the case, the utility of this thought experiment for actual decision problems seems to me to be asymptotically close to zero. Even if I were to follow the koan-like suggestion that I should cultivate myself to be the kind of person who chooses box B, I don’t see how that would translate to aiding me in making the kinds of decisions that I have to make in real life. The Newcomb problem is so arid and abstracted that I strongly question the idea that any implications derived from it would be useful for relevant decision-making in the real world.

I am, in general, deeply skeptical of thought experiments as such; I don’t think they illuminate what many of their practitioners think they illuminate. In some sense, I think much of it is busywork for philosophers, which hey, some of my friends are philosophers so I’m glad this kind of thing gives them a paycheck and keeps them out of trouble, but my deep suspicion is that most of this is really a kind of a cottage industry of refining already relatively useless abstractions into sharper and sharper points.


Alan Bostick 12.01.16 at 6:07 pm

The superbeing *cannot* exist. The world is at its foundation essentially random and unpredictable.

It is too easy to construct a decision-maker who is inherently unpredictable. (If a single photon known to be circularly polarized passes through a linearly polarized filter and sets off a photodetector, then take both boxes. If the photon is absorbed by the filter, then take box B.) The resulting choice *cannot* be predicted.

(I have seen formulations of Newcomb’s paradox that state explicitly that if the superbeing belives the decision-maker is intentionally randomizing their decision, then box B is empty.)

Given that the superbeing as described cannot exist, the question remains, if you are presented with this choice, what is really going on?

This is a test of willingness to lie for the sake of flattery.

If you intentionally choose box B, you are reassuring the supposed superbeing that you do believe in its awe-inspiring predictive powers. If you choose both boxes, you are calling the superbeing out as a fake.

Note that if you choose box B and it turns out to be empty, the superbeing will be revealed to be a fake for all to see. If you choose box B and it contains a million quid, you will have affirmed your belief to the superbeing, as well as being a million quid richer, and it may very well offer you later opportunities for gain in return for flattery.

Clearly the thing to do is to loudly and publicly declare your belief in the superbeing’s predictive powers, and then choose box B.


cs 12.01.16 at 6:13 pm

Re: Dave at 25 – I still don’t buy the paradox. Repeating what was already said but: in the scenario where the money is put in/removed after we make the decision, then both of your principles agreee – take one box. If we assume that the superbeing is effectively a perfect predictor then that is functionally equivalent to assuming the money is moved after we make the decision.


J-D 12.01.16 at 7:51 pm

I have bad news for everybody who takes just one box. As you open it, you are bitten by a Russell’s viper, and as the fatal symptoms set in you hear Newcomb’s being laughing hysterically at the joke.

I also have bad news for everybody who takes both boxes. As you open one, you are bitten by a Russell’s viper, and as the fatal symptoms set in you hear Newcomb’s being laughing hysterically at the joke.

Take A Third Option


Yankee 12.01.16 at 7:59 pm

The question about the existence of the super-intelligent being doesn’t arise within the problem, and as your due diligence has presumptively established. Having done so, taking both boxes is self-defeating chickenshit. John’s solution is to not accept the problem. Which seems to be astonishingly common.


bruce wilder 12.01.16 at 8:24 pm

You cannot petition the Lord with prayer.

Take both boxes.


Ike 12.01.16 at 8:24 pm

“Chuck Norris always takes both boxes; he has never received less than $1,001,000.”


Paul 12.01.16 at 8:52 pm

This is not really an interesting problem. How should I act if I do not believe in free will? The paradox is obvious. If I have free will, the being can at most be very very lucky.


J-D 12.01.16 at 9:16 pm

Sky Masterson

One of these days in your travels, a guy is going to show you a brand-new deck of cards on which the seal is not yet broken. Then this guy is going to offer to bet you that he can make the jack of spades jump out of this brand-new deck of cards and squirt cider in your ear. But, son, you do not accept this bet, because as sure as you stand there, you’re going to wind up with an ear full of cider.

Box B.

Right analysis, wrong conclusion. Recognising how three-card monte is a scam doesn’t teach you how to beat three-card monte, it teaches you to stay away from monte dealers.


graeme 12.01.16 at 9:18 pm

i think Z has it–really, your actions is dictated by the answer to the question: can the super being solve NP-complete problems in polynomial time? This is a hard requirement for it to be able to have a 100% success record for all prior runs (which are as I understand the question are arbitrary and therefore infinite). Which means really the question is no different than saying, oh, If you the Riemann hypothesis is false you should take one box, both otherwise. Then further, assuming that P=/NP is proved one day, later this question will be, If 1=2, take one box.

Can you conceive of a hypothetical universe in which the same mathematical axioms lead to different results?


Ethan 12.01.16 at 10:38 pm

The problem doesn’t actually stipulate that the superbeing is legit, at least not in the form presented here. What it stipulates is that I have investigated and can find no errors, and no explanation for its ability. Therefore, given that I do not believe in the possibility of the superbeing, I have made a mistake. Either my investigation has failed to uncover an elaborate scam, or my beliefs about the nature of time and choice are incorrect (there is also a highly unlikely third possibility, that there is no scam and no predictive powers, and the whole thing is just a coincidence). It seems easier to believe in a failure of the first sort than of the second to me, so it comes down to this: what do I think the point of the scam is? If the point is to establish this being’s credibility for some later purpose, then I should take box B: if these people can control the results of all elections, they can definitely get $1,000,000 into a box when they need to. If the point is to screw me personally out of $1,000, then I should take both boxes. That doesn’t seem worth the time and effort at all, so I take box B.


derrida derider 12.01.16 at 11:12 pm

Yep, it is impossible for you to have a choice and for a superbeing to infallibly predict (and act on) your actions; that is inherent in the terms “choice” and “infallibly predict” so is literally a contradiction in terms. Duns Scotus showed that once you allow one logical contradiction to apply to the world then you are permitting all. The problem as stated is gobbledegook.

That it is logically impossible for God to be simultaneously omniscient, omnipotent and allow choice is hardly a new insight. Philosophers should know better.


Manta 12.01.16 at 11:48 pm

I propose the following variant.
Assume moreover that 1.000 = 1.000.000.
Which box would you choose?


pnee 12.02.16 at 12:39 am

Just take the one box. If it’s empty, sue.

Let the Supreme [Being] Court decide.

More seriously, is there overlap between the two-boxers and people who defend “free will”? The two-boxer argument presented at the guardian seems to be that the decision you make now is independent of the Super-being’s prediction, so go for it. But if we’re all just deterministic decision-makers, that’s not true.


lagarita 12.02.16 at 12:40 am

All of these “solutions” accept that money is something of value. But money is as equally fictional as the Superbeing. So the correct response is to remain silent and walk away. There is no Superbeing and both boxes are empty no matter what they contain.


Alan White 12.02.16 at 1:06 am

Trump’s solution:

Somebody puts out these boxes, see? They might have money, and some website says maybe as much as $1,001,000. There’s all this stuff about Superbeings and crap, but all I know is somebody might be able to put lots of cash in these boxes, and maybe even more. I’m gonna Tweet at 3 am that unless this somebody forks over all the cash they have, they are gonna go to prison for fraud, right?. So I’m gonna take both boxes and Tweet what I found in them, but no matter how much it is, they probably have more and need to fork it over. Or you’d better look good in prison stripes! #Make Philosophy great again!


ZM 12.02.16 at 1:38 am

I don’t believe in a Super-Intelligent Being who likes undeclared psychological experiments myself. No one decent likes psychological experiments, definitely not anyone super-intelligent.


Dave Maier 12.02.16 at 1:55 am

Jerry: Fair enough.

cs: Fair enough.

Paul: Maybe the “superintelligent being” formulation (not necessary to get the problem going) is getting in the way here, but I don’t think that one’s actions being (even ideally) predictable means that one doesn’t have free will.


js. 12.02.16 at 2:14 am

is working?


js. 12.02.16 at 2:15 am

[Please delete last comment — sorry.]

Possibly the most annoying about Newcombe’s puzzle is that it’s a hypothetical about determinism (NB: not free will) masquerading as a problem of rationality. The obvious answer is to take a Geiger counter to the boxes and do whatever it tells you. Because fuck that super intelligent being.

And yes, I’m being a little flippant, but it’s an entirely misconstrued—as, happily, other people have pointed out too.


RichardM 12.02.16 at 2:31 am

The Guardian statement of the problem doesn’t make it obvious whether or not you are supposed to not know the Superbeing’s prediction. Pascal’s wager argument implies you don’t, any talk of her credibility implies you do.

One of Ian M Bank’s Minds says roughly ‘I am the most intelligent entity within 500 light years, and I can’t predict what will happen after 7 pool ball collisions’. Which I understand to be correct in terms of contemporary physics, because quantum and chaos.

Which in turn means that a super-predictor who can call Leicester on demand is not operating according to those physics, but using something indistiguishable from time travel. So if you know of her prediction, you pick B, and if you don’t, you take both.

At least unless you have a moral principle that says excess greed is bad, even outside a zero-sum situation. In which case you take A only, because who needs a million?


Terence 12.02.16 at 2:32 am

1. If the problem’s purely financial then you take box B only (setting aside the fact that windfall gains often don’t end up being gains at all). Surely the diminishing marginal utility of the prize is such that you’d hardly notice the extra $1000 you could have won.

2. If the problem’s really the issue of free will, you build some sort of device that generates a decision for you on the basis of the actions of one of those sub-atomic particles which behaves, to the best of our knowledge, purely randomly. You do this because, if you beat the immortal predictor, you can relish in the fact that you quite probably don’t live in a deterministic universe. On the other hand if you lose, you can tell yourself that she just got lucky (50% chance), and that it’s still possible the universe isn’t deterministic.


Gabriel 12.02.16 at 2:41 am

In what can only be described as an appalling deficit of intellectual imagination, some people seem very hung up on the idea of the SIB, imbuing it with all sorts of unnecessary properties unrelated to the problem. I would suggest, if this is indeed a problem for you, replacing the SIB with a Very Ordinary Human who, through some unknown mechanism likely involving the reading of subtle psychological clues, your body language in relation to the boxes, etc has said predictive power. Use your SFnal imagination to invent something plausible for you – or, even better, come to grips with the fact that thought experiments by nature ask to be granted one or more impossibilities in order to highlight something within the problem. It doesn’t change a thing.

If one wishes to criticize a thought experiment’s premises, one does so by showing that the introduced imaginary element distorts reality so much that the problem within the experiment has no bearing on our world. ‘There is no god!’ is not sufficient.

The original formulation of the problem also addresses attempts at random selection.


JimV 12.02.16 at 2:50 am

The existence of this problem tends to confirm and deepen my distrust of most philosophers.

It seems to tacitly ignore some scientific points which are more interesting to me than the problem:

1) Whether or not “free will” (whatever that means) exists, it is possible to access quantum events (such the the number of individual photons hitting a retina) and use them to add unpredictable randomness to a close decision. (This assumes quantum-level events are unpredictable which most physicists think is the case.)

2) One exception I can think of to 1) is if this universe is a simulation controlled by the SIB. In that case , and also assuming that most physicists are wrong and quantum events are pre-programmed in the simulation, then all sorts of miracles which are impossible for the code of the scenario to produce could be done by the analogous action of hex-editing the simulation data. However, given the size and complexity of this universe, it would be physically impossible (in this universe) to construct such a simulation.

3) However, neuro-science has determined that decisions are made well before they are consciously appreciated and acted upon, giving an SIB time to change box conditions accordingly.


Mark Dobrowolski 12.02.16 at 3:47 am

First, one will never know what your God thinks till afterwards. Second, what matters is what your God thinks of you. God is a 7yr old male child with a magnifying glass, and you are the ant. Take both boxes. They are light but bulky. You drop both. As you replace the kids you notice a “B” marked on each lid, both boxes are empty, and you hear the faint sound of laughter. Truly a lesson for us all.


keta 12.02.16 at 5:46 am

I take both boxes and put them in the trash, just like Super-Intelligent Being asked me to do the day before. Then I marvel, yet again, at the inventive ways she’s wrangled me into doing my chores all through these married years.


Z 12.02.16 at 7:01 am

The existence of the super-intelligent doesn’t depend on what he thinks. It is stipulated.

Yes, but that is a stipulation that entails the Universe is completely different from the one I know and consequently, in this Universe with super Beings, there are questions I am not sure how to answer, many of them much more elementary in this world than the Newcomb problem. For instance, what if the Being told me that one of my children would grow to destroy humanity? Should I then kill them all preemptively? Hell, what if the Being told me that 2 is an odd number, that 5 is an even number and that me believing otherwise is a sign that alien lizards are remotely controlling my brain? Then she tells to pick an odd number in the list 2,5 and instructs me that picking wrong would result in my horrendous death. What should I do now?

Or perhaps we should do as John a do a Locke on miracles. What is the overwhelmingly most probable case? That the Being exists as described or that this is all a scam and the “predictor” can simply change the content of the boxes or just fills them randomly? What


mark 12.02.16 at 7:01 am

I don’t get the “I can conduct a random number generator so the scenario is rendered ridiculous” approach. A relatively small number of people might flip a coin but presumably they don’t get the offer (or perhaps are the source of the 1% failure rate.)

Now, if someone is trying to kill you by predicting your actions perfectly then random number generator sounds great. I want to make it as tough as possible. In Newcomb’s setup I have an incentive to be as predictable as possible though.


Zamfir 12.02.16 at 7:28 am

What Gabriel says above. The problem doesn’t require godlike powers, not even a infallible track record. As long as the track record is very good, and its few failures don’t show a clear pattern of properties that you could emulate.

Such a record might perhaps require mind reading powers that no human currently has, but it’s hardly magic. After all, I can mind-read my toddler to this level. I know when she will peek at peekaboo. I know that she is awfully quiet and therefore raiding the kitchen drawers. I know when she runs behind the couch whether she will continue or reverse direction. Not perfect, but almost perfect.

All the problem requires, is a being with a similar insight in me. It would be strsnge if such an insight required magic.


Z 12.02.16 at 9:13 am

After all, I can mind-read my toddler to this level. […] All the problem requires, is a being with a similar insight in me

But your toddler cannot emulate randomness satisfyingly, while you can (or at least I can). So maybe you can predict your toddler’s behavior very well, but to predict yours or mine, one needs supernatural powers. So you’ll have a hard time convincing me that the Being has them, and if you could convince me, then I would start to doubt much more than domination or the maximization of expected utility.


casmilus 12.02.16 at 9:30 am


“However, neuro-science has determined that decisions are made well before they are consciously appreciated and acted upon, giving an SIB time to change box conditions accordingly.”

Daniel Dennett groans.


Nercules 12.02.16 at 9:54 am

My problem with this problem’s Superbeing is that it still hasn’t figured out a way to do away with our need for money.


Collin Street 12.02.16 at 9:56 am

The other principle is domination (I think that’s what it’s called). If one action does better than another no matter how things turn out to be, then that’s what we should do (so it’s not surprising that in most cases the two principles tell us to do the same thing). I won’t draw the payoff matrix (it’s easier to see than to say), but the idea is this: no matter how much is in the one box, you surely do better in each case if you take not only that one but also the other one as well.

The thing I think you’re missing is that the superbeing knows [is stipulated as knowing] your decision strategy. If you have a decision strategy that leads you to take both boxes: there’s a thousand in the boxes. If you have a decision strategy that leads you to take one box: there’s a million in the box. Which means the decision you make and the box contents aren’t independent: they both depend on the sorts of decisions you’d make.

[we can actually make this real-world by having the “superbeing” only make its offer to people who have expressed an opinion on the appropriate decision strategy on, like, a semi-popular group blog or similar.]

[or we could posit, say, 90%+ reliability instead of certainty: I don’t think this actually affects the choices all that much, and it’s within reach of reasonably attainable, I think.]


Mark D. 12.02.16 at 12:37 pm

We live in 3 dimensions subject to time, a 4th dimension. This SUB is a being who lives in say, 5 dimensions. Child such a being have any problem with manipulating time? Without paradoxes.


Jim Buck 12.02.16 at 1:06 pm

For instance, what if the Being told me that one of my children would grow to destroy humanity? Should I then kill them all preemptively?

“Arrival” (film currently on release) shows aliens whose cognition of the dimension of time is radically at odds to that of homo sapiens. Something a little similar to Z’s scenario is central to the plot. But whereas Z ‘s has faint echoes of the Abraham sacrifice story, Arrival’s has more similarity to the Jesus myth.


Dave Maier 12.02.16 at 1:29 pm

Collin: Yes, my view also is that that the contents depend on the decisions is what messes it up, as our supposedly now conflicting principles require that they not be. I was explaining why the paradox can seem appealing anyway. Your second bracketed point (that we don’t need certainty to get the ball rolling) is very important, at least if we are to sidestep some of the more fanciful irrelevant objections generally made here (about superbeings, time travel, free will, etc.).


James Wimberley 12.02.16 at 5:33 pm

The winning view in Islam is SFIK that Allah rules the universe by unconstrained free will. One Nigerian fundamentalist said that it can’t be true that evaporation from the sea causes rain, rain happens when God wills it to fall. It’s easy to see that this Muslim version of Yahweh is inimical to science, while the Christian version if Yahweh who sets the rules and walks away allows science to happen. A SIB that plays mind games with individual cases looks to me like that antiscience Allah.


stevenjohnson 12.02.16 at 10:10 pm

It’s really sad, I”ve read the article at the link several times now but all I get is this: When you pick Box B, the Super Intelligent Being has put a million bucks in it. The premises say She’s always right, and that She has a million bucks, and that She wants to give it to you. The text says you did the due diligence on Her existence, etc. So, the problem is whether you want a thousand bucks or a million bucks. How is this a problem?

It doesn’t have anything to do with free will, which should mean doing what you want to do without compulsion or restraint. One possible meaning of free will, the ability to somehow command yourself to desire something your rational self approves, or not to desire what your rational self disapproves. That seems like a reasonable definition of “will” to me, but it also seems anybody who thinks the exercise of will power over your emotions is ever “free” is a sadistic moron.

So what exactly is Newcomb’s problem?


Frank Ashe 12.03.16 at 2:12 am

Isaac Asimov is reported to have said he’d only choose Box A, just to show he had free will and didn’t have to stick with the choices given by the superintelligent being.

I like that style of answer.


js. 12.03.16 at 2:38 am

Well, since *everyone* seems to be very annoyed by how the problem is set up, it might actually be worth pointing out why people care about it. It’s (mostly) not because of Calvinism or whatever. It’s (again, mostly) because it’s one of the cases where a case-by-case analysis (i.e. determining the dominant strategy fails—i.e. it gives you a suboptimal outcome (obviously). So, structurally, the problem is not unlike the Prisoners’ Dilemma, some “assure and threaten” scenarios, etc. And according to certain prevalent models of rationality which a lot of people find *very, very intuitive*, case-by-case analysis should never fail—it’s as if it becomes impossible to understand how actions could violate a dominant strategy and still be counted as rational. The most interesting point to make in this area is probably that models of rationality that forces the utter intuitiveness of dominant strategies is deeply flawed (a point that comes out really nicely in prisoners’ dilemma type cases). Unfortunately, that point gets obscured with Newcombe because the set up is really annoying.

Also, JQ is wrong re developing the disposition. You don’t know what the mechanism of prediction is, so it shouldn’t matter whether you pick Box B, say, based on a general disposition or a one-time calculation. Other things equal (which they seem to be), you’d clearly want to do the latter rather the former—its less work for one thing.


js. 12.03.16 at 2:40 am

Jesus, there are a lot of typos in there. Sorry.


Gabriel 12.03.16 at 2:55 am

James W, your formulation of the “Christian” vs. “Muslim” God says a lot more about you, and your racism, than it does about theology or science. Crooked Timber is almost completely free of Islamophobia, and I’d prefer we keep it that way.


js. 12.03.16 at 3:47 am

Thinking about this thread a bit more, I think it’s worth thinking about this from a different angle. Forget about Newcombe’s problem, think about the prisoners’ dilemma. The standard model of rationality ruled out collective action — that’s really the point of PD. So either collective action is effectively impossible or the model of rationality is fucked. Well, I know how I would go here.

But here’s the thing. If you forget about the super intelligent being, Newcombe can be like a coordination problem. Dude will give you a million dollars if you give up your dumb model of rationality. Seriously, take the million. But more importantly, give up the dogma that rationality per se militates against collective action.


Ronan(rf) 12.03.16 at 8:33 am

I havent read all the comments, but …. you take B because if you are correct you (a) win 1 million (b) find out if there’s a supernatural being.
If you’re wrong you lose found money in the quest to become a millionaire and discover if there’s a God. Who cares? You lose literally 1k for these insights. Are you all really that strapped for money? You wouldnt pay 1k to find out the mysteries of life and have the chance to become a millionaire at the same time?


roger gathmann 12.03.16 at 7:09 pm

I suppose the decision depends as well on the non-superintelligent being making the choice. #2 in this thread thinks that missing a million by taking both is something that will remain as a permanent scar of some sort. Myself, I have never had an expectation of a million. I could look at my life as a trail of missed opportunities that could have lead to a million – but I don’t. Whereas a thousand would make a nice sum now for buying Christmas gifts, so i would certainly take both boxes. Given the info I have about the super intelligent being, it likes to fuck with your expectations with its prediction trick, so I wouldn’t worry too much about it. Sounds too much like a hedgefund manager to me.


SusanC 12.03.16 at 10:58 pm

An alternative take on this might be: Game theory implicitly assumes that the universe is causal (players cannot look into the future to see what other players will do). As our actual universe appears to be causal (with some possible exceptions due to quantum theory and the ERP paradox), we usually don’t need to worry about this assumption not holding. But if the explicit counterfactual is that you’re in a non-causal universe, then game theory notions like one strategy dominating another can’t be safely be relied on.

I am tempted to accuse this paradox of being bad science fiction. It postulates a universe that is explicit non-causal, but in other respects like our own. Is this necessarily false, not just contingently false? As far as we know, entities that can see into the future don’t exist in out universe. It seems plausible that in any universe where they did exist, things would be sufficiently different from our world that other parts of the setup cannot safely be assumed to hold.


roger gathman 12.04.16 at 5:07 am

ps Must be said that in this thought experiment it is rather a downer that the superintelligent being cares so much about money. I’d like to think that the visions of eternity that unroll before the eyes of such a being would make it immune to the art of the deal. But turns out its got the moral character of a tout at a race track. So much for the love that passes all understanding.


SusanC 12.05.16 at 8:28 am

@79. It’s the kind of thought experiment that is driven by mathematics, rather than the psychology of the protagonists, so its unsurprising if characters lack credible motives.

But: I think the setup implies that the precognitive being doesn’t care about money – it give away a million just to make a point – but it knows that the experimental subject does care. It somehow remnds me of the Adversary in the book of Job…


roger gathmann 12.05.16 at 8:26 pm

Susan, I like your suggestion about the adversary!
However, I think the thought experiment is driven by psychological aptitudes – especially those having to do with remorse concerning loss – as much as by math. The idea that one can “afford” to lose 1000 dollars – or risk 1000 dollars to make a million – is based, of course, on losing nothing. It isn’t my money that is in either of the baskets, yet it quickly translates into “my loss” if one of the alternatives turns out badly. Mathematically, nothing would change if we iterate the situation 100 or 1 million times, but if the player, each time, chose b, and each time lost, I imagine that there would come a time where the player would choose not to be a fool, and take the thousand. The problem with the paradox for me is that it is frozen in an uncontextualized present, but of course the adversary with the magic power of prediction is the only one in an uncontextualized present, one that encompasses all the future. The player on the other side, though, never lives in an uncontextualized present. Here I think one gets close to why theories of rational choice are such dead ends, for in a sense, the adversary here is equated, by a certain species of economist, with the “market”, which is always endowed magically with having all information at its markety fingertips. As many have pointed out – for instance, James Galbraith – no such market exists.
In other words – if there is such a market, that market is Satan. I like this leap from economics to theology!

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