Newcomb's paradox

[jack]

Links

Newcomb's paradox on wikiepedia
Newcomb's paradox on Overcoming Bias blog
Newcomb's paradox on Scott Aaronson's blog and lectures

I first came across it via overcoming bias, and discussed it with a few people, but then recently saw it again in one of the transcriptions of scott aaronson's philosophy/quantum/computing lectures.

Newcomb's paradox

In very short, Newcomb's paradox says, suppose you're a professor and a grad student (or, in some cases, a superintelligent alien) comes to you and demonstrates this experiment. She chooses a volunteer, examines them, then takes two boxes, puts £1000 in box A and either £1000000 or nothing in the box B (see below for how she decides). She brings the boxes into the room and explains the set-up to the volunteer and says that they're allowed to either take the mystery box (when they either get lots or nothing) or take both boxes (when they get at least £1000.)

She even lets them see the £100000 beforehand so they know it exists, and lets them peek into box A to show it does have the money in, though box B remains a secret until afterwards.

Choice	In box A	In box B	Total obtained
B only	£1000	£0	£0
Both	£1000	£0	£1000
B only	£1000	£1000000	£1000000
Both	£1000	£1000000	£1001000

"What's the catch," the volunteer asks. "Ah," begins the experimenter. "I have previously examined you, and worked out which choice you're going to make. If you were going to choose both boxes, I put nothing in box B. Only if you were going to take box B only, did I choose to put £1000000 in it.

"Hm", says the volunteer. "What do I do?"

A few caveats

"What if the volunteer would change their mind when they discovered the reasoning, or is going to choose based on a coin toss?" "Then I didn't accept them as a volunteer."

"How do I know it works?" You can't be sure, but she performs the experiment lots of times and is always right, so you are convinced. (Some examples ask you to presume as part of the conditions that she can, or take it on trust, but I think "having seen it work" makes it most convincing and concrete.)

"Ah, but I don't care about £1000, and certainly not if I've got £1000000, so I don't care," Well, ask what you would do if the numbers were a bit different. Can you pretend there's no combination where you'd risk something to get the little one, yet risk more to get the big one?

"How did they know what they'd pick when this experiment was performed the first time?" It doesn't really matter, just assume that you have seen it working with pretty-perfect prediction.

What would you do? An enumeration of the two obvious arguments.

11: "Why should you take both boxes?" Duh! Because whatever's in either of the boxes, you get all of it. And if that means I fail to get the million, then it's already too late to change that, isn't it?

22: "Why should you take box B?" Duh! Because you've just seen 50 people do the experiment, and all the ones who took both got £1000 and all the ones who took B got £1000000. Follow what works, even if you can't justify it with maths.

That's why it's a paradox, because, if you squint long enough, both answers seem perfectly reasonable.

I know this seems a little convoluted, but I tried to make it comprehensible if terse even to people without a very high opinion or training in philosophy (like me, in general). And hopefully get it to the point where at least asking the question makes sense.

Wait, if we use baysian reasoning, I bet the arguments will instantly become transparent and non-controversial. Right?

11: As above. Look at the table, and enumerate the possibilities. Choosing more boxes always gives a bigger payoff.

22: Ah, no, you're cheating. Based on the previous evidence, you must assume a priori that you are on row 2 or 3. After than, the choice is easy: row 3 gives more money. (See below for more "so, there's a 2/3 chance I'm in this universe..." type reasoning.)

Can we put this on a more rational footing? How does she predict what's going to happen

In fact, there are several ways.

1. You can do it if you postulate time travel, or determinism and a copy-teleport-machine, but those are not very realistic things to postulate, whether they would be physically possible or not.

2. A super-intelligent alien scans your brain and models it in a computer.

3. They give you a short-term-memory impairing drug, and try the experiment out several times beforehand while you remain the same person with the same experiences, but have no memory of the trials.

4. They discover that 94% of the time, all men choose one way, and all women choose the other. (But the experiment is double-blind, run by a technician who doesn't know the expected results, so the grad student peeks, then tells you that there's a 94% correlation, but not which way round it is, then invites you to participate yourself.)

Further arguments

33: Aha! In method 3, you don't know which one you are, one of the trial runs, or the final experiment. The only consistent answer which gets the big money is to assume you're more likely to be a trial run, and hence choose the money.

44: Aha! If so, then (*invokes Greg Egan*), the same reasoning applies with method 2. That suggests that you don't know if you're you, or the simulation of you!

55: Nope. Not so. What about method 4? Surely you can't claim that your consciousness might be either (a) you or (b) "the statistical correlation between gender and box choice"??

Which leaves us back where we started. (But remind me to come back to the "am I equally likely to be me, or some other human or simulation of a human".)

Free will

"What does it have to do with free will?" Well, the experiment is completely (sort-of) practical to do. In theory. And so you'd think it should be also actually possible to choose which to take. And yet it doesn't seem to be, and the answer seems to depend maybe on whether you believe in something you can call "free will".

In fact, people divide between take A&B, take B, and "problem is stupid, won't consider". In general, I think the last answer is often over-overlooked. In this case, if I'd seen it work out like that, I'd agree to take only box B, even if I couldn't explain the mathematics behind it. However, I also definitely feel I should be able to justify one case or the other.

Informally, it seems most people seem to eventually take B, but I don't know how important that is.

Apocrypha

Links to prisoner's dilemma, links to doomsday paradox, etc, etc.

Comments

[curig.livejournal.com]

Surely the point is that, assuming that the pre-determination of the choice you will make is never incorrect, then the fourth option in the enumeration doesn't exist. The choice is then between getting £0, getting £1000 and getting £1000000, which is, I assume, not a hard choice.

[cartesiandaemon.livejournal.com]

Well, exactly. That was argument #22. It should also say the first option in the enumeration (total=£0) is ruled out also, I think, so you choose between the other two.

But I don't find that a satisfactory conclusion, because (a) the other argument #11 also sounds pretty convincing, and (b) if you accept the "precondition the worlds I could be in" type argument, it seems like you're either affecting the past when you make your choice (otherwise it wouldn't matter what you chose) or choosing which of multiple universes you live in.

Come to think of it, a simplified version of the experiment would be "we have run this experiment many times, and we observe that everyone we try it on pushed this button, here". Do you push the button? That removes the choice, leaving only the stark assumption that you can be successfully predicted.

[teleute.livejournal.com]

Come to think of it, a simplified version of the experiment would be "we have run this experiment many times, and we observe that everyone we try it on pushed this button, here". Do you push the button? That removes the choice, leaving only the stark assumption that you can be successfully predicted.

I wouldn't, on principle. I suspect a lot of other people feel the same way. The difference with the original question is a matter of reward.

What happens to the question if the student reverses what she puts in box B; if you were going to take B only you get nothing, and if you were going to take both you get everything?

[cartesiandaemon.livejournal.com]

I wouldn't, on principle. I suspect a lot of other people feel the same way.

I think, me too. However, that has an interesting contrast to Newcomb, where many answers assume you should just accept the predestination.

What happens to the question if the student reverses what she puts in box B;

So if you take both, you're pretty much guaranteed all the money, but the alternative is to demonstrate you have free will? That's almost the experiment I perform every time I don't jump off a cliff (and so far have always chosen to accept my apparent destiny) :) That's interesting.

[robhu.livejournal.com]

Brilliant :)

[cartesiandaemon.livejournal.com]

Oh, thank you!

[leora.livejournal.com]

Ah yes, ran into this as a child with the super-intelligent alien version, complete with cute illustration. I take box b.

And if I don't get the huge sum, I hope I get some satisfaction out of proving the alien wrong about me. But as what I'd choose is something I've stated before and now written down, the super-intelligent alien should know and be prepared to give me the huge sum.

I'm ready to volunteer now.

[cartesiandaemon.livejournal.com]

the super-intelligent alien should know and be prepared to give me the huge sum.

Yeah. That's interesting in itself. Overcoming bias comments that if you can precommit to taking box B, that's convenient and non-paradoxical, and you're probably right to do so, as then the alien will examine you, discover you'll take box B, and put in the £1000000. In extreme cases you may even need to force yourself to do so, eg. by posting some sort of £2000 bond that you will forfeit if you don't, to protect against the possibility that you were going to take B, but change your mind at the last minute.

Although they also talk about problems where it's specifically a surprise, and the best strategy in that situation. I can't find a link, but I think the extreme version was that an apparently trustworthy superintelligence comes up to you with no warning and says "I flipped a coin. It came up tails. Will you give me some money? I previously worked out how much you are going to give, and if the coin had come up heads, I would have given you 10 times as much." Would you give him any money?

[leora.livejournal.com]

Do I have any reason to believe this will ever repeat? Does the alien need money? I assume it does, since it needs to give money to people whenever its coin flip goes the other way.

[cartesiandaemon.livejournal.com]

I can't quite remember how it's supposed to work, but I think:

* the alien turns up on earth out of the blue, and performs some other but non-paradoxical experiments, convincing everyone of its ability to predict what people will do in chosen experiments, and that it's always truthful.
* but you don't know about this particular one in advance
* you should treat the alien purely as a black box that can manufacture a small amount of money in some way (maybe the same way it became an interstellar superintelligence). And ignore potential effects of inflation (you could alternatively suppose it gave you something useful instead of money). It presumably is (afayk) just interested in the experiment, and not in the money.
* In the original, I think there were two fixed sums of money.

So, I think they tried to make the argument that (a) if you would take box B, the same sort of reasoning probably holds here, you should choose to be the person who might have got more money, even though you didn't (b) but that's counterintuitive, it doesn't seem possibly useful to give money away just because an alien flew up and asked for it.

[leora.livejournal.com]

Yes, that one is annoying. I'd probably give a small sum I could easily afford to part with. Which means I'd sometimes maybe have a chance of getting a modest sum that would be nice, but not life-changing. I can live with that.

[http://users.livejournal.com/vitriol_/]

It probably says something odd about my psyche that my initial answer (once I understood the problem) was to bet the tester £500000 that their 'perfect' prediction was wrong, and then take box B.

Reading the expanded thingies, answer 22 seems the right one; granting the premise that the tester is able to predetermine my response then only choices 2 and 3 apply and the rational answer is B.

In fact, I don't even need to be convinced that the tester can predict responses with perfect accuracy - the difference between £1000000 and £1000 is so large that even if I think they only get it right 50.1% of the time it's still most rational to just take box 2: if I take just B there's a 0.501 chance I'll get £1000000 and a 0.499 chance I'll get nothing (mean gain £501000), whereas if I take both there's a 0.499 chance I'll get £1001000 and a 0.501 chance I'll get £1000 (mean gain £500000).

[cartesiandaemon.livejournal.com]

was to bet the tester £500000 that their 'perfect' prediction was wrong, and then take box B.

ROFL! That's lovely, I hadn't thought of it. You could even bet with someone else, if the tester gave you a moment to confer but didn't want to enter a side-bet themself. Someone else would presumably bet on the tester being right for all the usual reasons, if they had £500000.

In fact, I don't even need to be convinced that the tester can predict responses with perfect accuracy

Yes, indeed.

[teleute.livejournal.com]

I think I'm too ill to see the paradox here. Initially, I would assume that every logical person plans to take both boxes. Therefore, there should never be anything in Box B. Why, before you understood the condition on Box B, would you chose to take it only, when you had the option of both? Thus, if you've seen people walking away with money in Box B, you know that the alien/grad student was eithe wrong, or picked some weird people.

In any event, there is at this point either GBP0 or GBP1000000 in box B and a guaranteed GBP1000 in Box A, so the only sensible thing to do is take both boxes.

What am I missing? Is it just the annoyance that someone worked out that you're not stupid to begin with? That wouldn't annoy me ;-)

[cartesiandaemon.livejournal.com]

*hugs* Of course. In any paradox people generally have a different gut reaction, and it's the other answer that needs to be explained "why this makes any sense at all".

Initially, I would assume that every logical person plans to take both boxes.

This was actually a theme on understanding bias. (pw may explain more). I think the argument goes "Taking both boxes SOUNDS sensible. However, if there WERE a rational reason to just take box B, then I would get £1000000 when I did so. Well, do I need a better justification? Even if I can't explain it, isn't taking box B going to work? I'll do that[1]."

[1] Come to think of it, maybe your faith in the experimenter could ALSO be put on a more rational footing -- if they offer you £10,000,000 if they get it wrong. That would complicate matters, but it would simplify "why you trust them"

Overcoming bias called this "rationalists should win": if a strategy works, it should be the rational approach, rather than logic being the be-all and end-all if it DOESN'T work. Examples include cases where believing something false is of measurable benefit to you -- should you?

[nameandnature]

I think Saunt Eliezer has convinced me to one-box with his whole "rationalists should win" thing (oddly, I also linked to that on livredor's journal today).

In the coin flipping example, am I assuming that Omega will only ask me once? Does Omega's prediction include the result of the coin toss?

[cartesiandaemon.livejournal.com]

:) Oh yes, I saw that. It's funny how it was relevant to both.

In the coin flipping example, am I assuming that Omega will only ask me once? Does Omega's prediction include the result of the coin toss?

Do you remember this example from overcoming bias? I can't find it.

However, my impression was "yes" and "no" -- it goes to a person at random, predicts how much money they WOULD give it, and then randomly either (tails) asks them to do so, or (heads) gives them money*lots. Thus argument #11 becomes "why would I give omega any money? what do I gain" and argument #22 becomes "contingent on believing the predictions are accurate, giving omega money increases your expected return".

I'm not sure how much sense it _does_ make, it's certainly supposed to sound ridiculous, yet to have similar reasoning to Newcomb. Would it make a difference if it were iterated?

[scribb1e.livejournal.com]

"What if the volunteer would change their mind when they discovered the reasoning...?" "Then I didn't accept them as a volunteer."

Don't the conditions of the test mean that no rational human would be accepted? After all, the sensible thing to do before the reasoning is explained is to take both boxes, and after hearing the reasoning to take just box B. That's the whole point. So there is no paradox.

If they only accept volunteers who will not change their mind, then that's just like asking the volunteer to make their choice in advance of hearing the reasoning.

[cartesiandaemon.livejournal.com]

Oh yes, you're right. I was trying to avoid any of the sorts of paradox that occur when someone knows there's a prediction, but in this case the volunteer only finds out the prediction after they've made the choice, so the prediction can be made modelling the room, the explanation, and the volunteer, but not needing to encompass the result of the prediction itself. So it's not needed.

[vyvyan.livejournal.com]

Oh good, that's not part of the scenario then. It seemed completely unanswerable to me otherwise: I believe I would change my mind from two boxes to one box when I discovered the reasoning, and thus I wouldn't have been accepted as a volunteer, and thus can't say what I should do in the situation, since I wouldn't be in the situation! So I would have to answer as though I were the sort of person who wouldn't change their mind when they discovered the reasoning. In which case, I would be deciding whether I'm the sort of person who would stick with two boxes in the face of the explanation (which seems stupid) or the sort of person who would have chosen one box before hearing the reasoning (which seems even more stupid). So I'd be choosing which of two hypothetical stupid people I'd rather be :-)

As revised in your comment, the problem doesn't present me with any concerns about free will because I don't believe I have free will anyway. It seems perfectly reasonable that an even moderately intelligent alien/computer/psychology researcher/close friend would be able to predict my behaviour in such a situation, since I think I can predict it. As to how to program a computer to make decisions in this sort of scenario (mentioned in one of the links you give), couldn't you just get it to look at previous runs of the same scenario? This one would effectively reduce to the very straightforward options: 1) person takes one box and gets £1m 2) person takes two boxes and gets £1000. The program could just act to maximise its outcome, ignoring all explanation of how the boxes came to be filled in the first place.

[scribb1e.livejournal.com]

OK, I still don't get why it's a paradox.

So they scan your brain beforehand (or, y'know, just ask you) to find out what you're intending to do. You have limited and misleading information now, but you make a choice.

Then they put stuff in the boxes, based on your initial choice.

Then they tell you how they made their choice, and you change your mind if you like about which box you take.

But really, at this point you might as well take both boxes, whatever your initial choice was, because you can't do worse and might do better.

[cartesiandaemon.livejournal.com]

Sorry, I think I might have misled you all a bit with the stuff about deciding before the explanation. I was trying to pre-emptively answer other criticisms. So, let me try and get it straight for myself:

1. You go in. Assuming your brain is reasonably deterministic, it's implicit in your brain what you're GOING to do when given the explanation, and the choice, but you've not even thought about it. Like how you might think, in a crisis, you'll react a certain way, but in actual fact, someone else might be able to predict it better than you.
2. They examine you.
3. You get the explanation and the boxes filled with (maybe) money.
4. *pause*
5. You make the choice and take 1-2 boxes.
6. You get the money.

In the magic computer simulation of your brain explanation, you're scanned at step 2, and successfully simulate your responses through 3, 4, 5. In the short term memory impairing drug explanation, in step 2, they drug you, and then perform steps 3-5 several times. (In order to make the experiment consistent, they'll have to leave you drugged up until you get through 3-6 for real too.) (Alternatively, the explanation comes in step 1 instead of step 3, it shouldn't actually make any difference.)

Maybe someone who said they'd take one box ought to explain their gut feeling.

But I think the point is that, although taking both boxes SOUNDS like the only reasonable choice, you've seen the experiment performed on other people, and know that taking one box WORKS even though you don't know why. So, wouldn't you do that? I think I would...

(I also think in the drugged case, you HAVE to take one box. What's mysterious is that it gives a different answer to the other explanations, even though they all sound like they WOULD be possible, and would be essentially the same to experience.)

[chess]

I would take box B, but you knew that already.

(Is this actually intended to be an analogy to religious belief of the 'pie in the sky when you die' variety? Because it works very well as such.

If you don't believe the 'super-intelligent alien' (i.e. God) you take both boxes and get the GBP1000 reward (you don't have to do awkward things for them in this life) but it turns out you have no afterlife / a bad afterlife (the GBP0 in the other box).

Whereas if you trust the 'super-intelligent alien' then you don't get the GBP1000 of having an easier time in this world due to not having to pay attention to them, but you do get the GBP1000000 of their help / the afterlife which is so much more that supposedly you don't miss the GBP1000 which was definitely in the first box but which you passed up to get the greater reward.)

[simont]

Well, hold on there. The situation isn't analogous, because the whole point of Newcomb's paradox is that the decision has already been made about whether or not you get the big reward – unless you're willing to accept reversed causality or some kind of magical thinking, your behaviour now cannot affect the contents of the opaque box. Whereas in the typical setup as presented by major world religions, whether you get the big reward absolutely is affected by the choices you make between now and then.

[chess]

I don't see that at all.

The decision *has* already been made about whether or not you get the big reward, if you look at it from the outside-of-time persepective. Either you are the kind of person who trusts the alien and takes the second box, or you are the kind of person who doesn't and takes both boxes. And the alien knows. The fact they offer you the choice anyway, and that it's still a choice that you make, doesn't affect their ability to know the outcome before you make the choice.

Possibly I'm slightly more on the 'predetermined elect' side of the debate (which I don't see as incompatible with free will, but the intersection is complicated) than some people, though.

[simont]

Hm. I still think it's different. In the situation where God knows what you do turn out to do because he can see the entire timeline from outside, he can make his prediction 100% accurate1 – and, from your point of view, it is absolutely the case that if you behave one way you get the big reward and if you behave the other way you don't. (Disregarding for the moment all the obvious objections about how you knew all this anyway and whether you might be wrong. For the sake of discussion, this is a universe in which we're sure God exists and is as you describe him.)

It's important to Newcomb's paradox that the predictor might in principle be wrong but it's very unlikely. If the predictor were 100% reliably, definitionally always right then it would have to be because there was causal contraflow, at which point one-boxing is a no-brainer. The in-principle possibility of a mistake arising from the causality constraint is what makes it tricky in the first place.

---

1. I don't feel right saying "100% accurate", actually, because what I want to say is "definitely never ever wrong in any conceivable situation" and I feel that "100% accurate" sounds too much like the weaker concept of "wrong with probability zero". The god we're hypothesising here isn't even wrong on an outcome set of measure zero, and I think that might actually be important!

[cartesiandaemon.livejournal.com]

If the predictor were 100% reliably, definitionally always right then it would have to be because there was causal contraflow,

And indeed, might lead to all sorts of "it depends on the physics of timetravel, which we don't know yet".

[chess]

But from the point of view of someone who doesn't believe in God, then the prediction made about them definitely might in principle be wrong.

Um. What I was mostly trying to say was, 'I think people who have religious leanings like mine are more likely to go one-box immediately without hesitation or overthinking, because they already made a decision to trust something which they believe is almost certainly right in order to acquire a prize they haven't seen yet and which many people tell them there is uncertainty about, over obtaining a prize which is more certain or attempting to obtain both at once'.

[simont]

Oh, well, sure; if I don't believe in God (in fact, never mind "if") then of course the situation is very much changed. Not only do I think the prediction might in principle be wrong, I don't even believe it was made at all, and neither do I think the big-reward afterlife exists in the first place. If we're doing this in the real world, I two-box on the question of God because nobody has even shown me the £1m and I have every reason to think it's completely fictional, and hence from my POV it's almost completely inaccurate as an analogy for Newcomb.

But it's interesting that your belief in God makes you immediately willing to one-box on the general Newcomb problem. You might trust God to make the right prediction, but surely that doesn't mean you would trust any other apparently accurate predictor as if it were God?

[cartesiandaemon.livejournal.com]

Is this actually intended to be an analogy to religious belief of the 'pie in the sky when you die' variety? Because it works very well as such.

I'd not seen that comparison -- certainly I wasn't think of it. That's a very interesting thought.

OK, suppose we have an analogy where alien=God, 1000=sinful-fleshy-pleasures (maybe) and 1000000=eternal-paradise. Box A is life, box B is death. God says "if you reject me and take selfish pleasures, death will contain nothing for you, but if you embrace me and reject them, death will contain salvation".

Indianna Jones is on the edge of the precipice. He thinks God will hold him up. Will he leap? Or is he too scared to trust, or too tempted by the things he's leaving behind?

Similarity: In both cases, some of the doubt comes from "what if it's NOT true," because it just seems so implausible, even if you're convinced that it is.

Difference: In the God case, it doesn't matter if it were set up in advance or not -- it would make as much sense if you choose how to live, and THEN afterwards that directly determines where you. In both cases, you doubt because "do I trust", but with God, you don't specifically need to trust His prediction, but you need to trust His word, whereas with the alien, you can fairly easily trust his word, but you may doubt his ability to predict the future.

Arguable: I was going to say the other difference is that in the case of the alien, I've seen actual evidence, the only doubt comes because I just don't want to believe, whereas I don't think I have seen any evidence that God DOES say that. But presumably you might say that I _have_ seen evidence, I only doubt because I don't want to believe.

[naath.livejournal.com]

I don't see why this is a *paradox*. Either I believe the alien or I don't - if I've seen enough evidence to think that it's a reasonable chance that the prediction is true I take only box B, if I haven't then I take both. Naturally the alien knows this and knows how much evidence I have seen (how many previous trials I have the data for) and can perform statistical analysis at least as well as I can (you want P(experimenter is correct) and you work that out from the experimental data you have observed, there is a Bayesian method but if you were lazy you could just throw it into whichever frequentist test looks most useful) and that how they know what I'll do :-)

[cartesiandaemon.livejournal.com]

if I've seen enough evidence to think that it's a reasonable chance that the prediction is true I take only box B

I think this is the step people may disagree with. That's one reasonable answer, but equally reasonable seems to be "it's too late, the alien has ALREADY filled the boxes, so choosing to take box B NOW can't have any affect -- whether I were going to be sensible or not, I might as well take everything I can."

[simont]

I do like arguments 33/44; I hadn't seen those before.

My previous favourite answer was out of Hofstadter's article on the subject, which was that one-boxing gives you a choice between two desirable outcomes – either you get the big cheque, or you get to catch the predictor out in a mistake and show that it was fallible after all. Several people in the comments here have reinvented that one, which is encouraging (Hofstadter asked the question of lots of his friends and was surprised nobody used that reasoning); the bet-half-a-million idea is a particularly nice tweak on the same thing.

But to some extent all of those answers are sort-of-cheating, in that they're dodging the question. The answers that say "proving the predictor wrong is also desirable" or "I start by making side bets" are essentially adjusting the outcome grid into something they can work with more easily, and hence avoiding the real question of "yes, but what would you do if the outcome grid weren't adjusted?". Same goes for answers like "depends how rich I was already" (if I considered £1000 a negligible sum then I might be more inclined to grandstand on the chance of the big cheque by one-boxing, whereas if I was at serious risk of starvation or eviction and £1000 was enough to save me then that might well bias me in favour of minimising my risk by two-boxing). I think that to answer in the spirit of the problem, one has to assume that what's in the boxes is not a thousand and a potential million pounds, but a thousand and a potential million units of pure linearly-valued utility.

As far as my actual personal answer goes, I incline towards "problem is stupid". I'm generally not a fan of using unrealistic hypothetical situations as a means of self-discovery, because (a) they tend to have the problem that your armchair speculation about what you'd do doesn't match what you'd actually do when the emotional stress was real rather than imagined, and (b) they also tend not to tell you what you really wanted to know, in that what they really tell you is which of your decision-making rules of thumb broke down first in the face of being stretched beyond its warranty limit, rather than which one is in some meaningful sense more fundamental to your nature.

So my position for the moment is that my brain's decision-making methodology is currently not equipped to cope with situations involving an almost-perfect Newcomb-predicting entity, and since there is neither such a thing nor a realistic prospect of such a thing I have not yet had reason to consider this an important flaw in that methodology. If one comes along, I may reconsider – but, as you suggest in your post, the right response will probably depend a lot on what I know about how the predictor works.

(In the even more unlikely situation that such a predictor existed but all I knew about it was that it had a track record established by unimpeachable empirical research, I suppose I'd have to consider all the possible mechanisms by which it might work and think about which was most likely to be the real answer. Which is one of those "pull a prior out of your arse" situations, and no matter how much you dress it up with Bayesian-sounding language the reality is that one just has to take a flying guess and be prepared to accept it as the fortunes of war if one guesses wrong.)

[cartesiandaemon.livejournal.com]

I do like arguments 33/44; I hadn't seen those before.

Thank you! It jumped right out at me -- I think I said something like "my God, my brain has been eaten by Egan, I can no-one look at anything without hypothesising infinite copies of myself existing in quantum noise..."

It jumped out when I saw the wikipedia suggestion of the short–term–memory-impairing drug. I was enchanted to see the experiment might be possible. And that in the stm-i drug example, there was a clear, unambiguous answer.

From there I went straight to the "is a simulation me" question of #44.

However, #55 shows that either (a) the experiment is meaningless when the method doesn't work or (b) the "which one am i" argument of #33 fails because it ought to apply equally well in case #55, but doesn't.

But to some extent all of those answers are sort-of-cheating, in that they're dodging the question.

Yes, exactly. Overcoming bias has a theme on that, saying "Is that REALLY the reason you chose that answer, or are you rationalising? If the problem were changed to maximally disadvantage that answer, would it still ring true?" That is, invite people to suppose that £1000 and £1000000 were things they really couldn't do without.

not to tell you what you really wanted to know, in that what they really tell you is which of your decision-making rules of thumb broke down first in the face of being stretched beyond its warranty limit, rather than which one is in some meaningful sense more fundamental to your nature.

Yeah. Particularly with moral questions: you often discover that between two unacceptable choices, neither is acceptable, which isn't really news once you've accepted your moral rules are rules-of-thumb.

But it does seem worth poking your guidelines and seeing what holds up where -- it still seems to me like there OUGHT to be an answer to Newcomb, and it throws up light on all sorts of "OK, suppose I'm equally likely to be any human who has X..." questions, which come up elsewhere too.

[douglas-reay.livejournal.com]

If all I had to go on was maths, I'd be the sort of person who would initially want to choose A and B, and after would want to choose only B, and therefore would be elliminated and not chosen as a volunteer.

However, having suspected something of the sort when the boxes were explained (because there has to be a purpose to the experiment, which is additional info), but before the alien explained how it decided whether to fill box B, I might well be the sort of person who would choose box B only.

How do I know which sort of person I am? The only way for me to tell is to actually go ahead and make the choice. Though I'm willing to conceed the possibility that a good enough personality questionnaire might make a better prediction about my than I could myself before actually doing it, and so am unlikely to bet against that possibility just to gain 0.1% more.

[http://users.livejournal.com/vitriol_/]

You know it's an interesting problem when you find yourself thinking about it in bed once you've turned in; thanks for posting it.

Anyway, while doing so I came to conclusion that this and the prisoner's dilemma can be considered restatements of the same underlying problem. In the cold light of day and wakefulness I'm no longer quite so certain about that as I was last night, but I think it still mostly holds up.

In both cases there are four outcomes, both based on choices made by you and by another party. Moreover, at the point of the your decision, the other party's choice will not affected by your action (either because it's already been made, in the case of the Newcomb's Paradox, or because they aren't aware of your choice until the end of the experiment, in the prisoner's dilemma). And at that point, the rational short-term decision that maximises your gain is always obvious (taking both boxes always nets more money in the Newcomb's Paradox case, since the position of the money is already set, ratting out your partner always nets you a lower sentence in the prisoner's dilemma).

And, of course, the interesting part of the question comes in once you consider some extra condition - the ability of the tester to predict your decision in the Newcomb's Paradox, the possibility of repeated tests in the prisoner's dilemma. And I think *these* can be cast as the same thing, since in the prisoner's dilemma the idea is that your partner's actions will be predicated on your past/probable behaviour.

For example, consider a case of the prisoner's dilemma where both parties can perfectly predict what their partner's decision will be. This is actually relatively straightforward to implement in real life - allow both parties to see what their opposing number has chosen, allow each to change their minds as many times as they like, and don't settle on any choice until both sides have agreed they are happy with the choice. In that case, it seems self-evident that both sides will settle on neither ratting out the other (since it's not in the interest of either to settle on a decision while their partner is ratting on them), even if this is the first test they've undertaken and there's no repitition. So, just like with Newcomb's Paradox, once perfect prediction enters the equation the rational choice becomes to take the option that seems irrational at the point of use (not ratting out your partner, not taking box A) because the extra information available to the other party means that they knew this would be your choice and hence the prizes/penalties available have been adjusted to make it more favorable to you.

Oof, OK, really hope all of that makes sense now...

[cartesiandaemon.livejournal.com]

Anyway, while doing so I came to conclusion that this and the prisoner's dilemma can be considered restatements of the same underlying problem.

Apparently that IS true, according to overcoming bias, but I've not analysed it yet: I'm worried I'll get different answers maybe :)

[angoel.livejournal.com]

"What if the volunteer would change their mind when they discovered the reasoning, or is going to choose based on a coin toss?" "Then I didn't accept them as a volunteer."

So the volunteer should decide on a coin-toss, just to prove that the alien is indeed faliable.

[cartesiandaemon.livejournal.com]

:)

Good point. I didn't necessarily think through all of the caveats; I'm fairly sure they're non-fundamental. Come to think of it, if you admitted that answer, you've admitted the "predict you will press the button" paradox of telling you what you're going to do before you do it, thus (potentially) affecting the outcome, or at least, putting you in a position where there could be a paradox.

One alternative would be that his method of "not accepting you" is to leave a note in both boxes saying "ha, i predicted you'd choose randomly (even though I can't predict a coin toss)", although that would be hard to prove.

[woodpijn.livejournal.com]

Fascinating.

I'd take box B, and I do sort of justify that with reverse causality. The people who reason "The boxes have already been filled; I may as well just take everything that's on the table" are effectively making box B be empty and doing themselves out of £1m, assuming the alien can correctly predict they'll reason like that (and I think questioning too strongly the alien's predictive abilities on grounds of practical realism is sidestepping the point of the thought experiment).

And by reasoning the way I do, I effectively make the alien put £1m in box B.

What I can't do is reason my way, make the alien put £1m in box B, and then quickly-before-the-change-has-time-to-percolate-back-to-when-the-boxes-were-filled change my mind and grab both boxes and get £1001k. If the alien foresees the first bit of reasoning, he also foresees the second bit; if reverse causality applies at all (even if as a mental model for understanding the experiment and not in reality) then it applies to all your decisions.

chess brought God into it; I might do so in a slightly different way. I don't have a problem with the idea that God might take into account the prayer I pray tomorrow as one of the many many factors he considers when making today's weather. (Although obviously because God has his own will I can't make him do anything, in the way that I can make Newcomb's alien do things because he has committed to fill the boxes according to the decision he foresees me taking.)

[simont]

Having said in my other comment that it's cheating to answer based on the nonlinear utility of money, I'm actually now thinking that it's not entirely unilluminating to examine what I think I would do if the amounts of money were changed.

Let A be the amount of money in box A (that is, the amount that's reliably there but you can decide whether or not to take), and B be the amount in box B (that may or may not be there but if it is you will get it no matter what you choose).

For a start, let's fix B at its original £1m, and vary A.

Suppose A=0. It seems fairly clear to me that one-boxing is the sensible answer, just on the grounds that you don't know for absolute certain that reverse causality doesn't exist (even if it exists with a very low probability, or even a perhaps-not-actually-impossible event of probability zero!) and there's no better reason to choose between the two options anyway. If anyone can justify two-boxing when A=0 I'd be interested to hear the argument :-)

Now suppose A=1p. I think I would have to say that I still one-box (even though I'm undecided in the original case), because really the 1p would matter to me so little that it might as well be zero.

At the other extreme, suppose A and B are both £1m. I can't see any reason to one-box this time: if you one-box, you get either £1m or nothing, and if you two-box you get either £1m or £2m. No matter what you think the probabilities are in each case, the expected gain for two-boxing is equal or greater. No-brainer.

Now suppose A = £999999.99. Two-box again for me, no question. The 1p difference is unimportant to me, as before.

All of which tells me that somewhere in between these extremes is the critical value of A which would cause me to be perfectly undecided between one- and two-boxing – which puts the whole question on a quantitative footing, and suggests that one can be more subtle than dividing sentiences into "one-boxer" and "two-boxer".

Allowing B to vary as well as A is the point where one really gets into the nonlinear utility of money: I currently feel as if I'd be much more likely to two-box with A=£1bn and B=£1tn than I would with A=£1000 and B=£1m. Even a billion is more money than I can imagine being able to spend, so who cares if it isn't the trillion it might have been? (Though, of course, after I two-boxed and "only" got my billion, a few years later when I'd become accustomed to the resulting lifestyle I'd be kicking myself for not having held out for the extra £999bn :-) And conversely, if you head in the other direction, I'm pretty sure I'd one-box with A=£10 and B=£10000, because £10 is pretty negligible but £10000 would definitely come in handy.

[cartesiandaemon.livejournal.com]

Allowing B to vary as well as A is the point where one really gets into the nonlinear utility of money:

Mum pointed out that there's too different reasons to "defect" and choose A: temptation of getting £1001000, and fear of getting nothing. Which can be fiddled with the amount of money -- is either or both what would cause two-boxing?

which puts the whole question on a quantitative footing,

That's a very good description. Trade-offs are not always linear, but playing the "compare A against B" game can give some insight into how much you DO value something, according to how much you'd risk.

[ptc24.livejournal.com]

This sounds like a good task for the underhanded C-code contest - produce a Newcomb-playing bot (the predicted, not the predictor), that will *obviously* one-box, but which exploits buffer overruns etc. in order to two-box.

[cartesiandaemon.livejournal.com]

Ooh! Yes, exactly.

I keep checking back to see if there's the results of their latest contest, but it seems not.