Torture vs. Dust Specks

Does this analysis focus on pure, monotone utility, or does it include the huge ripple effect putting dust specks into so many people's eyes would have? Are these people with normal lives, or created specifically for this one experience?

The answer that's obvious to me is that my mental moral machinery -- both the bit that says "specks of dust in the eye can't outweigh torture, no matter how many there are" and the bit that says "however small the badness of a thing, enough repetition of it can make it arbitrarily awful" or "maximize expected sum of utilities" -- wasn't designed for questions with numbers like 3^^^3 in. In view of which, I profoundly mistrust any answer I might happen to find "obvious" to the question itself.

Since there was a post about what seems obvious to the speaker might not be to the listener in this blog a few days ago, I thought I would point out that : It was NOT AT ALL obvious to me what should be preferred, torture 1 man for 50 years or speck of dust in 3^^^3 people. Can you please plase clarify/update what the point of the post was?

The dust speck is described as "barely enough to make you notice", so however many people it would happen to, it seems better than even something a lot less worse than 50 years of horrible torture. There are so many irritating things that a human barely notices in his/her life, what's an extra dust speck?

I think I'd trade the dust specks for even a kick in the groin.

But hey, maybe I'm missing something here...

Anon, I deliberately didn't say what I thought, because I guessed that other people would think a different answer was "obvious". I didn't want to prejudice the responses.

Even when applying the cold cruel calculus of moral utilitarianism, I think that most people acknowledge that egalitarianism in a society has value in itself, and assign it positive utility. Would you rather be born into a country where 9/10 people are destitute (<$1000/yr), and the last is very wealthy (100,000/yr)? Or, be born into a country where almost all people subsist on a modest (6-8000/yr) amount?

Any system that allocates benefits (say, wealth) more fairly might be preferable to one that allocates more wealth in a more unequal fashion. And, the same goes for negative benefits. The dust specks may result in more total misery, but there is utility in distributing that misery equally.

The dust specks seem like the "obvious" answer to me, but how large the tiny harm must be to cross the line where the unthinkably huge number of them outweighs a single tremendous one isn't something I could easily say, when clearly I don't think simply calculating the total amount of harm caused is the right measure.

It seems obvious to me to choose the dust specks because that would mean that the human species would have to exist for an awfully long time for the total number of people to equal that number and that minimum amount of annoyance would be something they were used to anyway.

I too see the dust specks as obvious, but for the simpler reason that I reject utilitarian sorts of comparisons like that. Torture is wicked, period. If one must go further, it seems like the suffering from torture is qualitatively worse than the suffering from any number of dust specks.

Anon prime: dollars are not utility. Economic egalitarianism is instrumentally desirable. We don't normally favor all types of equality, as Robin frequently points out.

Kyle: cute

Eliezer: My impulse is to choose the torture, even when I imagine very bad kinds of torture and very small annoyances (I think that one can go smaller than a dust mote, possibly something like a letter on the spine of a book that your eye sweeps over being in a shade less well selected a font). Then, however, I think of how much longer the torture could last and still not outweigh the trivial annoyances if I am to take the utilitarian perspective and my mind breaks. Condoning 50 years of torture, or even a day worth, is pretty much the same as condoning universes of agonium lasting for eons in the face of numbers like these, and I don't think that I can condone that for any amount of a trivial benefit.

Personally, I choose C: torture 3^^^3 people for 3^^^3 years. Why? Because I can.

Ahem. My morality is based on maximizing average welfare, while also avoiding extreme individual suffering, rather than cumulative welfare.

So torturing one man for fifty years is not preferable to annoying any number of people.

This is different when the many are also suffering extremely, though - then it may be worthwhile to torture one even more to save the rest.

Trivial annoyances and torture cannot be compared in this quantifiable manner. Torture is not only suffering, but lost opportunity due to imprisonment, permanent mental hardship, activation of pain and suffering processes in the mind, and a myriad of other unconsidered things.

And even if the torture was 'to have flecks of dust dropped in your eyes', you still can't compare a 'torturous amount' applied to one person, to substantial number dropped in the eyes of many people: We aren't talking about cpu cycles here - we are trying to quantify qualifiables.

If you revised the question, and specified stated exactly how the torture would affect the individual, and how they would react to it, and the same for each of the 'dust in the eyes' people (what if one goes blind? what of their mental capacity to deal with the hardship? what of the actual level of moisture in their eyes, and consequently the discomfort being felt?) then, maybe then, we could determine which was the worse outcome, and by how much.

There are simply too many assumptions that we have to make in this, mortal, world to determine the answer to such questions: you might as well as how many angels dance on the head of a pin. Or you could start more simply and ask: if you were to torture two people in exactly the same way, which one would suffer more, and by how much?

And you notice, I haven't even started to think about the ethical side of the question...

I think this all revolves around one question: Is "disutility of dust speck for N people" = N*"disutility of dust speck for one person"?

This, of course, depends on the properties of one's utility function.

How about this... Consider one person getting, say, ten dust specks per second for an hour vs 106060 = 36,000 people getting a single dust speck each.

This is probably a better way to probe the issue at its core. Which of those situations is preferable? I would probably consider the second. However, I suspect one person getting a billion dust specks in their eye per second for an hour would be preferable to 1000 people getting a million per second for an hour.

Suffering isn't linear in dust specks. Well, actually, I'm not sure subjective states in general can be viewed in a linear way. At least, if there is a potentially valid "linear qualia theory", I'd be surprised.

But as far as the dust specks vs torture thing in the original question? I think I'd go with dust specks for all.

But that's one person vs buncha people with dustspecks.

Oh, just had a thought. A less extreme yet quite related real world situation/question would be this: What is appropriate punishment for spammers?

Yes, I understand there're a few additional issues here, that would make it more analogous to, say, if the potential torturee was planning on deliberately causing all those people a DSE (Dust Speck Event)

But still, the spammer issue gives us a more concrete version, involving quantities that don't make our brains explode, so considering that may help work out the principles by which these sorts of questions can be dealt with.

The problem with spammers isn't the cause of a singular dust spec event: it's the cause of multiple dust speck events repeatedly to individuals in the population in question. It's also a 'tragedy of the commons' question, since there is more than one spammer.

To respond to your question: What is appropriate punishment for spammers? I am sad to conclude that until Aubrey DeGray manages to conquer human mortality, or the singularity occurs, there is no suitable punishment for spammers.

After either of those, however, I would propose unblocking everyone's toilets and/or triple shifts as a Fry's Electronics floor lackey until the universal heat death, unless you have even >less< interesting suggestions.

If you could take all the pain and discomfort you will ever feel in your life, and compress it into a 12-hour interval, so you really feel ALL of it right then, and then after the 12 hours are up you have no ill effects - would you do it? I certainly would. In fact, I would probably make the trade even if it were 2 or 3 times longer-lasting and of the same intensity. But something doesn't make sense now... am I saying I would gladly double or triple the pain I feel over my whole life?

The upshot is that there are some very nonlinear phenomena involved with calculating amounts of suffering, as Psy-Kosh and others have pointed out. You may indeed move along one coordinate in "suffering-space" by 3^^^3 units, but it isn't just absolute magnitude that's relevant. That is, you cannot recapitulate the "effect" of fifty years of torturing with isolated dust specks. As the responses here make clear, we do not simply map magnitudes in suffering space to moral relevance, but instead we consider the actual locations and contours. (Compare: you decide to go for a 10-mile hike. But your enjoyment of the hike depends more on where you go, than the distance traveled.)

Yes the answer is obvious. The answer is that this question obviously does not yet have meaning. It's like an ink blot. Any meaning a person might think it has is completely inside his own mind. Is the inkblot a bunny? Is the inkblot a Grateful Dead concert? The right answer is not merely unknown, because there is no possible right answer.

A serious person-- one who take moral dilemmas seriously, anyway-- must learn more before proceeding.

The question is an inkblot because too many crucial variables have been left unspecified. For instance, in order for this to be an interesting moral dilemma I need to know that it is a situation that is physically possible, or else analogous to something that is possible. Otherwise, I can't know what other laws of physics or logic apply or don't apply, and therefore can't make an assessment. I need to know what my position is in this universe. I need to know why this power has been invested in me. I need to know the nature of the torture and who the person is who will be tortured. I need to consider such factors as what the torture may mean to other people who are aware of it (such as the people doing the torture). I need to know something about the costs and benefits involved. Will the person being tortured know they are being tortured? Or can it be arranged that they are born into the torture and consider it a normal part of their life. Will the person being tortured have volunteered to have been tortured? Will the dust motes have peppered the eyes of all those people anyway? Will the torture have happened anyway? Will choosing torture save other people from being tortured?

It would seem that torture is bad. On the other hand, just being alive is a form of torture. Each of us has a Sword of Damocles hanging over us. It's called mortality. Some people consider it torture when I keep telling them they haven't finished asking their question...

The non-linear nature of 'qualia' and the difficulty of assigning a utility function to such things as 'minor annoyance' has been noted before. It seems to some insolvable. One solution presented by Dennett in 'Consciousness Explained' is to suggest that there is no such thing as qualia or subjective experience. There are only objective facts. As Searle calls it 'consciousness denied'. With this approach it would (at least theoretically) be possible to objectively determine the answer to this question based on something like the number of ergs needed to fire the neurons that would represent the outcomes of the two different choices. The idea of which would be the more/less pleasant experience is therefore not relevant as there is no subjective experience to be had in the first place. Of course I'm being sloppy here- the word choice would have to be re-defined to include that each action is determined by the physical configuration of the brain and that the chooser is in fact a fictional construct of that physical configuration. Otherwise, I admit that 3^^^3 people is not something I can easily contemplate, and that clouds my ability to think of an answer to this question.

Uh... If there's no such thing as qualia, there's no such thing as actual suffering, unless I misunderstand your description of Dennett's views.

But if my understanding is correct, and those views were correct, then wouldn't the answer be "nobody actually exists to care one way or another?" (Or am I sorely mistaken in interpreting that view?)

Regarding your example of income disparity: I might rather be born into a system with very unequal incomes, if, as in America (in my personal and biased opinion), there is a reasonable chance of upping my income through persistence and pluck. I mean hey, that guy with all that money has to spend it somewhere-- perhaps he'll shop at my superstore!

But wait, what does wealth mean? In the case where everyone has the same income, where are they spending their money? Are they all buying the same things? Is this a totalitarian state? An economy without disparity is pretty disturbing to contemplate, because it means no one is making an effort to do better than other people, or else no one can do better. Money is not being concentrated or funnelled anywhere. Sounds like a pretty moribund economy.

If it's a situation where everyone always gets what they want and need, then wealth will have lost its conventional meaning, and no one will care whether one person is rich and another one isn't. What they will care about is the success of their God, their sports teams, and their children.

I guess what I'm saying is that there may be no interesting way to simplify interesting moral dilemmas without destroying the dilemma or rendering it irrelevant to natural dilemmas.

If even one in a hundred billion of the people is driving and has an accident because of the dust speck and gets killed, that's a tremendous number of deaths. If one in a hundred quadrillion of them survives the accident but is mangled and spends the next 50 years in pain, that's also a tremendous amount of torture.

If one in a hundred decillion of them is working in a nuclear power plant and the dust speck makes him have a nuclear accident....

We just aren't designed to think in terms of 3^^^3. It's too big. We don't habitually think much about one-in-a-million chances, much less one in a hundred decillion. But a hundred decillion is a very small number compared to 3^^^3.

Douglas and Psy-Kosh: Dennett explicitly says that in denying that there are such things as qualia he is not denying the existence of conscious experience. Of course, Douglas may think that Dennett is lying or doesn't understand his own position as well as Douglas does.

James Bach and J Thomas: I think Eliezer is asking us to assume that there are no knock-on effects in either the torture or the dust-speck scenario, and the usual assumption in these "which economy would you rather have?" questions is that the numbers provided represent the situation after all parties concerned have exerted whatever effort they can. (So, e.g., if almost everyone is described as destitute, then it must be a society in which escaping destitution by hard work is very difficult.) Of course I agree with both of you that there's danger in this sort of simplification.

J Thomas: You're neglecting that there might be some positive-side effects for a small fraction of the people affected by the dust specks; in fact, there is some precedent for this. The resulting average effect is hard to estimate, but (considering that dust specks seem to mostly add entropy to the thought processes of the affected persons), would likely still be negative.

Copying g's assumption that higher-order effects should be neglected, I'd take the torture. For each of the 3^^^3 persons, the choice looks as follows:

1.) A 1/(3^^^3) chance of being tortured for 50 years. 2.) A 1 chance of getting a dust speck.

I'd definitely prefer the former. That probability is so close to zero that it vastly outweighs the differences in disutility.

Hmm, tricky one.

Do I get to pick the person who has to be tortured?

As I read this I knew my answer would be the dust specks. Since then I have been mentally evaluating various methods for deciding on the ethics of the situation and have chosen the one that makes me feel better about the answer I instinctively chose.

I can tell you this though. I reckon I personally would choose max five minutes of torture to stop the dust specks event happening. So if the person threatened with 50yrs of torture was me, I'd choose the dust specks.

What if it were a repeatable choice?

Suppose you choose dust specks, say, 1,000,000,000 times. That's a considerable amount of torture inflicted on 3^^^3 people. I suspect that you could find the number of times equivalent to torturing each of thoes 3^^^3 people 50 years, and that number would be smaller than 3^^^3. In other words, choose the dust speck enough times, and more people would be tortured effectually for longer than if you chose the 50-year torture an equivalent number of times.

If that math is correct, I'd have to go with the torture, not the dust specks.

Kyle wins.

Absent using this to guarantee the nigh-endless survival of the species, my math suggests that 3^^^3 beats anything. The problem is that the speck rounds down to 0 for me.

There is some minimum threshold below which it just does not count, like saying, "What if we exposed 3^^^3 people to radiation equivalent to standing in front of a microwave for 10 seconds? Would that be worse than nuking a few cities?" I suppose there must be someone in 3^^^3 who is marginally close enough to cancer for that to matter, but no, that rounds down to 0. For the speck, I am going to blink in the next few seconds anyway.

That in no way addresses the intent of the question, since we can just increase it to the minimum that does not round down. Being poked with a blunt stick? Still hard, since I think every human being would take one stick over some poor soul being tortured. Do I really get to be the moral agent for 3^^^3 people?

As others have said, our moral intuitions do not work with 3^^^3.

Wow. The obvious answer is TORTURE, all else equal, and I'm pretty sure this is obvious to Eliezer too. But even though there are 26 comments here, and many of them probably know in their hearts torture is the right choice, no one but me has said so yet. What does that say about our abilities in moral reasoning?

Given that human brains are known not to be able to intuitively process even moderately large numbers, I'd say the question can't meaningfully be asked - our ethical modules simply can't process it. 3^^^3 is too large - WAY too large.

I'm unconvinced that the number is too large for us to think clearly. Though it takes some machinery, humans reason about infinite quantities all the time and arrive at meaningful conclusions.

My intuitions strongly favor the dust speck scenario. Even if forget 3^^^^3 and just say that an infinite number of people will experience the speck, I'd still favor it over the torture.

Robin is absolutely wrong, because different instances of human suffering cannot be added together in any meaningful way. The cumulative effect when placed on one person is far greater than the sum of many tiny nuisances experienced by many. Whereas small irritants such as a dust mote do not cause "suffering" in any standard sense of the word, the sum total of those motes concentrated at one time and placed into one person's eye could cause serious injury or even blindness. Dispersing the dust (either over time or across many people) mitigates the effect. If the dispersion is sufficient, there is actually no suffering at all. To extend the example, you could divide the dust mote into even smaller particles, until each individual would not even be aware of the impact.

So the question becomes, would you rather live in a world with little or no suffering (caused by this particular event) or a world where one person suffers badly, and those around him or her sit idly by, even though they reap very little or no benefit from the situation?

The notion of shifting human suffering onto one unlucky individual so that the rest of society can avoid minor inconveniences is morally reprehensible. That (I hope) is why no one has stood up and shouted yeay for torture.

The obvious answer is TORTURE, all else equal, and I'm pretty sure this is obvious to Eliezer too.

That is the straightforward utilitarian answer, without any question. However, it is not the common intuition, and even if Eliezer agrees with you he is evidently aware that the common intuition disagrees, because otherwise he would not bother blogging it. It's the contradiction between intuition and philosophical conclusion that makes it an interesting topic.

Robin's answer hinges on "all else being equal." That condition can tie up a lot of loose ends, it smooths over plenty of rough patches. But those ends unravel pretty quickly once you start to consider all the ways in which everything else is inherently unequal. I happen to think the dust speck is a 0 on the disutility meter, myself, and 3^^^3*0 disutilities = 0 disutility.

I believe that ideally speaking the best choice is the torture, but pragmatically, I think the dust speck answer can make more sense. Of course it is more intuitive morally, but I would go as far as saying that the utility can be higher for the dust specks situation (and thus our intuition is right). How? the problem is in this sentence: "If neither event is going to happen to you personally," the truth is that in the real world, we can't rely on this statement. Even if it is promised to us or made into a law, this type of statements often won't hold up very long. Precedents have to be taken into account when we make a decision based on utility. If we let someone be tortured now, we are building a precedent, a tradition of letting people being tortured. This has a very low utility for people living in the affected society. This is well summarized in the saying "What goes around comes around".

If you take the strict idealistic situation described, the torture is the best choice. But if you instead deem the situation to be completely unrealistic and you pick a similar one by simply not giving a 100% reliability on the sentence: "If neither event is going to happen to you personally," the best choice can become the dust specks, depending on how much you believe the risk of a tradition of torture will be established. (and IMO traditions of torture and violence is the kind of thing that spreads easily as it stimulates resentment and hatred in the groups that are more affected.) The torture situation has much risk of getting worst but not the dust speck situation.

The scenario might have been different if torture was replaced by a kind of suffering that is not induced by humans. Say... an incredibly painful and long (but not contagious) illness.

Is it better to have the dust specks everywhere all the time or to have the existence of this illness once in history?

Torture. See Norcross: http://www.ruf.rice.edu/~norcross/ComparingHarms.pdf

Robin, could you explain your reasoning. I'm curious.

Humans get barely noticeable "dust speck equivalent" events so often in their lives that the number of people in Eliezer's post is irrelevant; it's simply not going to change their lives, even if it's a gazillion lives, even with a number bigger than Eliezer's (even considering the "butterfly effect", you can't say if the dust speck is going to change them for the better or worse -- but with 50 years of torture, you know it's going to be for the worse).

Subjectively for these people, it's going to be lost in the static and probably won't even be remembered a few seconds after the event. Torture won't be lost in static, and it won't be forgotten (if survived).

The alternative to torture is so mild and inconsequential, even if applied to a mind-boggling number of people, that it's almost like asking: Would you rather torture that guy or not?

@Robin,

"But even though there are 26 comments here, and many of them probably know in their hearts torture is the right choice, no one but me has said so yet."

I thought that Sebastian Hagen and I had said it. Or do you think we gave weasel answers? Mine was only contingent on my math being correct, and I thought his was similarly clear.

Perhaps I was unclear in a different way. By asking if the choice was repeatable, I didn't mean to dodge the question; I meant to make it more vivid. Moral questions are asked in a situation where many people are making moral choices all the time. If dust-speck displeasure is additive, then we should evaluate our choices based on their potential aggregate effects.

Essentially, it's a same-ratio problem, like showing that 6:4::9:6, because 6x3=9x2 and 4x3=6x2. If the aggregate of dust-specking can ever be greater than the equivalent aggregate of torturing, then it is always greater.

Hmm, thinking some more about this, I can see another angle (not the suffering angle, but the "being prudent about unintended consequences" angle):

If you had the choice between very very slightly changing the life of a huge number of people or changing a lot the life of only one person, the prudent choice might be to change the life of only one person (as horrible as that change might be).

Still, with the dust speck we can't really know if the net final outcome will be negative or positive. It might distract people who are about to have genius ideas, but it might also change chains of events that would lead to bad things. Averaged over so many people, it's probably going to stay very close to neutral, positive or negative. The torture of one person might also look very close to neutral if averaged with the other 3^^^3 people, but we know that it's going to be negative. Hmm..

Would you prefer that one person be horribly tortured for fifty years without hope or rest, or that 3^^^3 people get dust specks in their eyes?

The square of the number of milliseconds in 50 years is about 10^21.

Would you rather one person tortured for a millisecond (then no ill effects), or that 3^^^3/10^21 people get a dust speck per second for 50 centuries?

OK, so the utility/effect doesn't scale when you change the times. But even if each 1% added dust/torture time made things ten times worse, when you reduce the dust-speckled population to reflect that it's still countless universes worth of people.

I'm with Tomhs. The question has less value as a moral dilemma than as an opportunity to recognize how we think when we "know" the answer. I intentionally did not read the comments last night so I could examine my own thought process, and tried very hard to hold an open mind (my instinct was dust). It's been a useful and interesting experience. Much better than the brain teasers which I can generally get because I'm on hightened alert when reading El's posts. Here being on alert simply allowed me to try to avoid immediately giving in to my bias.

Averaging utility works only when law of large numbers starts to play a role. It's a good general policy, as stuff subject to it happens all the time, enough to give sensible results over the human/civilization lifespan. So, if Eliezer's experiment is a singular event and similar events don't happen frequently enough, answer is 3^^^3 specks. Otherwise, torture (as in this case, similar frequent enough choices would lead to a tempest of specks in anyone's eye which is about 3^^^3 times worse then 50 years of torture, for each and every one of them).

Benquo, your first answer seems equivocal, and so did Sebastian's on a first reading, but now I see that it was not.

Torture,

Consider three possibilities:

(a) A dusk speck hits you with probability one, (b) You face an additional probability 1/( 3^^^3) of being tortured for 50 years, (c) You must blink your eyes for a fraction of a second, just long enough to prevent a dusk speck from hitting you in the eye.

Most people would pick (c) over (a). Yet, 1/( 3^^^3) is such a small number that by blinking your eyes one more time than you normally would you increase your chances of being captured by a sadist and tortured for 50 years by more than 1/( 3^^^3). Thus, (b) must be better than (c). Consequently, most people should prefer (b) to (a).

There isn't any right answer. Answers to what is good or bad is a matter of taste, to borrow from Nietzsche.

To me the example has messianic quality. One person suffers immensely to save others from suffering. Does the sense that there is a 'right' answer come from a Judeo-Christian sense of what is appropriate. Is this a sort of bias in line with biases towards expecting facts to conform to a story?

Also, this example suggests to me that the value pluralism of Cowen makes much more sense than some reductive approach that seeks to create one objective measure of good and bad. One person might seek to reduce instances of illness, another to maximize reported happiness, another to maximize a personal sense of beauty. IMO, there isn't a judge who will decide who is right and who is wrong, and the decisive factor is who can marhsal the power to bring about his will, as unsavory as that might be (unless your side is winning).

Why is this a serious question? Given the physical unreality of the situation, the putative existence of 3^^^3 humans and the ability to actually create the option in the physical universe - why is this question taken seriously while something like is it better to kill Santa Claus or the Easter Bunny considered silly?

Fascinating, and scary, the extent to which we adhere to established models of moral reasoning despite the obvious inconsistencies. Someone here pointed out that the problem wasn't sufficiently defined, but then proceeded to offer examples of objective factors that would appear necessary to evaluation of a consequentialist solution. Robin seized upon the "obvious" answer that any significant amount of discomfort, over such a vast population, would easily dominate, with any conceivable scaling factor, the utilitarian value of the torture of a single individual. But I think he took the problem statement too literally; the discomfort of the dust mote was intended to be vanishingly small, over a vast population, thus keeping the problem interesting rather than "obvious."

But most interesting to me is that no one pointed out that fundamentally, the assessed goodness of any act is a function of the values (effective, but not necessarily explicit) of the assessor. And assessed morality as a function of group agreement on the "goodness" of an act, promoting the increasingly coherent values of the group over increasing scope of expected consequences.

Now the values of any agent will necessarily be rooted in an evolutionary branch of reality, and this is the basis for increasing agreement as we move toward the common root, but this evolving agreement in principle on the direction of increasing morality should never be considered to point to any particular destination of goodness or morality in any objective sense, for that way lies the "repugnant conclusion" and other paradoxes of utilitarianism.

Obvious? Not at all, for while we can increasingly converge on principles promoting "what works" to promote our increasingly coherent values over increasing scope, our expression of those values will increasingly diverge.

The hardships experienced by a man tortured for 50 years cannot compare to a trivial experience massively shared by a large number of individuals -- even on the scale that Eli describes. There is no accumulation of experiences, and it cannot be conflated into a larger meta dust-in-the-eye experience; it has to be analyzed as a series of discreet experiences.

As for larger social implications, the negative consequence of so many dust specked eyes would be negligible.

Wow. People sure are coming up with interesting ways of avoiding the question.

Eliezer wrote "Wow. People sure are coming up with interesting ways of avoiding the question."

I posted earlier on what I consider the more interesting question of how to frame the problem in order to best approach a solution.

If I were to simply provide my "answer" to the problem, with the assumption that the dust in the eyes is likewise limited to 50 years, then I would argue that the dust is to be preferred to the torture, not on a utilitarian basis of relative weights of the consequences as specified, but on the bigger-picture view that my preferred future is one in which torture is abhorrent in principle (noting that this entails significant indirect consequences not specified in the problem statement.)

Eliezer, are you suggesting that declining to make up one's mind in the face of a question that (1) we have excellent reason to mistrust our judgement about and (2) we have no actual need to have an answer to is somehow disreputable?

As for your link to the "motivated stopping" article, I don't quite see why declining to decide on this is any more "stopping" than choosing a definite one of the options. Or are you suggesting that it's an instance of motivated continuation? Perhaps it is, but (as you said in that article) the problem with excessive "continuation" is that it can waste resources and miss opportunities. I don't see either of those being an issue here, unless you're actually threatening to do one of those two things -- in which case I declare you a Pascal's mugger and take no notice.

What happens if there aren't 3^^^3 instanced people to get dust specks? Do those specks carry over such that person #1 gets a 2nd speck and so on? If so, you would elect to have the person tortured for 50 years for surely the alternative is to fill our universe with dust and annihilate all cultures and life.

Robin, of course it's not obvious. It's only an obvious conclusion if the global utility function from the dust specks is an additive function of the individual utilities, and since we know that utility functions must be bounded to avoid Dutch books, we know that the global utility function cannot possibly be additive -- otherwise you could break the bound by choosing a large enough number of people (say, 3^^^3).

From a more metamathematical perspective, you can also question whether 3^^3 is a number at all. It's perfectly straightforward to construct a perfectly consistent mathematics that rejects the axiom of infinity. Besides the philosophical justification for ultrafinitism (ie, infinite sets don't really exist), these theories corresponds to various notions of bounded computation (such as logspace or polytime). This is a natural requirement, if we want to require moral judgements to be made quickly enough to be relevant to decision making -- and that rules out seriously computing with numbers like 3^^^3.

Eliezer, are you suggesting that declining to make up one's mind in the face of a question that (1) we have excellent reason to mistrust our judgement about and (2) we have no actual need to have an answer to is somehow disreputable?

Yes, I am.

Regarding (1), we pretty much always have excellent reason to mistrust our judgments, and then we have to choose anyway; inaction is also a choice. The null plan is a plan. As Russell and Norvig put it, refusing to act is like refusing to allow time to pass.

Regarding (2), whenever a tester finds a user input that crashes your program, it is always bad - it reveals a flaw in the code - even if it's not a user input that would plausibly occur; you're still supposed to fix it. "Would you kill Santa Claus or the Easter Bunny?" is an important question if and only if you have trouble deciding. I'd definitely kill the Easter Bunny, by the way, so I don't think it's an important question.

Followup dilemmas:

For those who would pick SPECKS, would you pay a single penny to avoid the dust specks?

For those who would pick TORTURE, what about Vassar's universes of agonium? Say a googolplex-persons' worth of agonium for a googolplex years.

Fascinating question. No matter how small the negative utility in the dust speck, multiplying it with a number such as 3^^^3 will make it way worse than torture. Yet I find the obvious answer to be the dust speck one, for reasons similar to what others have pointed out - the negative utility rounds down to zero.

But that doesn't really solve the problem, for what if the harm in question was slightly larger? At what point does it cease rounding down? I have no meaningful criteria to give for that one. Obviously there must be a point where it does cease doing so, for it certainly is much better to torture one person for 50 years than 3^^^3 people for 49 years.

It is quite counterintuitive, but I suppose I should choose the torture option. My other alternatives would be to reject utilitarianism (but I have no better substitutes for it) or to modify my ethical system so that it solves this problem, but I currently cannot come up with an unproblematic way of doing so.

Still, I can't quite bring myself to do so. I choose specks, and admit that my ethical system is not consistent yet. (Not that it would be a surprise - I've noticed that all my attempts at building entirely consistent ethical systems tend to cause unwanted results at one point or the other.)

For those who would pick SPECKS, would you pay a single penny to avoid the dust specks?

A single penny to avoid one dust speck, or to avoid 3^^^3 dust specks? No to the first one. To the second one, depends on how often they occured - if I somehow could live for 3^^^3 years, getting one dust speck in my eye per year, then no. If they actually inconvenienced me, then yes - a penny is just a penny.

"Regarding (1), we pretty much always have excellent reason to mistrust our judgments, and then we have to choose anyway; inaction is also a choice. The null plan is a plan. As Russell and Norvig put it, refusing to act is like refusing to allow time to pass."

This goes to the crux of the matter, why to the extent the future is uncertain, it is better to decide based on principles (representing wisdom encoded via evolutionary processes over time) rather than on the flat basis of expected consequences.

Would you condemn one person to be horribly tortured for fifty years without hope or rest, to save every qualia-experiencing being who will ever exist one blink?

Is the question significantly changed by this rephrasing? It makes SPECKS the default choice, and it changes 3^^^3 to "all." Are we better able to process "all" than 3^^^3, or can we really process "all" at all? Does it change your answer if we switch the default?

Would you force every qualia-experiencing being who will ever exist to blink one additional time to save one person from being horribly tortured for fifty years without hope or rest?

> For those who would pick TORTURE, what about Vassar's universes of agonium? Say a googolplex-persons' worth of agonium for a googolplex years.

If you mean would I condemn all conscious beings to a googolplex of torture to avoid universal annihilation from a big "dust crunch" my answer is still probably yes. The alternative is universal doom. At least the tortured masses might have some small chance of finding a solution to their problem at some point. Or at least a googolplex years might pass leaving some future civilization free to prosper. The dust is absolute doom for all potential futures.

Of course, I'm assuming that 3^^^3 conscious beings are unlikely to ever exist and so that dust would be applied over and over to the same people causing the universe to be filled with dust. Maybe this isn't how the mechanics of the problem work.

> Would you condemn one person to be horribly tortured for fifty years without hope or rest, to save every qualia-experiencing being who will ever exist one blink?

That's assuming you're interpreting the question correctly. That you aren't dealing with an evil genie.

You never said we couldn't choose who specifically gets tortured, so I'm assuming we can make that selection. Given that, the once agonizingly difficult choice is made trivially simple. I would choose 50 years of torture for the person who made me make this decision.

Since I chose the specks -- no, I probably wouldn't pay a penny; avoiding the speck is not even worth the effort to decide to pay the penny or not. I would barely notice it; it's too insignificant to be worth paying even a tiny sum to avoid.

I suppose I too am "rounding down to zero"; a more significant harm would result in a different answer.

"For those who would pick SPECKS, would you pay a single penny to avoid the dust specks?"

To avoid all the dust specks, yeah, I'd pay a penny and more. Not a penny per speck, though ;)

The reason is to avoid having to deal with the "unintended consequences" of being responsible for that very very small change over such a large number of people. It's bound to have some significant indirect consequences, both positive and negative, on the far edges of the bell curve... the net impact could be negative, and a penny is little to pay to avoid responsibility for that possibility.

The first thing I thought when I read this question was that the dust specks were obviously preferable. Then I remembered that my intuition likes to round 3^^^3 down to something around twenty. Obviously, the dust specks are preferable to the torture for any number at all that I have any sort of intuitive grasp over.

But I found an argument that pretty much convinced me that the torture was the correct answer.

Suppose that instead of making this choice once, you will be faced with the same choice 10^17 times for the next fifty years (This number was chosen so that it was more than a million per second.) If you have a problem imagining the ability to make more than a million choices per second, imagine that you have a dial in front of you which goes from zero to a 10^17. If you set the dial to n, then 10^17-n people will get tortured starting now for the next fifty years, and n dust specks will fly into the eyes of each of 3^^^3 people during the next fifty years.

The dial starts at zero. For each unit that you turn the dial up, you are saving one person from being tortured by putting a dust speck in the eyes of each of the 3^^^3 people, the exact choice presented.

So, if you thought the correct answer was the dust specks, you'd turn the dial from zero to one right? And then you'd turn it from one to two, right?

But, if you turned the dial all the way up to 10^17, you'd effectively be rubbing the corneas of the 3^^^3 people with sandpaper for fifty years (of course, their corneas would wear through, and their eyes would come apart under that sort of abrasion. It would probably take less than a million dust specks per second to do that, but let's be conservative and make them smaller dust specks.) Even if you don't count the pain involved, they'd be blind forever. How many people would you blind in order to save one person from being tortured for fifty years? You probably wouldn't blind everyone on earth to save that one person from being tortured, and yet, there are (3^^^3)/(10^17) >> 7*10^9 people being blinded for each person you
have saved from torture.

So if your answer was the dust specks, you'd either end up turning the knob all the way up to 10^17, or you'd have to stop somewhere, because there's no escaping that in this scenario, there's a real dial in front of you, and you have to turn it to some n between 0 and a 10^17.

If you left the dial on, say, 10^10, I'd ask "Tell me, what is so special about the difference between hitting someone with 10^10 dust specs versus hitting them with 10^10+1, that wasn't special about the difference between hitting them with zero versus one?" If anything, the more dust specks there are, the less of a difference one more would make.

There are easily 10^17 continuous gradations between no inconvenience and having ones eyes turned to pulp, and I don't really see what would make any of them terribly different from each other. Yet n=0 is obviously preferable to n=10^17, and so, each individual increment of n must be bad.

"... whenever a tester finds a user input that crashes your program, it is always bad - it reveals a flaw in the code - even if it's not a user input that would plausibly occur; you're still supposed to fix it. "Would you kill Santa Claus or the Easter Bunny?" is an important question if and only if you have trouble deciding. I'd definitely kill the Easter Bunny, by the way, so I don't think it's an important question."

I write code for a living; I do not claim that it crashes the program. Rather the answer is irrelevant as I don't think that the question is important or insightful regarding our moral judgements since it lacks physical plausibility. BTW, since one can think of God as "Santa Claus for grown-ups", the Easter Bunny lives.

By "pay a penny to avoid the dust specks" I meant "avoid all dust specks", not just one dust speck. Obviously for one speck I'd rather have the penny.

what about Vassar's universes of agonium? Say a googolplex-persons' worth of agonium for a googolplex years.

To reduce suffering in general rather than your own (it would be tough to live with), bring on the coddling grinders. (10^10^100)^2 is a joke next to 3^^^3.

Having said that, it depends on the qualia-experiencing population of all existence compared to the numbers affected, and whether you change existing lives or make new ones. If only a few googolplex-squared people-years exist anyway, I vote dust.

I also vote to kill the bunny.

For those who would pick TORTURE, what about Vassar's universes of agonium? Say a googolplex-persons' worth of agonium for a googolplex years.

Torture, again. From the perspective of each affected individual, the choice becomes:

1.) A (10(10100))/(3^^^3) chance of being tortured for (10(10100)) years.
2.) A 1 chance of a dust speck.
(or very slightly different numbers if the (10(10100)) people exist in addition to the 3^^^3 people; the difference is too small to be noticable)

I'd still take the former. (10(10100))/(3^^^3) is still so close to zero that there's no way I can tell the difference without getting a larger universe for storing my memory first.

Eliezer, it's the combination of (1) totally untrustworthy brain machinery and (2) no immediate need to make a choice that I'm suggesting means that withholding judgement is reasonable. I completely agree that you've found a bug; congratulations, you may file a bug report and add it to the many other bug reports already on file; but how do you get from there to the conclusion that the right thing to do is to make a choice between these two options?

When I read the question, I didn't go into a coma or become psychotic. I didn't even join a crazy religion or start beating my wife. If for some reason I actually had to make such a choice, I still wouldn't go nuts. So I think analogies with crashing software are inappropriate. (Again, I don't deny that there's a valid bug report. I'm just questioning its severity.)

So what we have here is an architectural problem with the software, which produces a failure mode in which input radically different from any that will ever actually be supplied provokes a small user-interface glitch. It would be nice to fix it, but it doesn't strike me as unreasonable if it doesn't make it through some people's triage.

(Santa Claus versus the Easter Bunny is much nearer to being a realistic question, and so far as I can tell there isn't anything in my mental machinery that fundamentally isn't equipped to consider it. Kill the bunny.)

Let's suppose we measure pain in pain points (pp). Any event which can cause pain is given a value in [0, 1], with 0 being no pain and 1 being the maximum amount of pain perceivable. To calculate the pp of an event, assign a value to the pain, say p, and then multiply it by the number of people who will experience the pain, n. So for the torture case, assume p = 1, then:

torture: 1*1 = 1 pp

For the spec in eye case, suppose it causes the least amount of pain greater than no pain possible. Denote this by e. Assume that the dust speck causes e amount of pain. Then if e < 1/3^^^3

spec: 1 * e < 1 pp

and if e > 1/3^^^3

spec: 1 * e > 1 pp

So assuming our moral calculus is to always choose whichever option generates the least pp, we need only ask if e is greater than or less than 1/n.

If you've been paying attention, I now have an out to give no answer: we don't know what e is, so I can't decide (at least not based on pp). But I'll go ahead and wager a guess. Since 1/3^^^3 is very small, I think that most likely any pain sensing system of any present or future intelligence will have e > 1/3^^^3, then I must choose torture because torture costs 1 pp but the specs cost more than 1 pp.

This doesn't feel like what, as a human, I would expect the answer to be. I want to say don't torture the poor guy and all the rest of us will suffer the spec so he need not be tortured. But I suspect this is human inability to deal with large numbers, because I think about how I would be willing to accept a spec so the guy wouldn't be torture since e pp < 1 pp, and every other individual, supposing they were pp-fearing people, would make the same short-sighted choice. But the net cost would be to distribute more pain with the specs than the torture ever would.

Weird how the human mind can find a logical answer and still expect a nonlogical answer to be the truth.

"Wow. People sure are coming up with interesting ways of avoiding the question."

My response was a real request for information- if this is a pure utility test, I would select the dust specks. If this were done to a complex, functioning society, adding dust specks into everyone's eyes would disrupt a great deal of important stuff- someone would almost certainly get killed in an accident due to the distraction, even on a planet with only 10^15 people and not 3^^^^3.

Eliezer, in your response to g, are you suggesting that we should strive to ensure that our probability distribution over possible beliefs sum to 1? If so, I disagree: I don't think this can be considered a plausible requirement for rationality. When you have no information about the distribution, you ought to assign probabilities uniformly, according to Laplace's principle of indifference. But the principle of indifference only works for distributions over finite sets. So for infinite sets you have to make an arbitrary choice of distribution, which violates indifference.

"For those who would pick SPECKS, would you pay a single penny to avoid the dust specks?"

Yes. Note that, for the obvious next question, I cannot think of an amount of money large enough such that I would rather keep it than use it to save a person from torture. Assuming that this is post-Singularity money which I cannot spend on other life-saving or torture-stopping efforts.

"You probably wouldn't blind everyone on earth to save that one person from being tortured, and yet, there are (3^^^3)/(10^17) >> 7*10^9 people being blinded for each person you have saved from torture."

This is cheating, to put it bluntly- my utility function does not assign the same value to blinding someone and putting six billion dust specks in everyone's eye, even though six billion specks are enough to blind people if you force them into their eyes all at once.

"I'd still take the former. (10(10100))/(3^^^3) is still so close to zero that there's no way I can tell the difference without getting a larger universe for storing my memory first."

The probability is effectively much greater than that, because of complexity compression. If you have 3^^^^3 people with dust specks, almost all of them will be identical copies of each other, greatly reducing abs(U(specks)). abs(U(torture)) would also get reduced, but by a much smaller factor, because the number is much smaller to begin with.

My algorithm goes like this:
there are two variables, X and Y.
Adding a single additional dust speck to a person's eye over their entire lifetime increases X by 1 for every person this happens to.
A person being tortured for a few minutes increases Y by 1.

I would object to most situations where Y is greater than 1. But I have no preferences at all with regard to X.

See? Dust specks and torture are not the same. I do not lump them together as "disutility". To do so seems to me a preposterous oversimplification. In any case, it has to be argued that they are the same. If you assume they're the same, then you're just assuming the torture answer when you state the question - it's not a problem of ethical philosophy but a problem of addition.

I am not convinced that this question can be converted into a personal choice where you face the decision of whether to take the speck or a 1/3^^^3 chance of being tortured. I would avoid the speck and take my chances with torture, and I think that is indeed an obvious choice.

I think a more apposite application of that translation might be:
If I knew I was going to live for 3^^^3+50*365 days, and I was faced with that choice every day, I would always choose the speck, because I would never want to endure the inevitable 50 years of torture.

The difference is that framing the question as a one-off individual choice obscures the fact that in the example proffered, the torture is a certainty.

1/3^^^3 chance of being tortured... If I knew I was going to live for 3^^^3+50*365 days, and I was faced with that choice every day, I would always choose the speck, because I would never want to endure the inevitable 50 years of torture.

That wouldn't make it inevitable. You could get away with it, but then you could get multiple tortures. Rolling 6 dice often won't get exactly one "1".

Tom McCabe wrote:
The probability is effectively much greater than that, because of complexity compression. If you have 3^^^^3 people with dust specks, almost all of them will be identical copies of each other, greatly reducing abs(U(specks)). abs(U(torture)) would also get reduced, but by a much smaller factor, because the number is much smaller to begin with.

Is there something wrong with viewing this from the perspective of the affected individuals (unique or not)? For any individual instance of a person, the probability of directly experiencing the torture is (10(10100))/(3^^^3), regardless of how many identical copies of this person exist.

Mike wrote:
I think a more apposite application of that translation might be:
If I knew I was going to live for 3^^^3+50*365 days, and I was faced with that choice every day ...

I'm wondering how you would phrase the daily choice in this case, to get the properties you want. Perhaps like this:
1.) Add a period of (50*365)/3^^^3 days to the time period you will be tortured at the end of your life.
2.) Get a speck.

This isn't quite the same as the original question, as it gives choices between the two extremes. And in practice, this could get rather annoying, as just having to answer the question would be similarly bad to getting a speck. Leaving that aside, however, I'd still take the (ridiculously short) torture every day.

The difference is that framing the question as a one-off individual choice obscures the fact that in the example proffered, the torture is a certainty.
I don't think the math in my personal utility-estimation algorithm works out significantly differently depending on which of the cases is chosen.

Answer depends on the person's POV on consciousness.

because of complexity compression. If you have 3^^^^3 people with dust specks, almost all of them will be identical copies of each other, greatly reducing abs(U(specks)).

If so, I want my anti-wish back. Evil Genie never said anything about compression. No wonder he has so many people to dust. I'm complaining to GOD Over Djinn.

If they're not compressed, surely a copy will still experience qualia? Does it matter that it's identical to another? If the sum experience of many copies is weighted as if there was just one, then I'm officially converting from infinite set agnostic to infinite set atheist.

Bayesianism, Infinite Decisions, and Binding replies to Vann McGee's "An airtight dutch book", defending the permissibility of an unbounded utility function.

An option that dominates in finite cases will always provably be part of the maximal option in finite problems; but in infinite problems, where there is no maximal option, the dominance of the option for the infinite case does not follow from its dominance in all finite cases.

If you allow a discontinuity where the utility of the infinite case is not the same as the limit of the utilities of the finite cases, then you have to allow a corresponding discontinuity in planning where the rational infinite plan is not the limit of the rational finite plans.

It is clearly not so easy to have a non-subjective determination of utility.
After some thought I pick the torture. That is because the concept of 3^^^3 people means that no evolution will occur while that many people live. The one advantage to death is that it allows for evolution. It seems likely that we will have evovled into much more interesting life forms long before 3^^^3 of us have passed.
What's the utility of that?

Recovering Irrationalist:
True: my expected value would be 50 years of torture, but I don't think that changes my argument much.

Sebastian:
I'm not sure I understand what you're trying to say. (50*365)/3^^^3 (which is basically the same thing as 1/3^^^3) days of torture wouldn't be anything at all, because it wouldn't be noticeable. I don't think you can divide time to that extent from the point of view of human consciousness.

I don't think the math in my personal utility-estimation algorithm works out significantly differently depending on which of the cases is chosen.
To the extent that you think that and it is reasonable, I suppose that would undermine my argument that the personal choice framework is the wrong way of looking at the question. I would choose the speck every day, and it seems like a clear choice to me, but perhaps that just reflects that I have the bias this thought experiment was meant to bring out.

I'll go ahead and reveal my answer now: Robin Hanson was correct, I do think that TORTURE is the obvious option, and I think the main instinct behind SPECKS is scope insensitivity.

Some comments:

While some people tried to appeal to non-linear aggregation, you would have to appeal to a non-linear aggregation which was non-linear enough to reduce 3^^^3 to a small constant. In other words it has to be effectively flat. And I doubt they would have said anything different if I'd said 3^^^^3.

If anything is aggregating nonlinearly it should be the 50 years of torture, to which one person has the opportunity to acclimate; there is no individual acclimatization to the dust specks because each dust speck occurs to a different person. The only person who could be "acclimating" to 3^^^3 is you, a bystander who is insensitive to the inconceivably vast scope.

Scope insensitivity - extremely sublinear aggregation by individuals considering bad events happening to many people - can lead to mass defection in a multiplayer prisoner's dilemma even by altruists who would normally cooperate. Suppose I can go skydiving today but this causes the world to get warmer by 0.000001 degree Celsius. This poses very little annoyance to any individual, and my utility function aggregates sublinearly over individuals, so I conclude that it's best to go skydiving. Then a billion people go skydiving and we all catch on fire. Which exact person in the chain should first refuse?

I may be influenced by having previously dealt with existential risks and people's tendency to ignore them.

If anything is aggregating nonlinearly it should be the 50 years of torture, to which one person has the opportunity to acclimate; there is no individual acclimatization to the dust specks because each dust speck occurs to a different person

I find this reasoning problematic, because in the dust specks there is effectively nothing to acclimate to... the amount of inconvenience to the individual will always be smaller in the speck scenario (excluding secondary effects, such as the individual being distracted and ending up in a car crash, of course).

Which exact person in the chain should first refuse?

Now, this is considerably better reasoning - however, there was no clue to this being a decision that would be selected over and over by countless of people. Had it been worded "you among many have to make the following choice...", I could agree with you. But the current wording implied that it was once-a-universe sort of choice.

Well as long as we've gone to all the trouble to collect 85 comments on this topic, this seems like an great chance for a disagreement case study. It would be interesting to collect stats on who takes what side, and to relate that to their various kinds of relevant expertize. For the moment I disturbed by the fact that Eliezer and I seem to be in a minority here, but comforted a bit by the fact that we seem to know decision theory better than most. But I'm open to new data on the balance of opinion and the balance of relevant expertize.

The diagnosis of scope insensitivity presupposes that people are trying to perform a utilitarian calculation and failing. But there is an ordinary sense in which a sufficiently small harm is no wrong. A harm must reach a certain threshold before the victim is willing to bear the cost of seeking redress. Harms that fall below the threshold are shrugged off. And an unenforced law is no law. This holds even as the victims multiply. A class action lawsuit is possible, summing the minuscule harms, but our moral intuitions are probably not based on those.

Now, this is considerably better reasoning - however, there was no clue to this being a decision that would be selected over and over by countless of people. Had it been worded "you among many have to make the following choice...", I could agree with you. But the current wording implied that it was once-a-universe sort of choice.

The choice doesn't have to be repeated to present you with the dilemma. Since all elements of the problem are finite - not countless, finite - if you refuse all actions in the chain, you should also refuse the start of the chain even when no future repetitions are presented as options. This kind of reasoning doesn't work for infinite cases, but it works for finite ones.

One potential counter to the "global heating" example is that at some point, people begin to die who would not otherwise have done so, and that should be the point of refusal. But for the case of dust specks - and we can imagine getting more than one dust speck in your eye per day - it doesn't seem like there should be any sharp borderline.

We face the real-world analogue of this problem every day, when we decide whether to tax everyone in the First World one penny in order to save one starving African child by mounting a large military rescue operation that swoops in, takes the one child, and leaves.

There is no "special penny" where this logic goes from good to bad. It's wrong when repeated because it's also wrong in the individual case. You just have to come to terms with scope sensitivity.

Actually, that was a poor example because taxing one penny has side effects. I would rather save one life and everyone in the world poked with a stick with no other side effects, because I put a substantial probability on lifespans being longer than many might anticipate. So even repeating this six billion times to save everyone's life at the price of 120 years of being repeatedly poked with a stick, would still be a good bargain.

Where there are no special inflection points, a bad repeated action should be a bad individual action, a good repeated action should be a good individual action. Talking about the repeated case changes your intuitions and gets around your scope insensitivity, it doesn't change the normative shape of the problem (IMHO).

Robin: dare I suggest that one area of relevant expertise is normative philosophy for-@#%(^^$-sake?!

It's just painful -- really, really, painful -- to see dozens of comments filled with blinkered nonsense like "the contradiction between intuition and philosophical conclusion" when the alleged "philosophical conclusion" hinges on some ridiculous simplistic Benthamite utilitarianism that nobody outside of certain economics departments and insular technocratic computer-geek blog communities actually accepts! My model for the torture case is swiftly becoming fifty years of reading the comments to this post.

The "obviousness" of the dust mote answer to people like Robin, Eliezer, and many commenters depends on the following three claims:

a) you can unproblematically aggregate pleasure and pain across time, space, and individuality,

b) all types of pleasures and pains are commensurable such that for all i, j, given a quantity of pleasure/pain experience i, you can find a quantity of pleasure/pain experience j that is equal to (or greater or less than) it. (i.e. that pleasures and pains exist on one dimension)

c) it is a moral fact that we ought to select the world with more pleasure and less pain.

But each of those three claims is hotly, hotly contested. And almost nobody who has ever thought about the questions seriously believes all three. I expect there are a few (has anyone posed the three beliefs in that form to Peter Singer?), but, man, if you're a Bayesian and you update your beliefs about those three claims based on the general opinions of people with expertise in the relevant area, well, you ain't accepting all three. No way, no how.

dozens of comments filled with blinkered nonsense like "the contradiction between intuition and philosophical conclusion" when the alleged "philosophical conclusion" hinges on some ridiculous simplistic Benthamite utilitarianism that nobody outside of certain economics departments and insular technocratic computer-geek blog communities actually accepts!

You've quoted one of the few comments which your criticism does not apply to. I carry no water for utilitarian philosophy and was here highlighting its failure to capture moral intuition.

all types of pleasures and pains are commensurable such that for all i, j, given a quantity of pleasure/pain experience i, you can find a quantity of pleasure/pain experience j that is equal to (or greater or less than) it. (i.e. that pleasures and pains exist on one dimension)

Is a consistent and complete preference ordering without this property possible?

"An option that dominates in finite cases will always provably be part of the maximal option in finite problems; but in infinite problems, where there is no maximal option, the dominance of the option for the infinite case does not follow from its dominance in all finite cases."

From Peter's proof, it seems like you should be able to prove that an arbitrarily large (but finite) utility function will be dominated by events with arbitrarily large (but finite) improbabilities.

"Robin Hanson was correct, I do think that TORTURE is the obvious option, and I think the main instinct behind SPECKS is scope insensitivity."

And so we come to the billion-dollar question: Will scope insensitivity of this type be eliminated under CEV? So far as I can tell, a utility function is arbitrary; there is no truth which destroys it, and so the FAI will be unable to change around our renormalized utility functions by correcting for factual inaccuracy.

"Which exact person in the chain should first refuse?"

The point at which the negative utility of people catching on fire exceeds the positive utility of skydiving. If the temperature is 20 C, nobody will notice an increase of 0.00000001 C. If the temperature is 70 C, the aggregate negative utility could start to outweigh the positive utility. This is not a new idea; see http://en.wikipedia.org/wiki/Tragedy_of_the_commons.

"We face the real-world analogue of this problem every day, when we decide whether to tax everyone in the First World one penny in order to save one starving African child by mounting a large military rescue operation that swoops in, takes the one child, and leaves."

According to http://www.wider.unu.edu/research/2006-2007/2006-2007-1/wider-wdhw-launch-5-12-2006/wider-wdhw-press-release-5-12-2006.pdf, 10% of the world's adults, around 400 million people, own 85% of the world's wealth. Taxing them each one penny would give a total of $4 million, more than enough to mount this kind of a rescue operation. While incredibly wasteful, this would actually be preferable to some of the stuff we spend our money on; my local school district just voted to spend $9 million (current US dollars) to build a swimming pool. I don't even want to know how much we spend on $200 pants; probably more than $9 million in my town alone.

Elizer: "It's wrong when repeated because it's also wrong in the individual case. You just have to come to terms with scope sensitivity."

But determining whether or not a decision is right or wrong in the individual case requires that you be able to place a value on each outcome. We determine this value in part by using our knowledge of how frequently the outcomes occur and how much time/effort/money it takes to prevent or assuage them. Thus knowing the frequency that we can expect an event to occur is integral to assigning it a value in the first place. The reason it would be wrong in the individual case to tax everyone in the first world the penny to save one African child is that there are so many starving children that doing the same for each one would become very expensive. It would not be obvious, however, if there was only one child in the world that needed rescuing. The value of life would increase because we could afford it to if people didn't die so frequently.

People in a village might be willing to help pay the costs when someone's house burns down. If 20 houses in the village burned down, the people might still contribute, but it is unlikely they will contribute 20 times as much. If house-burning became a rampant problem, people might stop contributing entirely, because it would seem futile for them to do so. Is this necessarily scope insensitivity? Or is it reasonable to determine values based on frequencies we can realistically expect?

Where there are no special inflection points, a bad repeated action should be a bad individual action, a good repeated action should be a good individual action. Talking about the repeated case changes your intuitions and gets around your scope insensitivity, it doesn't change the normative shape of the problem (IMHO).

Hmm, I see your point. I can't help like feeling that there are cases where repetition does matter, though. For instance, assuming for a moment that radical life-extension and the Singularity and all that won't happen, and assuming that we consider humanity's continued existence to be a valuable thing - how about the choice of having/not having children? Not having children causes a very small harm to everybody else in the same generation (they'll have less people supporting them when old). Doesn't your reasoning imply that every couple should be forced into having children even if they weren't of the type who'd want that (the "torture" option), to avoid causing a small harm to all the others? This even though society could continue to function without major trouble even if a fraction of the population did choose to remain childfree, for as long as sufficiently many others had enough children?

Constant, my reference to your quote wasn't aimed at you or your opinions, but rather at the sort of view which declares that the silly calculation is some kind of accepted or coherent moral theory. Sorry if it came off the other way.

Nick, good question. Who says that we have consistent and complete preference orderings? Certainly we don't have them across people (consider social choice theory). Even to say that we have them within individual people is contestable. There's a really interesting literature in philosophy, for example, on the incommensurability of goods. (The best introduction of which I'm aware consists in the essays in Ruth Chang, ed. 1997. Incommensurability, Incomparability, and Practical Reason Cambridge: Harvard University Press.)

That being said, it might be possible to have complete and consistent preference orderings with qualitative differences between kinds of pain, such that any amount of torture is worse than any amount of dust-speck-in-eye. And there are even utilitarian theories that incorporate that sort of difference. (See chapter 2 of John Stuart Mill's Utilitarianism, where he argues that intellectual pleasures are qualitatively superior to more base kinds. Many indeed interpret that chapter to suggest that any amount of an intellectual pleasure outweighs any amount of drinking, sex, chocolate, etc.) Which just goes to show that even utilitarians might not find the torture choice "obvious," if they deny b) like Mill.

Who says that we have consistent and complete preference orderings?

Who says you need them? The question wasn't to quantify an exact balance. You just need to be sure enough to make the decision that one side outweighs the other for the numbers involved.

By my values, all else equal, for all x between 1 millisecond and fifty years, 10^1000 people being tortured for time x is worse than one person being tortured for time x*2. Would you disagree?

So, 10^1000 people tortured for (fifty years)/2 is worse than one person tortured for fifty years.
Then, 10^2000 people tortured for (fifty years)/4 is worse than one person tortured for fifty years.

You see where I'm going with this. Do something similar with the dust specs and unless I prefer countless people getting countless years of intense dust harassment to one person getting a millisecond of pain, I vote torture.

I recognize this is my opinion and relies on your c) it is a moral fact that we ought to select the world with more pleasure and less pain not being hopelessly outweighed by another criteria. I think this is definitely a worthwhile thing to debate and that your input would be extremely valuable.

Since Robin is interested in data... I chose SPECKS, and was shocked by the people who chose TORTURE on grounds of aggregated utility. I had not considered the possibility that a speck in the eye might cause a car crash (etc) for some of those 3^^^3 people, and it is the only reason I see for revising my original choice. I have no accredited expertise in anything relevant, but I know what decision theory is.

I see a widespread assumption that everything has a finite utility, and so no matter how much worse X is than Y, there must be a situation in which it is better to have one person experiencing X, rather than a large number of people experiencing Y. And it looks to me as if this assumption derives from nothing more than a particular formalism. In fact, it is extremely easy to have a utility function in which X unconditionally trumps Y, while still being quantitatively commensurable with some other option X'. You could do it with delta functions, for example. You would use ordinary scalars to represent the least important things to have preferences about, scalar multiples of a delta function to represent the utilities of things which are unconditionally more important than those, scalar multiples of a delta function squared to represent things that are even more important, and so on.

The qualitative distinction I would appeal to here could be dubbed pain versus inconvenience. A speck of dust in your eye is not pain. Torture, especially fifty years of it, is.

Eliezer, a problem seems to be that the speck does not serve the function you want it to in this example, at least not for all readers. In this case, many people see a special penny because there is some threshold value below which the least bad bad thing is not really bad. The speck is intended to be an example of the least bad bad thing, but we give it a badness rating of one minus .9-repeating.

(This seems to happen to a lot of arguments. "Take x, which is y." Well, no, x is not quite y, so the argument breaks down and the discussion follows some tangent. The Distributed Republic had a good post on this, but I cannot find it.)

We have a special penny because there is some amount of eye dust that becomes noticeable and could genuinely qualify as the least bad bad thing. If everyone on Earth gets this decision at once, and everyone suddenly gets >6,000,000,000 specks, that might be enough to crush all our skulls (how much does a speck weigh?). Somewhere between that and "one speck, one blink, ever" is a special penny.

If we can just stipulate "the smallest unit of suffering (or negative qualia, or your favorite term)," then we can move on to the more interesting parts of the discussion.

I also see a qualitative difference if there can be secondary effects or summation causes secondary effects. As noted above, if 3^^^3/10^20 people die due to freakishly unlikely accidents caused by blinking, the choice becomes trivial. Similarly, +0.000001C sums somewhat differently than specks. 1 speck/day/person for 3^^^3 days is still not an existential risk; 3^^^3 specks at once will kill everyone.

(I still say Kyle wins.)

Okay, here's the data: I choose SPECKS, and here is my background and reasons.

I am a cell biologist. That is perhaps not relevant.

My reasoning is that I do not think that there is much meaning in adding up individual instances of dust specks. Those of you who choose TORTURE seem to think that there is a net disutility that you obtain by multiplying epsilon by 3^^^3. This is obviously greater than the disutility of torturing one person.
I reject the premise that there is a meaningful sense in which these dust specks can "add up".

You can think in terms of biological inputs - simplifying, you can imagine a system with two registers. A dust speck in the eye raises register A by epsilon. Register A also resets to zero if a minute goes by without any dust specks. Torture immediately sets register B to 10. I am morally obliged to intervene if register B ever goes above 1. In this scheme register A is a morally irrelevant register. It trades in different units than register B. No matter how many instances of A*epsilon there are, it does not warrant intervention.

You are making a huge, unargued assumption if you treat both torture and dust-specks in equivalent terms of "disutility". I accept your question and argue for "SPECKS" by rejecting your premise of like units (which does make the question trivial). But I sympathize with people who reject your question outright.

Mitchell, I acknowledge the defensibility of the position that there are tiers of incommensurable utilities. But to me it seems that the dust speck is a very, very small amount of badness, yet badness nonetheless. And that by the time it's multiplied to ~3^^^3 lifetimes of blinking, the badness should become incomprehensibly huge just like 3^^^3 is an incomprehensibly huge number.

One reason I have problems with assigning a hyperreal infinitesimal badness to the speck, is that it (a) doesn't seem like a good description of psychology (b) leads to total loss of that preference in smarter minds.

(B) If the value I assign to the momentary irritation of a dust speck is less than 1/3^^^3 the value of 50 years' torture, then I will never even bother to blink away the dust speck because I could spend the thought or the muscular movement on my eye on something with a better than 1/3^^^3 chance of saving someone from torture.

(A) People often also think that money, a mundane value, is incommensurate with human life, a sacred value, even though they very definitely don't attach infinitesimal value to money.

I think that what we're dealing here is more like the irrationality of trying to impose and rationalize comfortable moral absolutes in defiance of expected utility, than anyone actually possessing a consistent utility function using hyperreal infinitesimal numbers.

The notion of sacred values seems to lead to irrationality in a lot of cases, some of it gross irrationality like scope neglect over human lives and "Can't Say No" spending.

Eliezer: Why does anything have a utility at all? Let us suppose there are some things to which we attribute an intrinsic utility, negative or positive - those are our moral absolutes - and that there are others which only have a derivative utility, deriving from the intrinsic utility of some of their consequences. This is certainly one way to get incommensurables. If pain has intrinsic disutility and inconvenience does not, then no finite quantity of inconvenience can by itself trump the imperative of minimizing pain. But if the inconvenience might give rise to consequences with intrinsic disutility, that's different.

"The notion of sacred values seems to lead to irrationality in a lot of cases, some of it gross irrationality like scope neglect over human lives and "Can't Say No" spending."

Could you post a scenario where most people would choose the option which unambiguously causes greater harm, without getting into these kinds of debates about what "harm" means? Eg., where option A ends with shooting one person, and option B ends with shooting ten people, but option B sounds better initially? We have a hard enough time getting rid of irrationality, even in cases where we know what is rational.

Dare I say that people may be overvaluing 50 years of a single human life? We know for a fact that some effect will be multiplied by 3^^^3 by our choice. We have no idea what strange an unexpected existential side effects this may have. It's worth avoiding the risk. If the question were posed with more detail, or specific limitations on the nature of the effects, we might be able to answer more confidently. But to risk not only human civilization, but ALL POSSIBLE CIVILIZATIONS, you must be DAMN SURE you are right. 3^^^3 makes even incredibly small doubts significant.

I wonder if my answers make me fail some kind of test of AI friendliness. What would the friendly AI do in this situation? Probably write poetry.

For Robin's statistics:
Given no other data but the choice, I would have to choose torture. If we don't know anything about the consequences of the blinking or how many times the choice is being made, we can't know that we are not causing huge amounts of harm. If the question deliberately eliminated these unknowns- ie the badness was limited to an eyeblink that does not immediately result in some disaster for someone or blindness for another, and you really are the one and only person making the choice ever, then I'd go with the dust-- But these qualifications are huge when you consider 3^^^3. How can we say the eyeblink didn't distract a surgeon and cause a slip of his knife? Given enough trials, something like that is bound to happen.

@Paul, I was trying to find a solution that didn't assume "b) all types of pleasures and pains are commensurable such that for all i, j, given a quantity of pleasure/pain experience i, you can find a quantity of pleasure/pain experience j that is equal to (or greater or less than) it. (i.e. that pleasures and pains exist on one dimension).", but rather established it for the case at hand. Unless it's specifically stated in the hypothetical that this is a true 1-shot choice (which we know it isn't in the real world, as we make analogous choices all the time), I think it's legitimate to assume the aggregate result of the test repeated by everyone. Thus, I'm not invoking utilitarian calculation, but Kantian absolutism! ;) I mean to appeal to your practical intuition by suggesting that a constant barrage of specks will create an experience of a like kind with torture.

@Robin Hanson, what little expertise I have is in the liberal arts and sciences; Euclid and Ptolemy, Aristotle and Kant, Einstein and Sophocles, etc.

Eliezer -- I think the issues we're getting into now require discussion that's too involved to handle in the comments. Thus, I've composed my own post on this question. Would you please be so kind as to approve it?

Recovering irrationalist: I think the hopefully-forthcoming-post-of-my-own will constitute one kind of answer to your comment. One other might be that one can, in fact, prefer huge dust harassment to a little torture. Yet a third might be that we can't aggregate the pain of dust harassment across people, so that there's some amount of single-person dust harassment that will be worse than some amount of torture, but if we spread that out, it's not.

For Robin's statistics:
Torture on the first problem, and torture again on the followup dilemma.

relevant expertise: I study probability theory, rationality and cognitive biases as a hobby. I don't claim any real expertise in any of these areas.

I think one of the reasons I finally chose specks is because the unlike implied, the suffering does not simply "add up": 3^^^3 people getting one dust speck in their eye is most certainly not equal to one person getting 3^^^3 dust specks in his eyes. It's not "3^^^3 units of disutility, total", it's one unit of disutility per person.

That still doesn't really answer the "one person for 50 years or two people for 49 years" question, though - by my reasoning, the second option would be preferrable, while obviously the first option is the preferrable one. I might need to come up with a guideline stating that only experiences of suffering within a few orders of magnitude are directly comparable with each other, or some such, but it does feel like a crude hack. Ah well.

If statistics are being gathered, I'm a second year cognitive science student.

It is my impression that human beings almost universally desire something like "justice" or "fairness." If everybody had the dust speck problem, it would hardly be percieved as a problem. If one person is beign tortured, both the tortured person and others percieve unfairness, and society has a problem with this.

Actually, we all DO get dust motes in our eyes from time to time, and this is not a public policy issue.
In fact relatively small numbers of people ARE being tortured today, and this is a big problem both for the victims and for people who care about justice.

Beyond the distracting arithmetic lesson, this question reeks of Christianity, positing a situation in which one person's suffering can take away the suffering of others.

For the moment I disturbed by the fact that Eliezer and I seem to be in a minority here, but comforted a bit by the fact that we seem to know decision theory better than most. But I'm open to new data on the balance of opinion and the balance of relevant expertize.

It seems like selection bias might make this data much less useful. (It applied it my case, at least.) The people who chose TORTURE were likely among those with the most familiarity with Eliezer's writings, and so were able to predict that he would agree with them, and so felt less inclined to respond. Also, voicing their opinion would be publicly taking an unpopular position, which people instinctively shy away from.

Paul: Yet a third might be that we can't aggregate the pain of dust harassment across people, so that there's some amount of single-person dust harassment that will be worse than some amount of torture, but if we spread that out, it's not.

My induction argument covers that. As long as, all else equal, you believe:

A googolplex people being dust speckled every second of their life without further ill effect

I don't think this is directly comparable, because the disutility of additional dust specking to one person in a short period of time probably grows faster than linearly - if I have to blink every second for an hour, I'll probably get extremely frustrated on top of the slight discomfort of the specks themselves. I would say that one person getting specked every second of their life is significantly worse than a couple billion people getting specked once.

the disutility of additional dust specking to one person in a short period of time probably grows faster than linearly

That's why I used a googolplex people to balance the growth. All else equal, do you disagree with: "A googolplex people dust specked x times during their lifetime without further ill effect is worse than one person dust specked for x*2 times during their lifetime without further ill effect" for the range concerned?

one person getting specked every second of their life is significantly worse than a couple billion people getting specked once.

I agree. I never said it wasn't.

Have to run - will elaborate later.

All else equal, do you disagree with: "A googolplex people dust specked x times during their lifetime without further ill effect is worse than one person dust specked for x*2 times during their lifetime without further ill effect" for the range concerned?

I agree with that. My point is that agreeing that "A googolplex people being dust speckled every second of their life without further ill effect is worse than one person being horribly tortured for the shortest period experiencable" doesn't oblige me to agree that "A few billion* googolplexes of people being dust specked once without further ill effect is worse than one person being horribly tortured for the shortest period experiencable". (Unless "a further ill effect" is meant to exclude not only car accidents but superlinear personal emotional effects, but that would be stupid.)

* 1 billion seconds = 31.7 years

I think that what we're dealing here is more like the irrationality of trying to impose and rationalize comfortable moral absolutes in defiance of expected utility

Since real problems never possess the degree of certainty that this dilemma does, holding certain heuristics as absolutes may be the utility-maximizing thing to do. In a realistic version of this problem, you would have to consider the results of empowering whatever agent is doing this to torture people with supposedly good but nonverifiable results. If it's a human or group of humans, not such a good idea; if it's a Friendly AI, maybe you can trust it but can't it figure out a better way to achieve the result? (There is a Pascal's Mugging problem here.)

One more thing for TORTURErs to think about: if every one of those 3^^^3 people is willing to individually suffer a dust speck in order to prevent someone from suffering torture, is TORTURE still the right answer? I lean towards SPECK on considering this, although I'm less sure about the case of torturing 3^^^3 people for a minute each vs. 1 person for 50 years.

Just thought I'd comment that the more I think about the question, the more confusing it becomes. I'm inclined to think that if we consider the max utility state of every person having maximal fulfilment, and a "dust speck" as the minimal amount of "unfulfilment" from the top a person can experience, then two people experiencing a single "dust speck" is not quite as bad as a sigle person two "dust specks" below optimal. I think the reason I'm thinking that is that the second speck takes away more proportionally than the first speck did.

Oh, one other thing. I was assuming for my replies both here and in the other thread that we're only talking about the actual "moment of suffering" caused by a dust speck event, with no potential "side effects"

If we consider that those can have consequences, I'm pretty sure that on average those would be negative/harmful, and when the law of large numbers is invoked via stupendously large numbers, well, in that case I'm going with TORTURE.

For the moment at least. :)

I agree with that. My point is that agreeing that "A googolplex people being dust speckled every second of their life without further ill effect is worse than one person being horribly tortured for the shortest period experiencable" doesn't oblige me to agree that "A few billion* googolplexes of people being dust specked once without further ill effect is worse than one person being horribly tortured for the shortest period experiencable".

Neither would I, you don't need to. :-)

The only reason I can pull this off is because 3^^^3 is such a ludicrous number of people, allowing me to actually divide my army by a googolplex a silly number of times. You couldn't cut the series up fine enough with a mere six billion people.

If you agree with my first two statements listed, you can use them (and your vast googolplex-cutter-proof army) to infer a series of small steps from each of Eliezer's options, meeting in the middle at my third statement in the list. You then have a series of steps when a is worse than b, b than c, c than d, all the way from SPECS to my third statement to TORTURE.

If for some reason you object to one of the first 3 statements, my 3^^^3 vast hoard of minions will just cut the series up even finer.

If that's not clear it's probably my fault - I've never had to explain anything like this before.

if every one of those 3^^^3 people is willing to individually suffer a dust speck in order to prevent someone from suffering torture, is TORTURE still the right answer?

I sure would, but I wouldn't ask 3^^^3 others to.

ok, without reading the above comments... (i did read a few of them, including robin hanson's first comment - don't know if he weighed in again).

dust specks over torture.

the apparatus of the eye handles dust specks all day long. i just blinked. it's quite possible there was a dust speck in there somewhere. i just don't see how that adds up to anything, even if a very large number is invoked. in fact with a very large number like the one described it is likely that human beings would evolve more efficient tear ducts, or faster blinking, or something like that. we would adapt and be stronger.

torturing one person for fifty years however puts a stain on the whole human race. it affects all of us, even if the torture is carried out fifty miles underground in complete secrecy.

Recovering irrationalist: in your induction argument, my first stab would be to deny the last premise (transitivity of moral judgments). I'm not sure why moral judgments have to be transitive.

Next, I'd deny the second-to-last premise (for one thing, I don't know what it means to be horribly tortured for the shortest period possible -- part of the tortureness of torture is that it lasts a while).

Eliezer, both you and Robin are assuming the additivity of utility. This is not justifiable, because it is false for any computationally feasible rational agent.

If you have a bounded amount of computation to make a decision, we can see that the number of distinctions a utility function can make is in turn bounded. Concretely, if you have N bits of memory, a utility function using that much memory can distinguish at most 2^N states. Obviously, this is not compatible with additivity of disutility, because by picking enough people you can identify more distinct states than the 2^N distinctions your computational process can make.

Now, the reason for adopting additivity comes from the intuition that 1) hurting two people is at least as bad as hurting one, and 2) that people are morally equal, so that it doesn't matter which people are hurt. Note that these intuitions mathematically only require that harm should be monotone in the number of people with dust specks in their eyes. Furthermore, this requirement is compatible with the finite computation requrements -- it implies that there is a finite number of specks beyond which disutility does not increase.

If we want to generalize away from the specific number N of bits we have available, we can take an order-theoretic viewpoint, and simply require that all increasing chains of utilities have limits. (As an aside, this idea lies at the heart of the denotational semantics of programming languages.) This forms a natural restriction on the domain of utility functions, corresponding to the idea that utility functions are bounded.

It's truly amazing the contortions many people have gone through rather than appear to endorse torture. I see many attempts to redefine the question, categorical answers that basically ignore the scalar, and what Eliezer called "motivated continuation".

One type of dodge in particular caught my attention. Paul Gowder phrased it most clearly, so I'll use his text for reference:

...depends on the following three claims:

a) you can unproblematically aggregate pleasure and pain across time, space, and individuality,

"Unproblematically" vastly overstates what is required here. The question doesn't require unproblematic aggregation; any slight tendency of aggregation will do just fine. We could stipulate that pain aggregates as the hundredth root of N and the question would still have the same answer. That is an insanely modest assumption, ie that it takes 2^100 people having a dust mote before we can be sure there is twice as much suffering as for one person having a dust mote.

"b" is actually inapplicable to the stated question and it's "a" again anyways - just add "type" or "mode" to the second conjunction in "a".

c) it is a moral fact that we ought to select the world with more pleasure and less pain.

I see only three possibilities for challenging this, none of which affects the question at hand.

• Favor a desideratum that roughly aligns with "pleasure" but not quite, such as "health". Not a problem.
• Focus on some special situation where paining others is arguably desirable, such as deterrence, "negative reinforcement", or retributive justice. ISTM that's already been idealized away in the question formulation.
• Just don't care about others' utility, eg Rand-style selfishness.

Recovering irrationalist: in your induction argument, my first stab would be to deny the last premise (transitivity of moral judgments). I'm not sure why moral judgments have to be transitive.

I acknowledged it won't hold for every moral. There are some pretty barking ones out there. I say it holds for choosing the option that creates less suffering. For finite values, transitivity should work fine.

Next, I'd deny the second-to-last premise (for one thing, I don't know what it means to be horribly tortured for the shortest period possible -- part of the tortureness of torture is that it lasts a while).

Fine, I still have plenty of googolplex-divisions left. Cut the series as fine as you like. Have billions of intervening levels of discomfort from spec->itch->ouch->"fifty years of reading the comments to this post." The point is if you slowly morph from TORTURE to SPEC in very small steps, every step gets worse because the population multiplies enormously while the pain differs by a incredibly tiny amount.

Recovering irrationalist, I hadn't thought of things in precisely that way - just "3^^4 is really damn big, never mind 3^^7625597484987" - but now that you point it out, the argument by googolplex gradations seems to me like a much stronger version of the arguments I would have put forth.

It only requires 3^^5 = 3^(3^7625597484987) to get more googolplex factors than you can shake a stick at. But why not use a googol instead of a googolplex, so we can stick with 3^^4? If anything, the case is more persuasive with a googol because a googol is more comprehensible than a googolplex. It's all about scope neglect, remember - googolplex just fades into a featureless big number, but a googol is ten thousand trillion trillion trillion trillion trillion trillion trillion trillion.

Tom, your claim is false. Consider the disutility function

D(Torture, Specks) = [10 * (Torture/(Torture + 1))] + (Specks/(Specks + 1))

Now, with this function, disutility increases monotonically with the number of people with specks in their eyes, satisfying your "slight aggregation" requirement. However, it's also easy to see that going from 0 to 1 person tortured is worse than going from 0 to any number of people getting dust specks in their eyes, including 3^^^3.

The basic objection to this kind of functional form is that it's not additive. However, it's wrong to assume an additive form, because that assumption mandates unbounded utilities, which are a bad idea, because they are not computationally realistic and admit Dutch books. With bounded utility functions, you have to confront the aggregation problem head-on, and depending on how you choose to do it, you can get different answers. Decision theory does not affirmatively tell you how to judge this problem. If you think it does, then you're wrong.

Again, not everyone agrees with the argument that unbounded utility functions give rise to Dutch books. Unbounded utilities only admit Dutch books if you do allow a discontinuity between infinite rewards and the limit of increasing finite awards, but you don't allow a discontinuity between infinite planning and the limit of increasing finite plans.

Oh geez. Originally I had considered this question uninteresting so I ignored it, but considering the increasing devotion to it in later posts, I guess I should give my answer.

My justification, but not my answer, depends upon what how the change is made.

-If the offer is made to all of humanity before being implemented ("Do you want to be the 'lots of people get specks race' or the 'one guy gets severe torture' race?") I believe people could all agree to the specks by "buying out" whoever eventually gets the torture. For an immeasurably small amount, less than the pain of a speck, they can together amass funds sufficient to return the torture to the indivdual's indifference curve. OTOH, the person getting the torture couldn't possibly buy out that many people. (In other words, the specks are Kaldor-Hicks efficient.)

-If the offer, at my decision, would just be thrown onto humanity without possibly of advance negotation, I would still take the specks because even if only people who feel bad for the tortured make a small contribution, it will still comparable to what they had to offer in the above paragraph, such is the nature of large numbers of people.

I don't think this is the result of my revulsion toward the torture, although I have that. I think my decision stems from how such large (and superlinearly increasing) utility differences imply the possibility of "evening it out" through some transfer.

the argument by googolplex gradations seems to me like a much stronger version of the arguments I would have put forth.

You just warmed my heart for the day :-)

But why not use a googol instead of a googolplex

Shock and awe tactics. I wanted a featureless big number of featureless big numbers, to avoid wiggle-outs, and scream "your intuition ain't from these parts". In my head, FBNs always carry more weight than regular ones. Now you mention it, their gravity could get lightened by incomprehensibility, but we we're already counting to 3^^^3.

Googol is better. Less readers will have to google it.

@Neel.

Then I only need to make the condition slightly stronger: "Any slight tendency to aggregation that doesn't beg the question." Ie, that doesn't place a mathematical upper limit on disutility(Specks) that is lower than disutility(Torture=1). I trust you can see how that would be simply begging the question. Your formulation:

D(Torture, Specks) = [10 * (Torture/(Torture + 1))] + (Specks/(Specks + 1))

...doesn't meet this test.

Contrary to what you think, it doesn't require unbounded utility. Limiting the lower bound of the range to (say) 2 * disutility(torture) will suffice. The rest of your message assumes it does.

For completeness, I note that introducing numbers comparable to 3^^^3 in an attempt to undo the 3^^^3 scaling would cause a formulation to fail the "slight" condition, modest though it is.

With so many so deep in reductionist thinking, I'm compelled to stir the pot by asking how one justifies the assumption that the SPECK is a net negative at all, aggregate or not, extended consequences or not? Wouldn't such a mild irritant, over such a vast and diverse population, act as an excellent stimulus for positive adaptations (non-genetic, of course) and likely positive extended consequences?

A brilliant idea, Jef! I volunteer you to test it out. Start blowing dust around your house today.

Hrm... Recovering's induction argument is starting to sway me toward TORTURE.

More to the point, that and some other comments are starting to sway me away from the thought that disutility of single dust speck events per person becomes sublinear as people experiencing it increases (but total population is held constant)

I think if I made some errors, they were partly was caused by "I really don't want to say TORTURE", and partly caused by my mistaking the exact nature of the nonlinearity. I maintain "one person experiencing two dust specks" is not equal to, and actually worse, I think, than two people experiencing one dust speck, but now I'm starting to suspect that two people each experiencing one dust speck is exactly twice as bad as one person experiencing one dust speck. (Assuming, as we shift number of people experiencing DSE that we hold the total population constant.)

Thus, I'm going to tentatively shift my answer to TORTURE.

"A brilliant idea, Jef! I volunteer you to test it out. Start blowing dust around your house today."

Although only one person, I've already begun, and have entered in my inventor's notebook some apparently novel thinking on not only dust, but mites, dog hair, smart eyedrops, and nanobot swarms!

Tom, if having an upper limit on disutility(Specks) that's lower than disutility(Torture1) is begging the question in favour of SPECKS then why isn't not* having such an upper limit begging the question in favour of TORTURE?

I find it rather surprising that so many people agree that utility functions may be drastically nonlinear but are apparently completely certain that they know quite a bit about how they behave in cases as exotic as this one.

Tom, if having an upper limit on disutility(Specks) that's lower than disutility(Torture1) is begging the question in favour of SPECKS then why isn't not* having such an upper limit begging the question in favour of TORTURE?

It should be obvious why. The constraint in the first one is neither argued for nor agreed on and by itself entails the conclusion being argued for. There's no such element in the second.

I think we may be at cross purposes; my apologies if we are and it's my fault. Let me try to be clearer.

Any particular utility function (if it's real-valued and total) "begs the question" in the sense that it either prefers SPECKS to TORTURE, or prefers TORTURE to SPECKS, or puts them exactly equal. I don't see how this can possibly be considered a defect, but if it is one then all utility functions have it, not just ones that prefer SPECKS to TORTURE.

Saying "Clearly SPECKS is better than TORTURE, because here's my utility function and it says SPECKS is better" would be begging the question (absent arguments in support of that utility function). I don't see anyone doing that. Neel's saying "You can't rule out the possibility that SPECKS is better than TORTURE by saying that no real utility function prefers SPECKS, because here's one possible utility function that says SPECKS is better". So far as I can tell you're rejecting that argument on the grounds that any utility function that prefers SPECKS is ipso facto obviously unacceptable; that is begging the question.

g: that's exactly what I'm saying. In fact, you can show something stronger than that.

Suppose that we have an agent with rational preferences, and who is minimally ethical, in the sense that they always prefer fewer people with dust specks in their eyes, and fewer people being tortured. This seems to be something everyone agrees on.

Now, because they have rational preferences, we know that a bounded utility function consistent with their preferences exists. Furthermore, the fact that they are minimally ethical implies that this function is monotone in the number of people being tortured, and monotone in the number of people with dust specks in their eyes. The combination of a bound on the utility function, plus the monotonicity of their preferences, means that the utility function has a well-defined limit as the number of people with specks in their eyes goes to infinity. However, the existence of the limit doesn't tell you what it is -- it may be any value within the bounds.

Concretely, we can supply utility functions that justify either choice, and are consistent with minimal ethics. (I'll assume the bound is the [0,1] interval.) In particular, all disutility functions of the form:

U(T, S) = A(T/(T+1)) + B(S/(S+1))

satisfy minimal ethics, for all positive A and B such that A plus B is less than one. Since A and B are free parameters, you can choose them to make either specks or torture preferred.

Likewise, Robin and Eliezer seem to have an implicit disutility function of the form

U_ER(T, S) = AT + BS

If you normalize to get [0,1] bounds, you can make something up like

U'(T, S) = (AT + BS)/(AT + BS + 1).

Now, note U' also satisfies minimal ethics, in that if T is set to 1, then in the limit as S goes to infinity, U' will still always go to one and exceed A/(A+1). So that's why they tend to have the intuition that torture is the right answer. (Incidentally, this disproves my suggestion that bounded utility functions vitiate the force of E's argument -- but the bounds proved helpful in the end by letting us use limit analysis. So my focus on this point was accidentally correct!)

Now, consider yet another disutility function,

U''(T,S) = (ST + S)/ (ST + S + 1)

This is also minimally ethical, and doesn't have any of the free parameters that Tom didn't like. But this function also always implies a preference for any number of dust specks to even a single instance of torture.

Basically, if you think the answer is obvious, then you have to make some additional assumptions about the structure of the aggregate preference relation.

I have argued in previous comments that the utility of a person should be discounted by his or her measure, which may be based on algorithmic complexity. If this "torture vs specks" dilemma is to have the same force under this assumption, we'd have to reword it a bit:

Would you prefer that the measure of people horribly tortured for fifty years increases by x/3^^^3, or that the measure of people who get dust specks in their eyes increases by x?

I argue that no one, not even a superintelligence, can actually face such a choice. Because x is at most 1, x/3^^^3 is at most 1/3^^^3. But how can you increase the measure of something by more than 0 but no more than 1/3^^^3? You might, perhaps, generate a random number between 0 and 3^^^3 and do something only if that random number is 0. But algorithmic information theory says that for any program (even a superintelligence), there are pseudorandom sequences that it cannot distinguish from truly random sequences, and the prior probability that your random number generator is generating such a pseudorandom sequence is much higher than 1/3^^^3. Therefore the probability of that "random" number being 0 (or being any other number that you can think of) is actually much larger than 1/3^^^3.

Therefore, if someone tells you "measure of ... increases by x/3^^^3", in your mind you've got to be thinking "... increases by y" for some y much larger than 1/3^^^3. I think my theories explains both those who answer SPECKS and those who say no answer is possible.

A consistent utilitarian would choose the torture, but I don't think it's the moral choice.

Let's bring this a little closer to home. Hypothetically, let's say you get to live your life again 3^^^3 times. Would you prefer to have an additional dust speck in your eye in each of your future lives, or else be tortured for 50 years in a single one of them?

Any takers for the torture?

I'd take it.

I'll take it, as long as it's no more likely to be one of the earliest lives. I don't trust any universe that can make 3^^^3 of me not to be a simulation that would get pulled early.

Hrm... Recovering's induction argument is starting to sway me toward TORTURE.

Interesting. The idea of convincing others to decide TORTURE is bothering me much more than my own decision.

I hope these ideas never get argued out of context!

Cooking something for two hours at 350 degrees isn't equivalent to cooking something at 700 degrees for one hour.

I'd rather accept one additional dust speck per lifetime in 3^^^3 lives than have one lifetime out of 3^^^3 lives involve fifty years of torture.

Of course, that's me saying that, with my single life. If I actually had that many lives to live, I might become so bored that I'd opt for the torture merely for a change of pace.

Recovering: chuckles no, I meant thinking about that, and rethinking about what the actual properties of what I'd consider to be a reasonable utility function led me to reject my earlier claim of the specific nonlinearity that lead to my assumption that as you increase the number of people that recieve a spec, the disutility is sublinear, and now I believe it to be linear. So huge bigbigbigbiggigantaenormous num specks would, of course, eventually have to have more disutility than the torture. But since to get to that point knuth arrow notation had to be invoked, I don't think there's any worry that I'm off to get my "rack winding certificate" :P

But yeah, out of context this debate would sound like complete nonsense... "crazy geeks find it difficult to decide between dust specks and extreme torture."

I do have to admit though, Andrew's comment about individual living 3^^^3 times and so on has me thinking again. If "keep memories and so on of all previous lives = yes" (so it's really one really long lifespan) and "permanent physical and psychological damage post torture = no") then I may take that. I think. Arrrgh, stop messing with my head. Actually, no, don't stop, this is fun! :)

I'd take it.
I find your choice/intuition completely baffling, and I would guess that far less than 1% of people would agree with you on this, for whatever that's worth (surely it's worth something.) I am a consequentialist and have studied consequentialist philosophy extensively (I would not call myself an expert), and you seem to be clinging to a very crude form of utilitarianism that has been abandoned by pretty much every utilitarian philosopher (not to mention those who reject utilitarianism!). In fact, your argument reads like a reductio ad absurdum of the point you are trying to make. To wit: if we think of things in equivalent, additive utility units, you get this result that torture is preferable. But that is absurd, and I think almost everyone would be able to appreciate the absurdity when faced with the 3^^^3 lives scenario. Even if you gave everyone a one week lecture on scope insensitivity.

So... I don't think I want you to be one of the people to initially program AI that might influence my life...

No Mike, your intuition for really large numbers is non-baffling, probably typical, but clearly wrong, as judged by another non-Utilitarian consequentialist (this item is clear even to egoists).

Personally I'd take the torture over the dust specks even if the number was just an ordinary incomprehensible number like say the number of biological humans who could live in artificial environments that could be built in one galaxy. (about 10^46th given a 100 year life span and a 300W (of terminal entropy dump into a 3K background from 300K, that's a large budget) energy budget for each of them). It's totally clear to me that a second of torture isn't a billion billion billion times worse than getting a dust speck in my eye, and that there are only about 1.5 billion seconds in a 50 year period. That leaves about a 10^10 : 1 preference for the torture.

The only considerations that dull my certainty here is that I'm not convinced that my utility function can even encompass these sorts of ordinary incomprehensible numbers, but it seems to me that there is at least a one-in-a-billion chance that it can.

So, if additive utility functions are naive, does that mean I can swap around your preferences at random like jerking around a puppet on a string, just by having a sealed box in the next galaxy over where I keep a googol individuals who are already being tortured for fifty years, or already getting dust specks in their eyes, or already being poked with a stick, etc., which your actions cannot possibly affect one way or the other?

It seems I can arbitrarily vary your "non-additive" utilities, and hence your priorities, simply by messing with the numbers of existing people having various experiences in a sealed box in a galaxy a googol light years away.

This seems remarkably reminiscent of E. T. Jaynes's experience with the "sophisticated" philosophers who sniffed that of course naive Bayesian probability theory had to be abandoned in the face of paradox #239; which paradox Jaynes would proceed to slice into confetti using "naive" Bayesian theory but with this time with rigorous math instead of the various mistakes the "sophisticated" philosophers had made.

There are reasons for preferring certain kinds of simplicity.

Michael Vassar:
Well, in the prior comment, I was coming at it as an egoist, as the example demands.
It's totally clear to me that a second of torture isn't a billion billion billion times worse than getting a dust speck in my eye, and that there are only about 1.5 billion seconds in a 50 year period. That leaves about a 10^10 : 1 preference for the torture.
I reject the notion that each (time,utility) event can be calculated in the way you suggest. Successive speck-type experiences for an individual (or 1,000 successive dust specks for 1,000,000 individuals) over the time period we are talking about would easily overtake 50 years of torture. It doesn't make sense to tally (total human disutility of torture (1 person/50 years in this case))(some quantification of the disutility of a time unit of torture) vs. (total human speck disutility)(some quantification of a unit of speck disutility).
The universe is made up of distinct beings (animals included), not the sum of utilities (which is just a useful contruct.)
All of this is to say:
If we are to choose for ourselves between these scenarios, I think it is incredibly bizarre to prefer 3^^^3 satisfying lives and one indescribably horrible life to 3^^^3 infinitesimally better lives than the alternative 3^^^3 lives. I think doing so ignores basic human psychology, from whence our preferences arise.

To continue this business of looking at the problem from different angles:

Another formulation, complementary to Andrew Macdonald's, would be: Should 3^^^3 people each volunteer to experience a speck in the eye, in order to save one person from fifty years of torture?

And with respect to utility functions: Another nonlinear way to aggregate individual disutilities x, y, z... is just to take the maximum, and to say that a situation is only as bad as the worst thing happening to any individual in that situation. This could be defended if one's assignment of utilities was based on intensity of experience, for example. There is no-one actually having a bad experience with 3^^^3 times the badness of a speck in the eye. As for the fact that two people suffering identically turns out to be no worse than just one - accepting a few counterintuitive conclusions is a small price to pay for simplicity, right?

I find it positively bizarre to see so much interest in the arithmetic here, as if knowing how many dust flecks go into a year of torture, just as one knows that sixteen ounces go into one pint, would inform the answer.

What happens to the debate if we absolutely know the equation:

3^^^3 dustflecks = 50 years of torture

or

3^^^3 dustflecks = 600 years of torture

or

3^^^3 dustfleck = 2 years of torture ?

The nation of Nod has a population of 3^^^3. By amazing coincidence, every person in the nation of Nod has $3^^^3 in the bank. (With a money suplly like that, those dollars are not worth much.) By yet another coincidence, the government needs to raise revenues of $3^^^3. (It is a very efficient government and doesn't need much money.) Should the money be raised by taking $1 from each person, or by simply taking the entire amount from one person?

I take $1 from each person. It's not the same dilemma.

----

Ri:The idea of convincing others to decide TORTURE is bothering me much more than my own decision.

PK:I don't think there's any worry that I'm off to get my "rack winding certificate" :P

Yes, I know. :-) I was just curious about the biases making me feel that way.

individual living 3^^^3 times...keep memories and so on of all previous lives

3^^^3 lives worth of memories? Even at one bit per life, that makes you far from human. Besides, you're likely to get tortured in googolplexes of those lifetimes anyway.

Arrrgh, stop messing with my head. Actually, no, don't stop, this is fun! :)

OK here goes... it's this life. Tonight, you start fifty years being loved at by countless sadistic Barney the Dinosaurs. Or, for all 3^^^3 lives you (at your present age) have to singalong to one of his songs. BARNEYLOVE or SONGS?

Andrew Macdonald asked:
Any takers for the torture?
Assuming the torture-life is randomly chosen from the 3^^^3 sized pool, definitely torture. If I have a strong reason to expect the torture life to be found close to the beginning of the sequence, similar considerations as for the next answer apply.

Recovering irrationalist asks:
OK here goes... it's this life. Tonight, you start fifty years being loved at by countless sadistic Barney the Dinosaurs. Or, for all 3^^^3 lives you (at your present age) have to singalong to one of his songs. BARNEYLOVE or SONGS?
The answer depends on whether I expect to make it through the 50 year ordeal without permanent psychological damage. If I know with close to certainty that I will, the answer is BARNEYLOVE. Otherwise, it's SONGS; while I might still acquire irreversible psychological damage, it would probably take much longer, giving me a chance to live relatively sane for a long time before then.

Cooking something for two hours at 350 degrees isn't equivalent to cooking something at 700 degrees for one hour.

Caledonian has made a great analogy for the point that is being made on either side. May I over-work it?

They are not equivalent, but there is some length of time at 350 degrees that will burn as badly as 700 degrees. In 3^^^3 seconds, your lasagna will be ... okay, entropy will have consumed your lasagna by then, but it turns into a cloud of smoke at some point.

Correct me if I am wrong here, but I don't think there is any length of time at 75 or 100 degrees that will burn as badly as one hour at 700 degrees. It just will not cook at all. Your food will sit there and rot, rather than burning.

There must be some minimum temperature at which various things can burn. Given enough time at that temperature, it is the equivalent of just setting it on fire. Below that temperature, it is qualitatively different. You do not get bronze no matter how long you leave copper and tin at room temperature.

(Or maybe I am wrong there. Maybe a couple of molecules will move properly at room temperature over a few centures, so the whole mass becomes bronze in less than 3^^^3 seconds. I assume that anything physically possible will happen at some point in 3^^^3 seconds.)

Are there any SPECKS advocates who say we should pick two people tortured for 49.5 years rather than one for 50 years? If there is any degree of summation possible, 3^^^3 will get us there.

But, SPECKS can reply, there can be levels across with summation is not possible. If lasagna physically cannot burn at 75 degrees, even letting it "cook" for 33^^^^33 seconds, then it will never be as badly burned as one hour at 700 degrees.

"Did I say 75?" TORTURE replies. "I meant whatever the minimum possible is for lasagna to burn, plus 1/3^^3 degrees." SPECKS must grant victory in that case, but wins at 2/3^^3 degrees lower.

Which just returns the whole thing back to the primordial question-begging on either side, whether specks can ever sum to torture. If any number of beings needing to blink ever adds to 10 seconds of torture, TORTURE is in a very strong position, unless you are again arguing that 10 seconds of TORTURE is like 75 degrees, and there is some magic penny somewhere.

(Am I completely wrong? Aren't physics and chemistry full of magic pennies like escape velocities and temperatures needed for physical reactions?)

TORTURE must argue that yes, it is the sort of thing that adds. SPECKS must argue that it is like asking how many blades of grades you must add to get a battleship. "Mu."

Zubon, we could formalize this with a tiered utility function (one not order-isomorphic to the reals, but containing several strata each order-isomorphic to the reals).

But then there is a magic penny, a single sharp divide where no matter how many googols of pieces you break it into, it is better to torture 3^^^3 people for 9.99 seconds than to torture one person for 10.01 seconds. There is a price for departing the simple utility function, and reasons to prefer certain kinds of simplicity. I'll admit you can't slice it down further than the essentially digital brain; at some point, neurons do or don't fire. This rules out divisions of genuine googolplexes, rather than simple billions of fine gradations. But if you admit a tiered utility function, it will sooner or later come down to one neuron firing.

And I'll bet that most Speckists disagree on which neuron firing is the magical one. So that for all their horror at us Unspeckists, they will be just as horrified at each other, when one of them claims that thirty seconds of waterboarding is better than 3^^^3 people poked with needles, and the other disagrees.

...except that, if I'm right about the biases involved, the Speckists won't be horrified at each other.

If you trade off thirty seconds of waterboarding for one person against twenty seconds of waterboarding for two people, you're not visibly treading on a "sacred" value against a "mundane" value. It will rouse no moral indignation.

Indeed, if I'm right about the bias here, the Speckists will never be able to identify a discrete jump in utility across a single neuron firing, even though the transition from dust speck to torture can be broken up into a series of such jumps. There's no difference of a single neuron firing that leads to the feeling of a comparison between a sacred and an unsacred value. The feeling of sacredness, itself, is quantitative and comes upon you in gradual increments of neurons firing - even though it supposedly describes a utility cliff with a slope higher than 3^^^3.

The prohibition against torture is clearly very sacred, and a dust speck is clearly very unsacred, so there must be a cliff sharper than 3^^^3 between them. But the distinction between one dust speck and two dust specks doesn't seem to involve a comparison between a sacred and mundane value, and the distinction between 50 and 49.99 years of torture doesn't seem to involve a comparison between a sacred and a mundane value...

So we're left with cyclical prefrences. The one will trade 3 people suffering 49.99 years of torture for 1 person suffering 50 years of torture; after having previously traded 9 people suffering 49.98 years of torture for 3 people suffering 49.99 years of torture; and so on back to the starting point where it's better for 3^999999999 people to feel two dust specks than for 3^1000000000 people to feel one dust speck; right after, a moment before, having traded one person suffering 50 years of torture for 3^1000000000 people feeling one dust speck.

Assuming that there are 3^^^3 distinct individuals in existence, I think the answer is pretty obvious- pick the torture. However, the fact that we cannot possibly hope to visualize so many individuals it's a pointlessly large number. In fact, I would go so low as one quadrillion human beings with dust specks in their eyes outweighs one individual's 50 years of torture. Consider- one quadrillion seconds of minute but noticeable pain versus a scant fifty years of tortured hell. One quadrillion seconds is about 31,709,792 years. Let's just go with 32 million years. Then factor in the magnitudes- torture is far worse than dust specks- 50 years versus 32 million good enough odds for you?

However, that being said, the question is yet another installment of lifeboat ethics, and has little bearing on the real world. If we are ever forced to make such a decision, that's one thing, but in the meantime let's work through systemic issues that might lead to such a situation instead.

My initial reaction (before I started to think...) was to pick the dust specks, given that my biases made the suffering caused by the dust specks morally equivalent to zero, and 0^^^3 is still 0.

However, given that the problem stated an actual physical phenomenon (dust specks), and not a hypothetical minimal annoyance, then you kind of have to take the other consequences of the sudden appearance of the dust specks under consideration, don't you?

If I was omnipotent, and I could make everyone on Earth get a dust speck in their eye right now, how many car accidents would occur? Heavy machinery accidents? Workplace accidents? Even if the chance is vanishingly small -- let's say 6 accidents occur on Earth because everyone got a dust speck in their eye. That's one in a billion.

That's one accident for every 10e9 people. Now, what percentage of those are fatal? Transport Canada currently lists the 23.7 of car accidents in 2003 as resulting in a fatality, which is 1 in 4. Let's be nice, and assume that everywhere else on earth safer, and take that down to 1 in 100 accidents being fatal.

Now, if everyone in existence gets a dust speck in their eye because of my decision, assuming the hypothetical 3^^^3 people live in something approximating the lifestyles on Earth, I've conceivably doomed 1 in 10e11 people to death.

That is, my cloud of dust specks have killed 3^^^3 / 10e11 people.

I have a question/answer in relation to this post that seems to be off-topic for the forum. Click on my name if interested.

If the poor bastard being tortured is G. W. Bush, I'm all for it . . .

Since I would not be one of the people affected I would not consider myself able to make that decision alone. In fact my preferences are irrelevant in that situation even if I consider situation to be obvious.

To have situation with 3^^^3 people we must have at least that many people capable of existing in some meaningful way. I assume we cannot query them about their preferences in any meaningful (omniscient) way. As I cannot choose who will be tortured or who gets dust specks I have to make collective decission.

I think that my solution would be to take three different groups of randomly chosen people. First group would be asked that question and given chance to discuss and change their minds. Second group would be asked would they save 3^^^3 people from dust specks by accepting torture. Third group would be asked would they agree to be dust specked giving person to be tortured 1/3^^^3 chance to be saved.

If one of the latter tests would show significant preference over one of the situations I would assume it is for some reason more acceptable given chance to choose. If it would seem that people are either willing to change scenario given chance in both situations or not willing to change situation in either scenario I would rely on their stated preference from first group and go by that.

I do not think this solution is good enough.

Evolution seems to have favoured the capacity for empathy (the specks choice) over the capacity for utility calculation, even though utility calculation would have been a 'no brainer' for the brain capacity we have.
The whole concept reminds me of the Turing test. Turing, as a mathematician, just seems to have completely failed to understand that we don't assign rationality, or sentience, to another object by deduction. We do it by analogy.

I know that this is only a hypothetical example, but I must admit that I'm fairly shocked at the number of people indicating that they would select the torture option (as long as it wasn't them being tortured). We should be wary of the temptation to support something unorthodox for the effect of: "Hey, look at what a hardcore rationalist I can be." Real decisions have real effects on real people.

And we should be wary to select something orthodox for fear of provoking shock and outrage. Do you have any reason to believe that the people who say they prefer TORTURE to SPECKS are motivated by the desire to prove their rationalist credentials, or that they don't appreciate that their decisions have real consequences?

Jeffrey, on one of the other threads, I volunteered to be the one tortured to save the others from the specks.

As for "Real decisions have real effects on real people," that's absolutely correct, and that's the reason to prefer the torture. The utility function implied by preferring the specks would also prefer lowering all the speed limits in the world in order to save lives, and ultimately would ban the use of cars. It would promote raising taxes by a small amount in order to reduce the amount of violent crime (including crimes involving torture of real people), and ultimately would promote raising taxes on everyone until everyone could barely survive on what remains.

Yes, real decisions have real effects on real people. That's why it's necessary to consider the total effect, not merely the effect on each person considered as an isolated individual, as those who favor the specks are doing.

Following your heart and not your head - refusing to multiply - has also wrought plenty of havoc on the world, historically speaking. It's a questionable assertion (to say the least) that condoning irrationality has less damaging side effects than condoning torture.

"Following your heart and not your head - refusing to multiply - has also wrought plenty of havoc on the world, historically speaking. It's a questionable assertion (to say the least) that condoning irrationality has less damaging side effects than condoning torture."

I'm not really convinced that multiplication of the dust-speck effect is relevant. Subjective experience is restricted to individuals, not collectives. To me, this specific exercise reduces to a simpler question: Would it be better (more ethical) to torture individual A for 50 years, or inflict a dust speck on individual B?

If the goal is to be a utilitarian ethicist with the well-being of humanity as your highest priority; then something may be wrong with your model when the vast majority of humans would choose the option that you wouldn't. (As I suspect they would). Utility isn't all that matters to most people. Is utilitarianism the only "real" ethics?

My criticisms can sometimes come across the wrong way. (And I know that you actually do care about humanity, Eli.) I don't mean to judge here, just strongly disagree. Not that I retract what I wrote; I don't.

Jeffrey wrote: To me, this specific exercise reduces to a simpler question: Would it be better (more ethical) to torture individual A for 50 years, or inflict a dust speck on individual B? Gosh. The only justification I can see for that equivalence would be some general belief that badness is simply independent of numbers. Suppose the question were: Which is better, for one person to be tortured for 50 years or for everyone on earth to be tortured for 49 years? Would you really choose the latter? Would you not, in fact, jump at the chance to be the single person for 50 years if that were the only way to get that outcome rather than the other one?

In any case: since you now appear to be conceding that it's possible for someone to prefer TORTURE to SPECKS for reasons other than a childish desire to shock, are you retracting your original accusation and analysis of motives? ... Oh, wait, I see you've explicitly said you aren't. So, you know that one leading proponent of the TORTURE option actually does care about humanity; you agree (if I've understood you right) that utilitarian analysis can lead to the conclusion that TORTURE is the less-bad option; I assume you agree that reasonable people can be utilitarians; you've seen that one person explicitly said s/he'd be willing to be the one tortured; but in spite of all this, you don't retract your characterization of that view as shocking; you don't retract your implication that people who expressed a preference for TORTURE did so because they want to show how uncompromisingly rationalist they are; you don't retract your implication that those people don't appreciate that real decisions have real effects on real people. I find that ... well, "fairly shocking", actually.

(It shouldn't matter, but: I was not one of those advocating TORTURE, nor one of those opposing it. If you care, you can find my opinions above.)

Jeffrey, do you really think serial killing is no worse than murdering a single individual, since "Subjective experience is restricted to individuals"?

In fact, if you kill someone fast enough, he may not subjectively experience it at all. In that case, is it no worse than a dust speck?

"Suppose the question were: Which is better, for one person to be tortured for 50 years or for everyone on earth to be tortured for 49 years? Would you really choose the latter? Would you not, in fact, jump at the chance to be the single person for 50 years if that were the only way to get that outcome rather than the other one?"

My criticism was for this specific initial example, which yes did seem "obvious" to me. Very few, if any, ethical opinions can be generalized over any situation and still seem reasonable. At least by my definition of "reasonable".

Notice that I didn't single anyone out as being "bad". Morality is subjective and I don't dispute that. "Every man is right by his own mind". I cautioned that we shouldn't allow a desire to stand-out factor into a decision such as this. I know well that theatrics isn't an uncommon element on mailing lists/blogs. This example shocked me because toy decisions can become real decisions. I have a hunch that I wouldn't be the only person shocked by this. If this specific example were put before all of humanity, I imagine that the people who were not shocked by it, would be the minority. I don't think that I'm being unreasonable.

I can see myself spending too much time here, so I'm going to finish-up and ya'll can have the last word. I'll admit that it's possible that one or more of you actually would sacrifice yourself to save others from a dust speck. Needless to say, I think it would be a huge mistake on your part. I definitely wouldn't want you to do it on my behalf, if for nothing more than selfish reasons: I don't want it weighing on my conscience. Hopefully this is a moot point anyway, since it should be possible to avoid both unwanted dust specks and unwanted torture (eg. via a Friendly AI). We should hope that torture dies-away with the other tragedies of our past, and isn't perpetuated into our not-yet-tarnished future.

I know you're all getting a bit bored, but I'm curious what you think about a different scenario:

What if you have to choose between (a) for the next 3^^^3 days, you get an extra speck in your eye per day than normally, and 50 years you're placed in stasis, or (b) you get the normal amount of specks in your eyes, but during the next 3^^^3 days you'll pass through 50 years of atrocious torture.

Everything else is considered equal in the other cases, including the fact that (i) your total lifespan will be the same in both cases (more than 3^^^3 days), (ii) the specks are guaranteed to not cause any physical effects other than those mentioned in the original post (i.e., you're minimally annoyed and blink once more each day; there are no "tricks" about hidden consequences of specks), (iii) any other occurrence of specks in the eye (yours or others') or torture (you or others) will happen exactly the same for either choice, (iv) the 50 years of either stasis or torture would happen at the same points and (v) after the end of the 3^^^3 days the state of the world is exactly the same except for you (e.g., the genie doesn't come back with something tricky).

Also assume that the 3^^^3 days you are human-shaped and human-minded, except for the change that your memory (and ability to use it) is stretched to work over the duration as a typical human's does during a typical life.

Does your answer change if either:
A) it's guaranteed that everything else is perfectly equal (e.g., the two possible cases will magically be forbidden to interfere with any of your decisions during the 3^^^3 days, but afterwards you'll remember them; in the case of torture, any remaining trauma will remain until healed "physically". More succinctly, there are no side effects during the 3^^^3 days, and none other than the "normal" ones afterwards).
B) the 50 years of torture happen at the start, end, or distributed throughout the period.
C) we replace the life period with either (i) your entire lifespan or (ii) infinity, and/or the period of torture with (i) any constant length larger than one year or (ii) any constant fraction of the lifespan discussed.
D) you are magically justified to put absolute certain trust in the offer (i.e., you're sure the genie isn't tricking you).
E) replace "speck in the eye" by "one hair on your body grows by half the normal amount" for each day.

Of course, you don't have to address every variation mentioned, just those that you think relevant.

OK, I see I got a bit long-winded. The interesting part of my question is if you'd take the same decision if it's about you instead of others. The answer is obvious, of course ;-)

The other details/versions I mentioned are only intended to explore the "contour of the value space" of the other posters. (: I'm sure Eliezer has a term for this, but I forget it.)

Bogdan's presented almost exactly the argument that I too came up with while reading this thread. I would choose the specks in that argument and also in the original scenario (as long as I am not committing to the same choice being repeated an arbitrary number of times, and I am not causing more people to crash their cars than I cause not to crash their cars; the latter seems like an unlikely assumption, but thought experiments are allowed to make unlikely assumptions, and I'm interested in the moral question posed when we accept the assumption). Based on the comments above, I expect that Eliezer is perfectly consistent and would choose torture, though (as in the scenario with 3^^^3 repeated lives).

Eliezer and Marcello do seem to be correct in that, in order to be consistent, I would have to choose a cut-off point such that n dust specks in 3^^^3 eyes would be less bad than one torture, but n+1 dust specks would be worse. I agree that it seems counterintuitive that adding just one speck could make the situation "infinitely" worse, especially since the speckists won't be able to agree exactly where the cut-off point is.

But it's only the infinity that's unique to speckism. Suppose that you had to choose between inflicting one minute of torture on one person, or putting n dust specks into that person's eye over the next fifty years. If you're a consistent expected utility altruist, there must be some n such that you would choose n specks, but not n+1 specks. What makes the n+1st speck different? Nothing, it just happens to be the cut-off point you must choose if you don't want to choose 10^57 specks over torture, nor torture over zero specks. If you make ten altruists consider the question independently, will they arrive at exactly the same value of n? Prolly not.

The above argument does not destroy my faith in decision theory, so it doesn't destroy my provisional acceptance of speckism, either.

I came across this post only today, because of the current comment in the "recent comments" column. Clearly, it was an exercise that drew an unusual amount of response. It further reinforces

my impression of much of the OB blog, posted in August, and denied by email.

I think you should ask everyone until you have at least 3^^^3 people whether they would consent to having a dust speck fly into their eye to save someone from torture. When you have enough people just put dust specks into their eyes and save the others.

The question is, of course, silly. It is perfectly rational to decline to answer. I choose to try to answer.

It is also perfectly rational to say "it depends". If you really think "a dust speck in 3^^^3 eyes" gives a uniquely defined probability distribution over different subsets of possibilityverse, you are being ridiculous. But let's pretend it did - let's pretend we had 3^^^^3 parallel Eleizers, standing on flat golden surfaces in 1G and one atmosphere, for just long enough to ask each other enough enough questions to define the problem properly. (I'm sorry, Eleizer, if by stating that possibility, I've increased the "true"ness of that part of the probabilityverse by ((3^^^3+1)/3^^^3) :) ).

You can or "I've thought about it, but I don't trust my thought processes". That is not my position.

My position is that this question does not, in fact, have an answer. I think that that fact is very important.

It's not that the numbers are meaningless. 3^^^3 is a very exact number, and you can prove any number of things about it. A different question using ridiculous numbers - say, would you rather torture 4^^^4 people for 5 minutes or 3^^^3 of them for 50 years - has a single correct answer which is very clear (of course, the 3^^^3 ones; 4^^^4 >>> (3^^^3)^2). (Unless there were very bizarre extra conditions on the problem.)

It's just that there is no universal moral utility function which inputs a probability distribution over a finite subset of the possibilityverse and outputs a number. It's more like relativistic causality - substitute "better" for "after". A is after B and B is a spacelike distance from C, but C can also be spacelike from A. The dust specks and the torture are incomparable, a spacelike distance.

I think that, philosophically, that makes a big difference. If you pilosophically can't always go around morally comparing near-infinite sets, then it's silly to try to approximate how you would behave if you could. Which means you consider the moral value of the consequences which you could possibly anticipate. So yeah, if you are working on AI, you are morally obligated to think about FAI, because that's intentional action, and you would have to be a monster to say you didn't care. But you don't get to use FAI and the singularity to trump the here-and-now, because in many ways they're just not comparable.

Which means, to me, for instance, that people can understand the singularity idea and believe it has a non-0 probability, and have abilities or resources that would be meaningful to the FAI effort, and still morally choose to simply live as "good people" in a more traditional sense (have a good life in which they make the people with whom they interact overall happier). It's not just a lack of ability to trace the consequences; it's also the possibility that the consequences of this or that outcome will be literally incomparable by any finite halting algorithm, whereas even our desperately-limited brains have decent approximations of algorithms for morally comparing the effect of, say, posting on OB versus washing the dishes.

Going to wash the dishes now.

Tim: You're right - if you are a reasonably attractive and charismatic person. Otherwise, the question (from both sides) is worse than the dust speck.

(Asking people also puts you in the picture. You must like to spend eternity asking people a silly question, and learning all possible linguistic vocalizations in order to do so. There are many fewer vocalizations than possible languages, and many fewer possible human languages than 3^^^3. You will be spending more time going from one person of the SAME language to another, at 1 femtosecond per journey, than you would spend learning all possible human languages. That would be true even if the people were fully shuffled by language - just 1 femtosecond each for all the times when coincidence gives you two of the same language in a row. 3^^^3 is that big.)

Torture is not the obvious answer, because torture-based suffering and dust-speck-based suffering are not scalar quantities with the same units.

To be able to make a comparison between two quantities, the units must be the same. That's why we can say that 3 people suffering torture for 49.99 years is worse than 1 person suffering torture for 50 years. Intensity Duration Number of People gives us units of PainIntensity-Person-Years, or something like that.

Yet torture-based suffering and dust-speck-based suffering are not measured in the same units. Consequently, we cannot solve this question as a simple math problem. For example, the correct units of torture-based suffering might involve Sanity-Destroying-Pain. There is no reason to believe that we can quantitatively compare Easily-Recoverable-Pain to Sanity-Destroying-Pain; at least, the comparison is not just a math problem.

To be able to do the math, we would have to convert both types of suffering to the same units of disutility. Some folks here seem to think that no matter what the conversion functions are, 3^^^3 is just so big that the converted disutility of 3^^3 dust specs is greater than the converted disutility of 50 years of torture for one person. But determination of the correct disutility conversion functions is itself a philosophical problem that cannot be waved away, and it's impossible to evaluate that claim until those conversion functions have at least been hinted at.

One way to get different types of suffering to have the same units would be to represent them as vectors, and find a way to get the magnitude of those vectors.

The torture position seems to do the math by using pain intensity as a scalar. Yet there is no reason to to believe that suffering is a scalar quantity, or that the disutility accorded to suffering is a scalar quantity. Even pain intensity is case where "quantity has a quality all of its own": as you increase it, the suffering goes through qualitative changes. For example, if just a 10% increase in pain duration/intensity causes Post-Traumatic Stress Disorder, that pain is more than 10% worse, and it's because a qualitatively different type of suffering. The units change.

Suffering may well be better represented as a vector. Other dimensions in the vector might include variables such as chance of Post-Traumatic Stress Disorder (0 in the case of dust specks which are uncomfortable but not traumatic, and approaching 100% in the case of torture), non-recovery chance (0% in the case of dust specks, approaching 100% in the case of torture), recovery time (<1 second in the case of dust specks, approaching infinity in the case of 50 years of torture), insanity, human rights violation, career-destruction, mental-health destruction, life destruction...

Choice of pain intensity only over other variables relevant to suffering is begging the question. We could cherry-pick another dimension out of the vector to get a different result, such as life destruction. LifeDestructionChance(50YearsOfTorture) could be greater than LifeDestructionChance(DustSpeck) * 3^^^3 (I might be committing scope insensitivity saying this, but the point is that the answer isn't self-evident). Of course, life destruction isn't the only relevant variable to the calculation of suffering, but neither is pain intensity.

Now, if there is a way to take the magnitude of a suffering vector (another philosophical problem), it's not at all self-evident that Magnitude( SpeckVector ) * 3^^^3 > Magnitude( 50YearsOfTortureVector), because the SpeckVector has virtually all its dimensions approaching 0 while the TortureVector has many dimensions approaching infinity or their max value (which I think reflects why people think torture is so bad). That would depend on what the dimensions of those vectors are and how the magnitude function works.

There is a false choice being offered, because every person in every lifetime is going to experience getting something in their eye, I get a bug flying into my eye on a regular basis whenever I go running (3 of them the last time!) and it'll probably have happened thousands of times to me at the end of my life. It's pretty much a certainty of human experience (Although I suppose it's statistically possible for some people to go through life without ever getting anything in their eyes).

Is the choice being offered to make all humanities eyes for all eternity immune to small inconveniences such as bugs, dust or eyelashes? Otherwise we really aren't being offered anything at all.

Doesn't "harm", to a consequentialist, consist of every circumstance in which things could be better, but aren't ? If a speck in the eye counts, then why not, for example, being insufficiently entertained ?

If you accept consequentialism, isn't it morally right to torture someone to death so long as enough people find it funny ?

It seems that many, including Yudkowsky, answer this question by making the most basic mistake, i.e. by cheating - assuming facts not in evidence.

We don't know anything about (1) the side-effects of picking SPECKS (such as car crashes); and definitely don't know that (2) the torture victim can "acclimate". (2) in particular seems like cheating in a big way - especially given the statement "without hope or rest".

There's nothing rational about posing a hypothetical and then adding in additional facts in your answer. However, that's a great way to avoid the question presented.

The obvious answer is that torture is preferable.

If you have to pick yourself a chance of 1/3^^^3 of 50 years torture vs the dust spec you will pick the torture.

We actually do this every day: we eat foods that can poison us rather than be hungry, we cross the road rather than stay at home, etc.

Imagine there is a safety improvement to your car that will cost 0.0001 cent but will save you from an event that will happen once in 1000 universe lifetimes would you pay for it?

Very-Related Question: Typical homeopathic dilutions are 10^(-60). On average, this would require giving two billion doses per second to six billion people for 4 billion years to deliver a single molecule of the original material to any patient.

Could one argue that if we administer a homeopathic pill of vitamin C in the above dilution to every living person for the next 3^^^3 generations, the impact would be a humongous amount of flu-elimination?

If anyone convinces me that yes, I might accept to be a Torturer. Otherwise, I assume that the negligibility of the speck, plus people's resilience, would make no lasting effects. Disutility would vanish in miliseconds. If they wouldn't even notice or have memory of the specks after a while, it'd equate to zero disutility.

It's not that I can't do the maths. It's that the evil of the speck seems too diluted to do harm.

Just like homeopathy is too diluted to do good.

I doubt anybody's going to read a comment this far down, but what the heck.

Perhaps going from nothing to a million dust specks isn't a million times as bad as going from nothing to one dust speck. One thing is certain though: going from nothing to a million dust specks is exactly as bad as going from nothing to one dust speck plus going from one dust speck to two dust specks etc.

If going from nothing to one dust speck isn't a millionth as bad as nothing to a million dust specks, it has to be made up somewhere else, like going from 999,999 to a million dust specks being more than a millionth as bad.

What if the 3^^^3 were also horribly tortured for fifty years? Would going from that to that plus a dust speck change everything? It's now the worst dust speck you're adding, right?

Ask this to yourself to make the question easier. What would you prefer, getting 3^^^3 dust specks in your eye or being hit with a spiked whip for 50 years.

You must live long enough to feel the 3^^^3 specks in your eye, and each one lasts a fraction of a second. You can feel nothing else but that speck in your eye.

So, it boils down to this question. Would you rather be whipped for 50 years or get specks in your eye for over a googleplex of years.

If I could possible put a marker of the utility of bad that a speck of dust in the eye is, and compare that to the negative utility that a year of depression could be, or being whipped once or having arms broken, it seems impossible that the 50 years of torture could give a more negative value.

In the real world the possiblity of torture obviously hurts more people than just the person being tortured. By theorizing about the utility of torture you are actually subjecting possibly billions of people to periodic bouts of fear and pain.

Forgive me if this has been covered before. The internet here is flaking out and it makes it hard to search for answers.

What is the correct answer to the following scenario: Is it preferable to have one person be tortured if it gives 3^^^3 people a miniscule amount of pleasure?

The source of this question was me pondering the claim, "Pain is temporary; a good story lasts forever."

So, I'm very late into this game, and not through all the sequences (where the answer might already be given), but still, I am very interested in your positions (probably nobody answers, but who knows):

1. Is there a natural number N for which you'd kill one person vs. giving N people one-single dust-speck? (I assume this depends on whether one expects an ever-lasting universe.)
2. Do you "integrate" utility over time (or "experience-moments", as per timeless bla), or is it better to just maximize the "final" point, however one got there?
3. Does breaking up the utility function into several categories really allow dutch-booking, as is indicated in one of the comments? (I hope you understand what I mean with the categories; you've a total strict-order for them, with no two identical, elements within categories "add up", but not even an infinite number of "bad" things in one category can add up to a single one in the next higher one)
4. If "no" for 3, then: For a (current) human we only have neurons, and a real break-point can probably not be determined; but a re-engineered person could implement such a thing. Is it then preferable?

I expect "yes" for 1, and I have to expect "yes" for 3 (I personally do not see this, but I'm bad at math, and have to trust the comments anyway). If "no" for 3, I still expect "no" for 4, per simplicity-argument, retold many times.

I'm very curious for answer on question 2. Once Eliezer quoted "the end does not justify the means", but this sentence is so very much re-interpretable that it's worthless (even if he said otherwise). But as per updating: why should the order of when information is revealed change the final result? Whatever.

When the answers of these questions are somewhere in the sequences, just ignore this, I will sooner or later get to them.

I'd gladly get a speck of dust in my eye as many times as I can, and I'm sure those 3^^^3 people would join me, to keep one guy from being tortured for 50 years.

"Would you prefer that one person be horribly tortured for fifty years without hope or rest, or that 3^^^3 people get dust specks in their eyes?

I think the answer is obvious. How about you?"

Yes, Eliezer, the answer is obvious. The answer is that this is a false dilemma, and that I should go searching for the third alternative, with neither 3^^^3 dust specks nor 50 years of torture. These are not optimal alternatives.

Construct a thought experiment in which every single one of those 3^^^3 is asked whether he would accept a dust speck in the eye to save someone from being tortured, take the answers as a vote. If the majority would deem it personally acceptable, then acceptable it is.

Interesting question. I think a similar real-world situation is when people cut in line.

Suppose there is a line of 100 people, and the line is moving at a rate of 1 person per minute.

Is it ok for a new person to cut to the front of the line, because it only costs each person 1 extra minute, or should the new person stand at the back of the line and endure a full 100 minute wait?

Of course, not everyone in line endures the same wait duration; a person near the front will have a significantly shorter wait than a person near the back. To address that issue one could average the wait times of everyone in line and say that there is an average wait time of 49.5 minutes per person in line [Avg(n) = (n-1) + Avg(n-1)].

Is it ok for a second person to also cut to the front of the line? How many people should be allowed to cut to the front, and which people of those who could possibly cut to the front should be allowed to do so?

I would prefer the dust motes, and strongly. Pain trumps inconvenience.

And yet...we accept automobiles, which kill tens of thousands of people per year, to avoid inconvenience. (That is, automobiles in the hands of regular people, not just trained professionals like ambulance drivers.) But it's hard to calculate the benefits of having a vehicle.

Reducing the national speed limit to 30mph would probably save thousands of lives. I would find it unconscionable to keep the speed limit high if everyone were immortal. At present, such a measure would trade lives for parts of lives, and it's a matter of math to say which is better...though we could easily rearrange our lives to obviate most travel.

Idea 1: dust specks, because on a linear scale (which seems to be always assumed in discussions of utility here) I think 50 years of torture is more than 3^^^3 times worse than a dust speck in one's eye.

Idea 2: dust specks, because most people arbitrarily place bad things into incomparable categories. The death of your loved one is deemed to be infinitely worse than being stuck in an airport for an hour. It is incomparable; any amount of 1 hour waits are less bad than a single loved one dying.

I think it might be interesting to reflect on the possibility that among the 3^^^3 dust speck victims there might be a smaller-but-still-vast number of people being subjected to varying lengths of "constantly-having-dust-thrown-in-their-eyes torture". Throwing one more dust speck at each of them is, up to permuting the victims, like giving a smaller-but-still-vast number of people 50 years of dust speck torture instead of leaving them alone.

(Don't know if anyone else has already made this point - I haven't read all the comments.)

These ethical questions become relevant if we're implementing a Friendly AI, and they are only of academic interest if I interpret them literally as a question about me.

If it's a question about me, I'd probably go with the dust specs. A small fraction of those people will have time to get to me, and of those, none of those people are likely to bother me if it's just a dust speck. If I were to advocate the torture, the victim or someone who knows him might find me and try to get revenge. I just gave you a data point about the psychology of one unmodified human, which is relatively useless, so I don't think that's the question you really wanted answered.

Perhaps the question is really what a non-buggy omnipotent Friendly AI would do. If it has been constructed to care equally about that absurd number of people, IMO it should choose torture. If it's not omnipotent, then it has to consider revenge of the victim, so the correct answer depends on the details of how omnipotent it isn't.

I wonder if some people's aversion to "just answering the question" as Eliezer notes in the comments many times has to do with the perceived cost of signalling agreement with the premises.

It's straightforward to me that answering should take the question at face value; it's a thought experiment, you're not being asked to commit to a course of action. And going by the question as asked the answer for any utilitarian is "torture", since even a very small increment of suffering multiplied by a large enough number of people (or an infinite number) will outweigh a great amount of suffering by one person.

Signalling that would be highly problematic for some people because of what might be read into our answer -- does Eliezer expect that signalling assent here means signalling assent to other, as-yet-unknown conclusions he's made about (whatever issue where that bears some resemblance)? Does Eliezer intend to codify the terms of this premise into the basis for a decision theory underlying the cognitive architecture of a putative Friendly AI? Does Eliezer think that the real world, in short, maps to his gedankenexperiment sufficiently well that the terms of this scenario can meaningfully stand in for decisions made in that domain by real actors (human or otherwise)?

For my own part I'd be very, very hesitant to signal any of that. Hence I find it difficult to answer the question as asked. It's analogous to my discomfort with the Ticking Time Bomb scenario -- by a straight reading of the premise you should trade a finite chance of finding and disabling the bomb, thereby saving a million lives, for the act of torturing the person who planted it. The logic is internally-consistent, but it doesn't map to any real-world situation I can plausibly imagine (where torture is not terribly effective in soliciting confessions, and the scenario of a "ticking time bomb with a single suspect unwilling to talk mere minutes beforehand" has AFAIK never happened as presented, and would be extremely difficult to set up).

I recognize the internal consistency, yet I'm troubled by my uncertainty about what the author thinks I'm signing up for when I reply.

I choose the specks. My utility function u(what happens to person 1, what happens to person 2, ..., what happens to person N) doesn't equal f_1(what happens to person 1) + f_2(what happens to person 2) + ... + f_N(what happens to person N) for any choice of f_1, ..., f_N, not even allowing them to be different; in particular, u(each of n people gets one speck in their eye) doesn't approaches a finite limit as n approaches infinity, and this limit is less negative than u(one person gets tortured than 50 years)

I spent quite a while thinking about this one, and here is my "answer".

My first line of questioning is "can we just multiply and compare the sufferings ?" Well, no. Our utility functions are complicated. We don't even fully know them. We don't exactly know what are terminal values, and what are intermediate values in them. But it's not just "maximize total happiness" (with suffering being negative happiness). My utility function also values things like fairness (it may be because I'm a primate, but still, I value it). The "happiness" part of my utility function will be higher for torture, the "fairness" part of it, lower. Since I don't know the exact coefficient of those two parts, I can't really "shut up and multiply".

But... well... 3^^^3 is well... really a lot. I can't get out this way, even adding correcting terms, even if it's not totally linear, even taking into account fairness, well, 3^^^3 is still going to trump over 1.

So for any realistic computation I would make of my utility function, it seems that "torture" will score higher than "dust speck". So I should chose torture ? Well, not sure yet. For I've ethical rules. What's an ethical rule ? It's an internal law (somehow, a cached thought, from my own computation, or coming from outside) that says "don't ever do that". It includes "do not torture !" it includes "nothing can ever justify torturing someone for 50 years". Why are those rules for ? There are here to protect myself from doing mistakes. Because I can't trust myself fully. I've biases. I don't have full knowledge. I've limited amount of time to take decisions, and I only run at 100Hz. So I need safeguards. I need rules, that I'll follow even when my computation tells me I shouldn't. Those rules can be overridden. But they need to be overridden by something with almost absolute certitude, and to be of the same (or higher) level. No amount of dust speck can trigger an override of the "no torture" rule. I know my history well enough to know that when you allow yourself to torture, because you're "sure" that if you don't something worse will happen, well, you end up becoming the worse. I've high ideals, I've the will to change the world for better - therefore I need rules to prevent me from becoming Stalin or the Holy Inquisition. And that's typically the case. 3^^^3 persons will receive dust speck ? Well, too bad. Sure, it'll be a less optimal utility function than allowing just one person to be tortured. But I don't trust myself to sentence that person to be tortured. So I'll chose dust specks for me and everyone.

If you allow me to argue by fictional evidence, well, that reminds me to the end of Asimov Robot cycle (Robots and Empire, mostly). Warning: spoilers coming. If you didn't read it, go read it, and skip the rest of that paragraph ;) So... when the two robots, Daneel and Giskard, realize the limitations of the First Law: « A robot may not injure a human being or, through inaction, allow a human being to come to harm. », and try to craft the Law Zero: « A robot may not harm humanity, or, by inaction, allow humanity to come to harm. », they end up facing a very difficult problem - one for which they'll need Psychohistory to solve, and even then, only partially. It's relatively easy to know that a human being is in danger,or suffering, and how to help me. It's much, much harder to know that humanity is in danger and how to help it. That's a deep reason behind ethical rules : torture someone is just plain wrong. I may think it's good in that situation, because it'll prevent a Terror Attack, or help me win the war against that horrible Enemy, or because it'll deter crime, or because it'll save 3^^^3 persons from a dust speck. But I just don't trust myself enough to go as far as to torture someone because I computed it would do good overall.

And the last important point on the issue is social rules. There is, in XXIest century western societies at least, a strong taboo on torture. That taboo is a shield. It means than when a president of the USA uses torture, he loses the elections (of course, it's much more complicated, but I think it did play a role). It makes using torture a very, very costly strategy. We have the same with political violence. When the cops attacked a anti-war protest at the Charonne metro station on Feb 8, 1962, killing 9 demonstrators including a 16 years old boy, that was the end of Algeria war. Of course, it wasn't just that. De Gaulle was already trying to stop war, it was lost. But the uproar (nearly half a million of people attended their burial) was so high that the political cost of still supporting the war was made much bigger, so that the end of the war was hastened.

I won't take the responsibility of weakening those taboo (against torture, against political violence, ...) by breaking them myself. The consequences on society, on further people using more torture later on, are too scary.

So, to conclude, I'll chose dust specks. Not because my utility function scores higher on dust speck. But because I can't trust myself enough to wield something as horrible as torture (I've ethical rules, and I'll follow them, even when my computations tell me to do otherwise, for it's the only safeguard I know against becoming Stalin) and because I value way too much the societal taboo against torture to take the responsibility of lowering it.

Now... I've a feeling of discontent for reaching that conclusion, because it coincide with my initial gut-level reaction to the post. It somehow feel like I wrote the bottom line, and then the rationalization. But... I did my best, I did overcome the first "excuse" (non-linearity and valuing fairness) my mind gave me. But I don't find flaws in the two others. And well, reversed stupidity is not intelligence. Reaching the same conclusion that I had intuitively doesn't always mean it's a wrong conclusion.

Let me attempt to shut up and multiply.

Let's make the assumption that a single second of torture is equivalent to 1 billion dust specks to the eye. Since that many dust specks is enough to sandblast your eye, it seems reasonable approximation.

This means that 50 years of this torture is equivalent to giving 1 single person (50 365.25 24 60 60 * 1,000,000,000) dust specks to the eye.

According to Google's calculator,

(50 365.25 24 60 60 1,000,000,000)/(3^39) = 0.389354356 (50 365.25 24 60 60 1,000,000,000)/(3^38) = 1.16806307

Ergo, If someone convinces you 50 years of Torture, or 3^^3(3^27) people get Specks, pick Specks.

But If someone convinces you 50 years of Torture, or (3^50) people get Specks, pick Torture,

This appears to be a fair attempt to shut up and multiply.

However, 3^^^3 is incomprehensibly bigger than any of that.

You could turn every atom into the observable universe into a speck of dust. At wikipedia's almost 10^80 atoms, that is still not enough dust. http://en.wikipedia.org/wiki/Observable_universe

You could turn every planck length in the obseravble universe into a speck of dust. At Answerbag's 2.5 x 10^184 cubic planck lengths, that's still not enough dust. http://www.answerbag.com/q_view/33135

At this point, I thought maybe that another universe made of 10^80 computronium atoms is running universes like ours as simulation on individual atoms. That means 10^80 2.5 x 10^184 cubic planck lengths of dust. But that's still not enough dust. Again. 2.510^264 specks of dust is still WAY less than 3^^^3

At this point, I considered checking if I could get enough dust specks if I literally converted everything in all Everett branches since the big bang beginning of time into dust, but my math abilities fail me. I'll try coming back to this later.

Edit: My multiplication symbols were getting turned into Italics. Should be fixed now.

I tentatively like to measure human experience with logarithms and exponentials. Our hearing is logarithmic, loudness wise, hence the unit dB. Human experiences are rarely linear, thus is it is almost never true that f(x*a) = f(x)*a.

In the above hypothetical, we can imagine the dust specks and the torture. If we propose that NO dust speck ever does anything other than cause mild annoyance, never one enters the eye of a driver who blinks at an inopportune time and crashes; then I would propose we can say: awfulness(pain) = k^pain.

A dust speck causes approximately Dust = epsilon Dols (unit of pain, think the opposite of hedons) while intense, effective torture causes possibly several kiloDols per second. Now it is simply a matter to say Torture = W kDol/s * 50 years, for some reasonable W; Lastly compare k^Dust * 3^^^3 <=> k^Torture.

My utility function has non-zero terms for preferences of other people. If I asked each one of the 3^^^3 people whether they would prefer a dust speck if it would save someone a horrible fifty-year torture, they (my simulation of them) would say YES in 20*3^^^3-feet letters.

The mathematical object to use for the moral calculations needs not be homologous to real numbers.

My way of seeing it is that the speck of dust barely noticeable will be strictly smaller than torture no matter how many instances of speck of dust happen. That's just how my 'moral numbers' operate. The speck of dust equals A>0, the torture equals B>0, the A*N<B holds for any finite N . . I forbid infinities (the number of distinct beings is finite).

If you think that's necessarily irrational you have a lot of mathematics to learn. You can start with ordinal numbers.

edit: note, i am ignoring consequences of the specks in the eyes as I think they are not the point of the exercise and only obfuscate everything plus one has to make assumptions like specks ending up in eyes of people whom are driving.

Choosing TORTURE is making a decision to condemn someone to fifty years of torture, while knowing that 3^^^3 people would not want you to do so, would beg you not to, would react with horror and revulsion if/when they knew you did it. And you must do it for the sake of some global principle or something. I'd say it puts one at least into Well-intentioned Extremist / KnightTemplar category, if not outright villain.

If an AI had made a choice like that, against known wishes of practically everyone, I'd say it was rather unfriendly.

ADDED: Detailed

People who choose torture, if the question was instead framed as the following would you still choose torture?

"Assuming you know your lifespan will be at least 3^^^3 days, would you choose to experience 50 years worth of torture, inflicted a day at a time at intervals spread evenly across your life span starting tomorrow, or one dust speck a day for the next 3^^^3 days of your life?"

Common sense tells me the torture is worse. Common sense is what tells me the earth is flat. Mathematics tells me the dust specks scenario is worse. I trust mathematics and will damn one person to torture.

This "moral dilemma" only has force if you accept strict Bentham-style utilitarianism, which treats all benefits and harms as vectors on a one-dimensional line, and cares about nothing except the net total of benefits and harms. That was the state of the art of moral philosophy in the year 1800, but it's 2012 now.

There are published moral philosophies which handle the speck/torture scenario without undue problems. For example if you accepted Rawls-style, risk-averse choice from a position where you are unaware whether you will be one of the speck-victims or the torture victim, you would immediately choose the specks. Choosing the specks maximises the welfare of the least well off (they are subject to a speck, not torture) and, if you don't know which role you will play, eliminates the risk you might be the torture victim.

(Bentham-style utility calculations are completely risk-neutral and care only about expected return on investment. However nothing about the universe I'm aware of requires you to be this way, as opposed to being risk-averse).

Or for that matter if you held a modified version of utilitarianism that subscribed to some notion of "justice" or "what people deserve", and cared about how utility was distributed between persons instead of being solely concerned with the strict mathematical sum of all utility and disutility, you could just say that you don't care how many dust specks you pile up, the degree of unfairness in a distribution where 3^^^3 people get out of a dust speck and one person gets tortured makes the torture scenario a less preferable distribution.

I know Eliezer's on record as advising people not to read philosophy, but I think this is a case where that advice is misguided.

The dusk speck is a slight irritation. Hearing about somone being tortured is a bigger irritation. Also, pain depends on greatly on concentration. Something that hurts "twice as much" is actually much worse: lets say it is a hundred times worse. Offcourse this levels off (it is a curve) at some point, but in this case that is not problem as we can say that the torture is very close to the physical max and the speck's are very close to the physical minimum pain. The difference between the Speck and the torture is immense. Differense in time = 1.5 M. Difference in hurting 2 M. So we can have a huge number (like 2 Million to the power of 24 Mi to the power of 1.5 Mi). This number is going to be huge. Even if this does not add up to our number of specks one can see that one can define perimeters to make either side the better choice. In the end it is just a moral question.

At first, I picked the dust specks as being the preferable answer, and it seemed obvious. What eventually turned me around was when I considered the opposite situation -- with GOOD things happening, rather than BAD things. Would I prefer that one person experience 50 years of the most happiness realistic in today's world, or that 3^^^3 people experience the least good, good thing?

I was very surprised to find that a supporter of the Complexity of Value hypothesis and the author who warns against simple utility functions advocates torture using simple pseudo-scientific utility calculus.

My utility function has constraints that prevent me from doing awful things to people, unless it would prevent equally awful things done to other people. That this is a widely shared moral intuition is demonstrated by the reaction in the comments section. Since you recognize the complexity of human value, my widely-shared preferences are presumably valid.

In fact, the mental discomfort caused by people who heard of the torture would swamp the disutility from the dust specks. Which brings us to an interesting question - is morality carried by events or by information about events? If nobody else knew of my choice, would that make it better?

For a utilitarian, the answer is clearly that the information about morally significant events is what matters. I imagine so-called friendly AI bots built on utilitarian principles doing lots of awful things in secret to achieve its ends.

Also, I'm interested to hear how many torturers would change their mind if we kill the guy instead of just torturing him. How far does your "utility is all that matters" philosophy go?

No. One of those actions, or something different, happens if I take no action. Assuming that neither the one person nor the 3^^^3 people have consented to allow me to harm them, I must choose the course of action by which I harm nobody, and the abstract force harms people.

If you instead offer me the choice where I prevent the harm (and that the 3^^^3+1 people all consent to allow me to do so), then I choose to prevent the torture.

My maximal expected utility is one in which there is a universe in which I have taken zero additional actions without the consent of every other party involved. With that satisfied, I seek to maximize my own happiness. It would make me happier to prevent a significant harm than to prevent an insignificant harm, and both would be preferable to preventing no harm, all other things being equal.

If the people in question consented to the treatment, then the decision is amoral, and I would choose to inflict the insignificant harm.

From a strict utility perspective, if you describe the value the torture as -1, do you describe the value of the speck of dust in one person's eye as less than -1/(3^^^3)? There is some epsilon for which it is preferable to have harm of epsilon done to any real number of people than to have harm of -1 done to one person. Admitting that does not prohibit you from comparing epsilons, either.

How bad is the torture option?

Let's say a human brain can have ten thoughts per second; or the rate of human awareness is ten perceptions per second. Fifty years of torture means just over one and a half billion tortured thoughts, or perceptions of torture.

Let's say a human brain can distinguish twenty logarithmic degrees of discomfort, with the lowest being "no discomfort at all", the second-lowest being a dust speck, and the highest being torture. In other words, a single moment of torture is 2^19 = 524288 times worse than a dust speck; and a dust speck is the smallest discomfort possible. Let's call a unit of discomfort a "dol" (from Latin dolor).

In other words, the torture option means 1.5 billion moments × 2^19 dols; whereas the dust-specks option means 3^^^3 moments × 1 dol.

The assumptions going into this argument are the speed of human thought or perception, and the scale of human discomfort or pain. These are not accurately known today, but there must exist finite limits — humans do not think or perceive infinitely fast; and the worst unpleasantness we can experience is not infinitely bad. I have assumed a log scale for discomfort because we use log scales for other senses, e.g. brightness of light and volume of sound. However, all these assumptions can be empirically corrected based on facts about human neurology.

Torture is really, really bad. But it is not infinitely bad.

That said, there may be other factors in the moral calculation of which to prefer. For instance, the moral badness of causing a particular level of discomfort may not be linear in the amount of discomfort: causing three dols once may be worse than causing one dol three times. However, this seems difficult to justify. Discomfort is subjective, which is to say, it is measured by the beholder — and the beholder only has so much brain to measure it with.

I think I have to go with the dust specks. Tomorrow, all 3^^^3 of those people will have forgotten entirely about the speck of dust. It is an event nearly indistinguishable from thermal noise. People, all of them everywhere, get dust specks in their eyes just going about their daily lives with no ill effect.

The torture actually hurts someone. And in a way that's rather non-recoverable. Recoverability plays a large part in my moral calculations.

But there's a limit to how many times I can make that trade. 3^^^3 people is a LOT of people, and it doesn't take a significant fraction of THAT at all before I have to stop saving torture victims, lest everyone everywhere's lives consist of nothing but a sandblaster to the face.

If asked independently whether or not I would take an eyeball speck in the eye to spare a stranger 50 years of torture, i would say "sure". I suspect most people would if asked independently. It should make no difference to each of those 3^^^3 dust speck victims that there are another (3^^^3)-1 people that would also take the dust speck if asked.

It seems then that there are thresholds in human value. Human value might be better modeled by sureals than reals. In such a system we could represent the utility of 50 years of torture as -Ω and represent the utility of a dust speck in one's eye as -1. This way, no matter how many dust specks end up in eyes, they don't add up to torturing someone for 50 years. However we would still minimize torture, and minimize dust specks.

The greater problem is to exhibit a general procedure for when we should treat one fate as being infinitely worse than another, vs. treating it as merely being some finite amount worse.

The other day, I got some dirt in my eye, and I thought "That selfish bastard, wouldn't go and get tortured and now we all have to put up with this s#@$".

I don't see that it's necessary -- or possible, for that matter -- for me to assign dust specks and torture to a single, continuous utility function. On a scale of disutility that includes such events as "being horribly tortured," the disutility of a momentary irritation such as a dust speck in the eye has a value of precisely zero -- not 0.000...0001, but just plain 0, and of course, 0 x 3^^^3 = 0.

Furthermore, I think the "minor irritations" scale on which dust specks fall might increase linearly with the time of exposure, and would certainly increase linearly with number of individuals exposed to it. On the other hand, the disutility of torture, given my understanding of how memory and anticipation affect people's experience of pain, would increase exponentially over time from a range of a few microseconds to a few days, then level off to something less than a linear increase with acclimatization over the range of days to years. It would increase linearly with the number of people suffering a given degree of pain for a given amount of time. (All other things being equal, of course. People's pain tolerance varies with age, experience, and genetics; it would be much worse to inflict any given amount of pain on a young child than on an adult who's already gone through, say, Navy S.E.A.L. training, and thus demonstrated a far higher-than-average pain tolerance.)

Thus, it would be enormously worse to inflict X amount of pain on one individual for sixty minutes than on 60 individuals for one minute each, which in turn would be much worse than inflicting the same pain on 3600 individuals for one second each -- and if we could spread it out to a microsecond each for 36,000,000 people, the disutility might vanish altogether as the "experience" becomes too brief for the human nervous system to register at all, and thus ceases to be an experience. However, once we get past where acclimatization inflects the curve, it would be much worse to torture 52 people for one week each than to torture one person for an entire year. It might even be worse to torture ten people for one week each than one for an entire year -- I'm not sure of the precise values involved in this utility function, and happily, at the fine scale, I'll probably never need to work them out (the empirical test is possible in principle, of course, but could only be performed in practice by a fiend like Josef Mengele).

There's also the fact that knowing many people can and have endured a particular pain seems to make it more endurable for others who are aware of that fact. As Spider Robinson says, "Shared joy is increased, shared pain is lessened" -- I don't know if that really "refutes entropy," but both of those clauses are true individually. That's part of the reason egalitarianism, as other commenters have pointed out, has positive utility value.

Incidentally, I think that if you pick "dust specks," you're asserting that you would walk away from Omelas; if you pick torture, you're asserting that you wouldn't.

Bravo, Eliezer. Anyone who says the answer to this is obvious is either WAY smarter than I am, or isn't thinking through the implications.

Suppose we want to define Utility as a function of pain/discomfort on the continuum of [dust speck, torture] and including the number of people afflicted. We can choose whatever desiderata we want (e.g. positive real valued, monotonic, commutative under addition).

But what if we choose as one desideratum, "There is no number n large enough such that Utility(n dust specks) > Utility(50 yrs torture)." What does that imply about the function? It can't be analytic in n (even if n were continuous). That rules out multaplicative functions trivially.

Would it have singularities? If so, how would we combine utility functions at singular values? Take limits? How, exactly?

Or must dust specks and torture live in different spaces, and is there no basis that can be used to map one to the other?

The bottom line: is it possible to consistently define utility using the above desideratum? It seems like it must be so, since the answer is obvious. It seems like it must not be so, because of the implications for the utility function as the arguments change.

Edit: After discussing with my local meetup, this is somewhat resolved. The above desiderata require the utility to be bounded in the number of people, n. For example, it could be a staurating exponential function. This is self-consistent, but inconsistent with the notion that because experience is independent, utilities should add.

Interestingly, it puts strict mathematical rules on how utility can scale with n.

To me, this experiment shows that absolute utilitarianism does not make a good society. Conversely, a decision between, say, person A getting $100 and person B getting $1 or both of them getting $2 shows absolute egalitarianism isn't satisfactory either (assuming simple transfers are banned). Perhaps the inevitable realization...is that some balance between them is possible, such as the weighted sum (sum indicating utilitarianism) with more weight applied to those who have less (this indicating egalitarianism) can provide such a balance?