The "Intuitions" Behind "Utilitarianism"

Followup toCircular AltruismResponse toKnowing your argumentative limitations, OR "one [rationalist's] modus ponens is another's modus tollens."

(Still no Internet access.  Hopefully they manage to repair the DSL today.)

I haven't said much about metaethics - the nature of morality - because that has a forward dependency on a discussion of the Mind Projection Fallacy that I haven't gotten to yet.  I used to be very confused about metaethics.  After my confusion finally cleared up, I did a postmortem on my previous thoughts.  I found that my object-level moral reasoning had been valuable and my meta-level moral reasoning had been worse than useless.  And this appears to be a general syndrome - people do much better when discussing whether torture is good or bad than when they discuss the meaning of "good" and "bad".  Thus, I deem it prudent to keep moral discussions on the object level wherever I possibly can.

Occasionally people object to any discussion of morality on the grounds that morality doesn't exist, and in lieu of jumping over the forward dependency to explain that "exist" is not the right term to use here, I generally say, "But what do you do anyway?" and take the discussion back down to the object level.

Paul Gowder, though, has pointed out that both the idea of choosing a googolplex dust specks in a googolplex eyes over 50 years of torture for one person, and the idea of "utilitarianism", depend on "intuition".  He says I've argued that the two are not compatible, but charges me with failing to argue for the utilitarian intuitions that I appeal to.

Now "intuition" is not how I would describe the computations that underlie human morality and distinguish us, as moralists, from an ideal philosopher of perfect emptiness and/or a rock. But I am okay with using the word "intuition" as a term of art, bearing in mind that "intuition" in this sense is not to be contrasted to reason, but is, rather, the cognitive building block out of which both long verbal arguments and fast perceptual arguments are constructed.

I see the project of morality as a project of renormalizing intuition.  We have intuitions about things that seem desirable or undesirable, intuitions about actions that are right or wrong, intuitions about how to resolve conflicting intuitions, intuitions about how to systematize specific intuitions into general principles.

Delete all the intuitions, and you aren't left with an ideal philosopher of perfect emptiness, you're left with a rock.

Keep all your specific intuitions and refuse to build upon the reflective ones, and you aren't left with an ideal philosopher of perfect spontaneity and genuineness, you're left with a grunting caveperson running in circles, due to cyclical preferences and similar inconsistencies.

"Intuition", as a term of art, is not a curse word when it comes to morality - there is nothing else to argue from.  Even modus ponens is an "intuition" in this sense - it's just that modus ponens still seems like a good idea after being formalized, reflected on, extrapolated out to see if it has sensible consequences, etcetera.

So that is "intuition".

However, Gowder did not say what he meant by "utilitarianism".  Does utilitarianism say...

  1. That right actions are strictly determined by good consequences?
  2. That praiseworthy actions depend on justifiable expectations of good consequences?
  3. That probabilities of consequences should normatively be discounted by their probability, so that a 50% probability of something bad should weigh exactly half as much in our tradeoffs?
  4. That virtuous actions always correspond to maximizing expected utility under some utility function?
  5. That two harmful events are worse than one?
  6. That two independent occurrences of a harm (not to the same person, not interacting with each other) are exactly twice as bad as one?
  7. That for any two harms A and B, with A much worse than B, there exists some tiny probability such that gambling on this probability of A is preferable to a certainty of B?

If you say that I advocate something, or that my argument depends on something, and that it is wrong, do please specify what this thingy is... anyway, I accept 3, 5, 6, and 7, but not 4; I am not sure about the phrasing of 1; and 2 is true, I guess, but phrased in a rather solipsistic and selfish fashion: you should not worry about being praiseworthy.

Now, what are the "intuitions" upon which my "utilitarianism" depends?

This is a deepish sort of topic, but I'll take a quick stab at it.

First of all, it's not just that someone presented me with a list of statements like those above, and I decided which ones sounded "intuitive".  Among other things, if you try to violate "utilitarianism", you run into paradoxes, contradictions, circular preferences, and other things that aren't symptoms of moral wrongness so much as moral incoherence.

After you think about moral problems for a while, and also find new truths about the world, and even discover disturbing facts about how you yourself work, you often end up with different moral opinions than when you started out.  This does not quite define moral progress, but it is how we experience moral progress.

As part of my experienced moral progress, I've drawn a conceptual separation between questions of type Where should we go? and questions of type How should we get there?  (Could that be what Gowder means by saying I'm "utilitarian"?)

The question of where a road goes - where it leads - you can answer by traveling the road and finding out.  If you have a false belief about where the road leads, this falsity can be destroyed by the truth in a very direct and straightforward manner.

When it comes to wanting to go to a particular place, this want is not entirely immune from the destructive powers of truth.  You could go there and find that you regret it afterward (which does not define moral error, but is how we experience moral error).

But, even so, wanting to be in a particular place seems worth distinguishing from wanting to take a particular road to a particular place.

Our intuitions about where to go are arguable enough, but our intuitions about how to get there are frankly messed up.  After the two hundred and eighty-seventh research study showing that people will chop their own feet off if you frame the problem the wrong way, you start to distrust first impressions.

When you've read enough research on scope insensitivity - people will pay only 28% more to protect all 57 wilderness areas in Ontario than one area, people will pay the same amount to save 50,000 lives as 5,000 lives... that sort of thing...

Well, the worst case of scope insensitivity I've ever heard of was described here by Slovic:

Other recent research shows similar results. Two Israeli psychologists asked people to contribute to a costly life-saving treatment. They could offer that contribution to a group of eight sick children, or to an individual child selected from the group. The target amount needed to save the child (or children) was the same in both cases. Contributions to individual group members far outweighed the contributions to the entire group.

There's other research along similar lines, but I'm just presenting one example, 'cause, y'know, eight examples would probably have less impact.

If you know the general experimental paradigm, then the reason for the above behavior is pretty obvious - focusing your attention on a single child creates more emotional arousal than trying to distribute attention around eight children simultaneously.  So people are willing to pay more to help one child than to help eight.

Now, you could look at this intuition, and think it was revealing some kind of incredibly deep moral truth which shows that one child's good fortune is somehow devalued by the other children's good fortune.

But what about the billions of other children in the world?  Why isn't it a bad idea to help this one child, when that causes the value of all the other children to go down?  How can it be significantly better to have 1,329,342,410 happy children than 1,329,342,409, but then somewhat worse to have seven more at 1,329,342,417?

Or you could look at that and say:  "The intuition is wrong: the brain can't successfully multiply by eight and get a larger quantity than it started with.  But it ought to, normatively speaking."

And once you realize that the brain can't multiply by eight, then the other cases of scope neglect stop seeming to reveal some fundamental truth about 50,000 lives being worth just the same effort as 5,000 lives, or whatever.  You don't get the impression you're looking at the revelation of a deep moral truth about nonagglomerative utilities.  It's just that the brain doesn't goddamn multiply.  Quantities get thrown out the window.

If you have $100 to spend, and you spend $20 each on each of 5 efforts to save 5,000 lives, you will do worse than if you spend $100 on a single effort to save 50,000 lives.  Likewise if such choices are made by 10 different people, rather than the same person.  As soon as you start believing that it is better to save 50,000 lives than 25,000 lives, that simple preference of final destinations has implications for the choice of paths, when you consider five different events that save 5,000 lives.

(It is a general principle that Bayesians see no difference between the long-run answer and the short-run answer; you never get two different answers from computing the same question two different ways.  But the long run is a helpful intuition pump, so I am talking about it anyway.)

The aggregative valuation strategy of "shut up and multiply" arises from the simple preference to have more of something - to save as many lives as possible - when you have to describe general principles for choosing more than once, acting more than once, planning at more than one time.

Aggregation also arises from claiming that the local choice to save one life doesn't depend on how many lives already exist, far away on the other side of the planet, or far away on the other side of the universe.  Three lives are one and one and one.  No matter how many billions are doing better, or doing worse. 3 = 1 + 1 + 1, no matter what other quantities you add to both sides of the equation.  And if you add another life you get 4 = 1 + 1 + 1 + 1.  That's aggregation.

When you've read enough heuristics and biases research, and enough coherence and uniqueness proofs for Bayesian probabilities and expected utility, and you've seen the "Dutch book" and "money pump" effects that penalize trying to handle uncertain outcomes any other way, then you don't see the preference reversals in the Allais Paradox as revealing some incredibly deep moral truth about the intrinsic value of certainty.  It just goes to show that the brain doesn't goddamn multiply.

The primitive, perceptual intuitions that make a choice "feel good" don't handle probabilistic pathways through time very skillfully, especially when the probabilities have been expressed symbolically rather than experienced as a frequency.  So you reflect, devise more trustworthy logics, and think it through in words.

When you see people insisting that no amount of money whatsoever is worth a single human life, and then driving an extra mile to save $10; or when you see people insisting that no amount of money is worth a decrement of health, and then choosing the cheapest health insurance available; then you don't think that their protestations reveal some deep truth about incommensurable utilities.

Part of it, clearly, is that primitive intuitions don't successfully diminish the emotional impact of symbols standing for small quantities - anything you talk about seems like "an amount worth considering".

And part of it has to do with preferring unconditional social rules to conditional social rules.  Conditional rules seem weaker, seem more subject to manipulation.  If there's any loophole that lets the government legally commit torture, then the government will drive a truck through that loophole.

So it seems like there should be an unconditional social injunction against preferring money to life, and no "but" following it.  Not even "but a thousand dollars isn't worth a 0.0000000001% probability of saving a life".  Though the latter choice, of course, is revealed every time we sneeze without calling a doctor.

The rhetoric of sacredness gets bonus points for seeming to express an unlimited commitment, an unconditional refusal that signals trustworthiness and refusal to compromise.  So you conclude that moral rhetoric espouses qualitative distinctions, because espousing a quantitative tradeoff would sound like you were plotting to defect.

On such occasions, people vigorously want to throw quantities out the window, and they get upset if you try to bring quantities back in, because quantities sound like conditions that would weaken the rule.

But you don't conclude that there are actually two tiers of utility with lexical ordering.  You don't conclude that there is actually an infinitely sharp moral gradient, some atom that moves a Planck distance (in our continuous physical universe) and sends a utility from 0 to infinity.  You don't conclude that utilities must be expressed using hyper-real numbers.  Because the lower tier would simply vanish in any equation.  It would never be worth the tiniest effort to recalculate for it.  All decisions would be determined by the upper tier, and all thought spent thinking about the upper tier only, if the upper tier genuinely had lexical priority.

As Peter Norvig once pointed out, if Asimov's robots had strict priority for the First Law of Robotics ("A robot shall not harm a human being, nor through inaction allow a human being to come to harm") then no robot's behavior would ever show any sign of the other two Laws; there would always be some tiny First Law factor that would be sufficient to determine the decision.

Whatever value is worth thinking about at all, must be worth trading off against all other values worth thinking about, because thought itself is a limited resource that must be traded off.  When you reveal a value, you reveal a utility.

I don't say that morality should always be simple.  I've already said that the meaning of music is more than happiness alone, more than just a pleasure center lighting up.  I would rather see music composed by people than by nonsentient machine learning algorithms, so that someone should have the joy of composition; I care about the journey, as well as the destination.  And I am ready to hear if you tell me that the value of music is deeper, and involves more complications, than I realize - that the valuation of this one event is more complex than I know. 

But that's for one event.  When it comes to multiplying by quantities and probabilities, complication is to be avoided - at least if you care more about the destination than the journey.  When you've reflected on enough intuitions, and corrected enough absurdities, you start to see a common denominator, a meta-principle at work, which one might phrase as "Shut up and multiply."

Where music is concerned, I care about the journey.

When lives are at stake, I shut up and multiply.

It is more important that lives be saved, than that we conform to any particular ritual in saving them.  And the optimal path to that destination is governed by laws that are simple, because they are math.

And that's why I'm a utilitarian - at least when I am doing something that is overwhelmingly more important than my own feelings about it - which is most of the time, because there are not many utilitarians, and many things left undone.

</rant>

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Eliezer, to be clear, do you still think that 3^^^3 people having momentary eye irritations--from dust-specs--is worth torturing a single person for 50 years, or is there a possibility that you did the math incorrectly for that example?

No. I used a number large enough to make math unnecessary.

I specified the dust specks had no distant consequences (no car crashes etc.) in the original puzzle.

Unless the torture somehow causes Vast consequences larger than the observable universe, or the suicide of someone who otherwise would have been literally immortal, it doesn't matter whether the torture has distant consequences or not.

I confess I didn't think of the suicide one, but I was very careful to choose an example that didn't involve actually killing anyone, because there someone was bound to point out that there was a greater-than-tiny probability that literal immortality is possible and would otherwise be available to that person.

So I will specify only that the torture does not have any lasting consequences larger than a moderately sized galaxy, and then I'm done. Nothing bound by lightspeed limits in our material universe can morally outweigh 3^^^3 of anything noticeable. You'd have to leave our physics to do it.

You know how some people's brains toss out the numbers? Well, when you're dealing with a number like 3^^^3 in a thought experiment, you can toss out the event descriptions. If the thing being multiplied by 3^^^3 is good, it wins. If the thing being multiplied by 3^^^3 is bad, it loses. Period. End of discussion. There are no natural utility differences that large.

Unless the torture somehow causes Vast consequences larger than the observable universe, or the suicide of someone who otherwise would have been literally immortal, it doesn't matter whether the torture has distant consequences or not.

What about the consequences of the precedent set by the person making the decision that it is ok to torture an innocent person, in such circumstances? If such actions get officially endorsed as being moral, isn't that going to have consequences which mean the torture won't be a one-off event?

There's a rather good short story about this, by Ursula K LeGuin:

The Ones Who Walk Away From Omelas

If such actions get officially endorsed as being moral, isn't that going to have consequences which mean the torture won't be a one-off event?

Why would it?

And I don't think LeGuin's story is good - it's classic LeGuin, by which I mean enthymematic, question-begging, emotive substitution for thought, which annoyed me so much that I wrote my own reply.

I've read your story three times now and still don't know what's going on in it. Can I have it in the form of an explanation instead of a story?

I really don't see why I can't say "the negative utility of a dust speck is 1 over Graham's Number." or "I am not obligated to have my utility function make sense in contexts like those involving 3^^^^3 participants, because my utility function is intended to be used in This World, and that number is a physical impossibility in This World."

As a separate response, what's wrong with this calculation: I base my judgments largely on the duration of the disutility. After 1 second, the dust specks disappear and are forgotten, and so their disutility also disappears. The same is not true of the torture; the torture is therefore worse. I can foresee some possible problems with this line of thought, but it's 2:30 am in New Orleans and I just got done with a long evening of drinking and Joint Mathematics Meeting, so please forgive me if I don't attempt to formalize it now.

An addendum: 2 more things. The difference between a life with n dust specks hitting your eye and n+1 dust specks is not worth considering, given how large n is in any real life. Furthermore, if we allow for possible immortality, n could literally be infinity, so the difference would be literally 0.

Secondly, by virtue of your asserting that there exists an action with minimal disutility, you've shown that the Field of Utility is very different from the field of, say, the Real numbers, and so I am incredulous that we can simply "multiply" in the usual sense.

I really don't see why I can't say "the negative utility of a dust speck is 1 over Graham's Number."

You can say anything, but Graham's number is very large; if the disutility of an air molecule slamming into your eye were 1 over Graham's number, enough air pressure to kill you would have negligible disutility.

or "I am not obligated to have my utility function make sense in contexts like those involving 3^^^^3 participants, because my utility function is intended to be used in This World, and that number is a physical impossibility in This World."

If your utility function ceases to correspond to utility at extreme values, isn't it more of an approximation of utility than actual utility? Sure, you don't need a model that works at the extremes - but when a model does hold for extreme values, that's generally a good sign for the accuracy of the model.

An addendum: 2 more things. The difference between a life with n dust specks hitting your eye and n+1 dust specks is not worth considering, given how large n is in any real life. Furthermore, if we allow for possible immortality, n could literally be infinity, so the difference would be literally 0.

If utility is to be compared relative to lifetime utility, i.e. as (LifetimeUtility + x / LifetimeUtility), doesn't that assign higher impact to five seconds of pain for a twenty-year old who will die at 40 than to a twenty-year old who will die at 120? Does that make sense?

Secondly, by virtue of your asserting that there exists an action with minimal disutility, you've shown that the Field of Utility is very different from the field of, say, the Real numbers, and so I am incredulous that we can simply "multiply" in the usual sense.

Eliezer's point does not seem to me predicated on the existence of such a value; I see no need to assume multiplication has been broken.

if the disutility of an air molecule slamming into your eye were 1 over Graham's number, enough air pressure to kill you would have negligible disutility.

Yes, this seems like a good argument that we can't add up disutility for things like "being bumped into by particle type X" linearly. In fact, it seems like having 1, or even (whatever large number I breathe in a day) molecules of air bumping into me is a good thing, and so we can't just talk about things like "the disutility of being bumped into by kinds of particles".

If your utility function ceases to correspond to utility at extreme values, isn't it more of an approximation of utility than actual utility?

Yeah, of course. Why, do you know of some way to accurately access someone's actually-existing Utility Function in a way that doesn't just produce an approximation of an idealization of how ape brains work? Because me, I'm sitting over here using an ape brain to model itself, and this particular ape doesn't even really expect to leave this planet or encounter or affect more than a few billion people, much less 3^^^3. So it's totally fine using something accurate to a few significant figures, trying to minimize errors that would have noticeable effects on these scales.

Sure, you don't need a model that works at the extremes - but when a model does hold for extreme values, that's generally a good sign for the accuracy of the model.

Yes, I agree. Given that your model is failing at these extreme values and telling you to torture people instead of blink, I think that's a bad sign for your model.

doesn't that assign higher impact to five seconds of pain for a twenty-year old who will die at 40 than to a twenty-year old who will die at 120? Does that make sense?

Yeah, absolutely, I definitely agree with that.

Sean, one problem is that people can't follow the arguments you suggest without these things being made explicit. So I'll try to do that:

Suppose the badness of distributed dust specks approaches a limit, say 10 disutility units.

On the other hand, let the badness of (a single case of ) 50 years of torture equal 10,000 disutility units. Then no number of dust specks will ever add up to the torture.

But what about 49 years of torture distributed among many? Presumably people will not be willing to say that this approaches a limit less than 10,000; otherwise we would torture a trillion people for 49 years rather than one person for 50.

So for the sake of definiteness, let 49 years of torture, repeatedly given to many, converge to a limit of 1,000,000 disutility units.

48 years of torture, let's say, might converge to 980,000 disutility units, or whatever.

Then since we can continuously decrease the pain until we reach the dust specks, there must be some pain that converges approximately to 10,000. Let's say that this is a stubbed toe.

Three possibilities: it converges exactly to 10,000, to less than 10,000, or more than 10,000. If it converges to less, than if we choose another pain ever so slightly greater than a toe-stubbing, this greater pain will converge to more than 10,000. Likewise, if it converges to more than 10,000, we can choose an ever so slightly less pain that converges to less than 10,000. If it converges to exactly 10,000, again we can choose a slightly greater pain, that will converge to more than 10,000.

Suppose the two pains are a stubbed toe that is noticed for 3.27 seconds, and one that is noticed for 3.28 seconds. Stubbed toes that are noticed for 3.27 seconds converge to 10,000 or less, let's say 9,999.9999. Stubbed toes that are notice for 3.28 seconds converge to 10,000.0001.

Now the problem should be obvious. There is some number of 3.28 second toe stubbings that is worse than torture, while there is no number of 3.27 second toe stubbings that is worse. So there is some number of 3.28 second toe stubbings such that no number of 3.27 second toe stubbings can ever match the 3.28 second toe stubbings.

On the other hand, three 3.27 second toe stubbings are surely worse than one 3.28 second toe stubbings. So as you increase the number of 3.28 second toe stubbings, there must be a magical point where the last 3.28 second toe stubbing crosses a line in the sand: up to that point, multiplied 3.27 second toe stubbings could be worse, but with that last 3.28 second stubbing, we can multiply the 3.27 second stubbings by a googleplex, or by whatever we like, and they will never be worse than that last, infinitely bad, 3.28 second toe stubbing.

So do the asymptote people really accept this? Your position requires it with mathematical necessity.

I assert the use of 3^^^3 in a moral argument is to avoid the effort of multiplying.

Yes, that's what I said. If the quantities were close enough to have to multiply, the case would be open for debate even to utilitarians.

Demonstration: what is 3^^^3 times 6?

3^^^3, or as close as makes no difference.

What is 3^^^3 times a trillion to the trillionth power?

3^^^3, or as close as makes no difference.

...that's kinda the point.

So it seems you have two intuitions. One is that you like certain kinds of "feel good" feedback that aren't necessarily mathematically proportional to the quantifiable consequences. Another is that you like mathematical proportionality.

Er, no. One intuition is that I like to save lives - in fact, as many lives as possible, as reflected by my always preferring a larger number of lives saved to a smaller number. The other "intuition" is actually a complex compound of intuitions, that is, a rational verbal judgment, which enables me to appreciate that any non-aggregative decision-making will fail to lead to the consequence of saving as many lives as possible given bounded resources to save them.

I'm feeling a bit of despair here... it seems that no matter how I explain that this is how you have to plan if you want the plans to work, people just hear, "You like neat mathematical symmetries." Optimal plans are neat because optimality is governed by laws and the laws are math - it has nothing to do with liking neatness.

50 years of being tortured is not (50 years 365 days 24 hours * 3600 seconds)-times worse than 1-second of torture. It is much (non-linearly) worse than that.

Utilitarianism does not assume that multiple experiences to the same person aggregate linearly.

Yes, I agree that it is non-linearly worse.

It is not infinitely worse. Just non-linearly worse.

The non-linearity factor is nowhere within a trillion to the trillionth power galaxies as large as 3^^^3.

If it were, no human being would ever think about anything except preventing torture or goals of similar importance. You would never take a single moment to think about putting an extra pinch of salt in your soup, if you felt a utility gradient that large. For that matter, your brain would have to be larger than the observable universe to feel a gradient that large.

I do not think people understand the largeness of the Large Number here.

I share El's despair. Look at the forest, folks. The point is that you have to recognize that harm aggregates (and not to an asymptote) or you are willing to do terrible things. The idea of torture is introduced precisely to make it hard to see. But it is important, particularly in light of how easily our brains fail to scale harm and benefit. Geez, I don't even have to look at the research El cites - the comments are enough.

Stop saying the specks are "zero harm." This is a thought experiment and they are defined as positive harm.

Stop saying that torture is different. This is a thought experiment and torture is defined to be absolutely terrible, but finite, harm.

Stop saying that torture is infinite harm. That's just silly.

Stop proving the point over and over in the comments!

/rant/

A dust speck in the eye with no external ill effects was chosen as the largest non-zero negative utility. Torture, absent external effects (e.g., suicide), for any finite time, is a finite amount of negative utility. Death in a world of literal immortality cuts off an infinite amount of utility. There is a break in the continuum here.

If you don't accept that dust specks are negative utility, you didn't follow the rules. Pick a new tiny ill effect (like a stubbed toe) and rethink the problem.

If you still don't like it because for a given utility n, n + n != 2n, there are then issues with circular preferences. Two units of utility are defined as twice as "utilitous" as one unit of utility. (This is not saying that two dollars are twice as good as one dollar.)

Bob: "The point of using 3^^^3 is to avoid the need to assign precise values".

But then you are not facing up to the problems of your own ethical hypothesis. I insist that advocates of additive aggregation take seriously the problem of quantifying the exact ratio of badness between torture and speck-of-dust. The argument falls down if there is no such quantity, but how would you arrive at it, even in principle? I do not insist on an impersonally objective ratio of badness; we are talking about an idealized rational completion of one's personal preferences, nothing more. What considerations would allow you to determine what that ratio should be?

Unknown has pointed out that anyone who takes the opposite tack, insisting that 'any amount of X is always preferable to just one case of Y!', faces the problem of boundary cases: keep substituting worse and worse things for X, and eventually one will get into the territory of commensurable evils, and one will start trying to weigh up X' against Y.

However, this is not a knockdown argument for additivism. Let us say that I am clear about my preferences for situations A, D and E, but I am in a quandary with respect to B and C. Then I am presented with an alternative moral philosophy, which offers a clear decision procedure even for B and C, but at the price of violating my original preferences for A, D or E. Should I say, oh well, the desirability of being able to decide in all situations is so great that I should accept the new system, and abandon my original preferences? Or should I just keep thinking about B and C until I find a way to decide there as well? A utility function needs only to be able to rank everything, nothing more. There is absolutely no requirement that the utility (or disutility) associated with n occurrences of some event should scale linearly with n.

This is an important counterargument so I'll repeat it: The existence of problematic boundary cases is not yet a falsification of an ethical heuristic. Give your opponent a chance to think about the boundary cases, and see what they come up with! The same applies to my challenge to additive utilitarians, to say how they would arrive at an exact ratio: I am not asserting, apriori, that it is impossible. I am pointing out that it must be possible for your argument to be valid, and I'm giving you a chance to indicate how this can be done.

This whole thought experiment was, I believe, meant to illustrate a cognitive bias, a preference which, upon reflection, would appear to be mistaken, the mistake deriving from the principle that 'sacred values', such as an aversion to torture, always trump 'nonsacred values', like preventing minor inconveniences. But premises which pass for rational in a given time and culture - which are common sense, and just have to be so - can be wrong. The premise here is what I keep calling additivism, and we have every reason to scrutinize as critically as possible any premise which would endorse an evil of this magnitude (the 50 years of torture) as a necessary evil.

One last thought, I don't think Ben Jones's observation has been adequately answered. What if those 3^^^3 people are individually willing to endure the speck of dust rather than have someone tortured on their behalf? Again boundary cases arise. But if we're seriously going to resolve this question, rather than just all reaffirm our preferred intuitions, we need to keep looking at such details.

"Well, when you're dealing with a number like 3^^^3 in a thought experiment, you can toss out the event descriptions. If the thing being multiplied by 3^^^3 is good, it wins. If the thing being multiplied by 3^^^3 is bad, it loses. Period. End of discussion. There are no natural utility differences that large."

Let's assume the eye-irritation lasts 1-second (with no further negative consequences). I would agree that 3^^^3 people suffering this 1-second irritation is 3^^^3-times worse than 1 person suffering thusly. But this irritation should not be considered to be equal to 3^^^3 seconds of wasted lives. In fact, this scenario is so negligibly bad, as to not be worth the mental effort to consider it.

And for the torture option, let's assume that the suffering stops the instant the person finishes their 50 years of pain (the person leaves in exactly the same psychological state they were in before they found out that they would be tortured). However, in this case, 50 years of being tortured is not (50 years 365 days 24 hours * 3600 seconds)-times worse than 1-second of torture. It is much (non-linearly) worse than that. There are other variables to consider. In those 50-years, the person will miss 50 years of life. Unlike the dust-speck irritation distributed across 3^^^3 people, 50 years of torture is worth considering.

Adding experiences across people should linearly impact the estimated utility, but things do not add linearly when considering the experiences of a single person. Even if it doesn't lead to further negative consequences, the one-second of irritation is less than 3^^^3-times as bad as the 50 years of torture.

If you're multiplication has taken you so far afield of your intuitions, re-check the math. If it still comes out the same way, check your assumptions. If it still comes out the same way, go with the calculations.

So it seems you have two intuitions. One is that you like certain kinds of "feel good" feedback that aren't necessarily mathematically proportional to the quantifiable consequences. Another is that you like mathematical proportionality. The "Shut up and multiply" mantra is simply a statement that your second preference is stronger than the first.

In some ways it seems reasonable to define morality in a way that treats all people equally. If we do so, than our preference for multiplying can be more moral, by definition, than our less rational sympathies. But creating a precise definition generally has the result of creating a gap between that definition and common usage. People use the term "morality" and accompanying concepts in a number of ways. Restricting its usage may make a debate more intelligible, but it tends to obscure the fact that morality is a multi-faceted concept that represents a number of different preferences and beliefs. Even meta-morality can do no more than articulate certain kinds of meta-preferences.

Also, equating utilitarianism with Pol Pot and Stalin is a bit disingenuous. Those people weren't utilitarian in any recognizable sense because the total consequences of their actions (millions dead), didn't justify their intended consequences (whatever those were). Millions dead shouldn't be placed solely in the "means" category.

"'A moral action is one which you choose (== that makes you feel good) without being likely to benefit your genes.'"

So using birth control is an inherently moral act? Overeating sweet and fatty foods to the point of damaging your health is an inherently moral act? Please. "Adaptation-executers," &c.

Krishnaswami: I think claims like "exactly twice as bad" are ill-defined. Suppose you have some preference relation on possible states R, so that X is preferred to Y if and only if R(X, Y) holds. Next, suppose we have a utility function U, such that if R(X, Y) holds, then U(X) > U(Y). Now, take any monotone transformation of this utility function. For example, we can take the exponential of U, and define U'(X) = 2^(U(X)). Now, note that U(X) > U(Y) if and only if that U'(X) > U'(Y). Now, even if U is additive along some dimension of X, U' won't be.

Utility functions over outcomes have additional structure beyond tehir ordering, because of how utilities interact with scalar probabilities to produce expected utilities that imply preferences over actions (as distinct from preferences over outcomes).

Taking the exponential of a positive utility function will produce the same preference ordering over outcomes but not the same preference ordering over actions (which is itself a quite interesting observation!) given fixed beliefs about conditional probabilities.

So when I say that two punches to two faces are twice as bad as one punch, I mean that if I would be willing to trade off the distance from the status quo to one punch in the face against a billionth (probability) of the distance between the status quo and one person being tortured for one week, then I would be willing to trade off the distance from the status quo to two people being punched in the face against a two-billionths probability of one person being tortured for one week. ("If...then" because I don't necessarily defend this as a good preference - the actual comparison here is controversial even for utilitarians, since there are no overwhelming quantities involved.)

Any positive affine transformation of the utility function preserves the preference ordering over actions. The above statement is invariant under positive affine transformations of the utility function over outcomes, and thus exposes the underlying structure of the utility function. It's not that events have some intrinsic number of utilons attached to them - a utility function invariantly describes the ratios of intervals between outcomes. This is what remains invariant under a positive affine transformation.

(I haven't heard this pointed out anywhere, come to think, but surely it must have been observed before.)

If harm aggregates less-than-linearly in general, then the difference between the harm caused by 6271 murders and that caused by 6270 is less than the difference between the harm caused by one murder and that caused by zero. That is, it is worse to put a dust mote in someone's eye if no one else has one, than it is if lots of other people have one.

If relative utility is as nonlocal as that, it's entirely incalculable anyway. No one has any idea of how many beings are in the universe. It may be that murdering a few thousand people barely registers as harm, because eight trillion zarquons are murdered every second in Galaxy NQL-1193. However, Coca-Cola is relatively rare in the universe, so a marginal gain of one Coca-Cola is liable to be a far more weighty issue than a marginal loss of a few thousand individuals.

(This example is deliberately ridiculous.)

Ben: suppose the lever has a continuous scale of values between 1 and 3^^^3. When the lever is set to 1, 1 person is being tortured (and the torture will last for 50 years.). If you set it to 2, two people will be tortured by an amount less the first person by 1/3^^^3 of the difference between the 50 years and a dust speck. If you set it to 3, three people will be tortured by an amount less than the first person by 2/3^^^3 of the difference between the 50 years and the dust speck. Naturally, if you pull the lever all the way to 3^^^3, that number of people will suffer the dust specks.

Will you pull the lever over to 3^^^3? And if so, will you assert that things are getting better during the intermediate stages (for example when you are torturing a google persons by an amount less than the first person by an entirely insignificant quantity?) And if things first get worse and then get better, where does it change?

Will you try to pull the lever over to 3^^^3 if there's a significant chance the lever might get stuck somewhere in the middle?

Doug, I do not agree because my utility function depends on the identity of the people involved, not simply on N. Specifically, it might be possible for an agent to become confident that Bob is much more useful to whatever is the real meaning of life than Charlie is, in which case a harm to Bob has greater disutility in my system than a harm to Charlie. In other words, I do not consider egalitarianism to be a moral principle that applies to every situation without exception. So, for me U is not a function of (N,I,T)

I think claims like "exactly twice as bad" are ill-defined.

Suppose you have some preference relation on possible states R, so that X is preferred to Y if and only if R(X, Y) holds. Next, suppose we have a utility function U, such that if R(X, Y) holds, then U(X) > U(Y). Now, take any monotone transformation of this utility function. For example, we can take the exponential of U, and define U'(X) = 2^(U(X)). Now, note that U(X) > U(Y) if and only if that U'(X) > U'(Y). Now, even if U is additive along some dimension of X, U' won't be.

But there's no principled reason to believe that U is a "truer" reflection of the agent's preferences than U', since both of them are equally faithful to the underlying preference relation. So if you want to do meaningful comparisons of utility you have to do them in a way that's invariant under monotone transformations. Since "twice as bad" isn't invariant such a transformation, it's not evidently a meaningful claim.

Now, there might be some additional principle you can advance to justify claims like that, but I haven't seen it, or its justification, yet.

Care to advance an argument, Caledonian? (Not saying I disagree... or agree, for that matter.)

Bob: Sure, if you specify a disutility function that mandates lots-o'-specks to be worse than torture, decision theory will prefer torture. But that is literally begging the question, since you can write down a utility function to come to any conclusion you like. On what basis are you choosing that functional form? That's where the actual moral reasoning goes. For instance, here's a disutility function, without any of your dreaded asymptotes, that strictly prefers specks to torture:

U(T,S) = ST + S

Freaking out about asymptotes reflects a basic misunderstanding of decision theory, though. If you've got a rational preference relation, then you can always give a bounded utility function. (For example, the function I wrote above can be transformed to U(T,S) = (ST + S)/(ST + S + 1), which always gives you a function in [0,1], and gives rise to the same preference relation as the original.) If you absolutely require unbounded utilities in utility functions, then you become subject to a Dutch book (see Vann McGee's "An Airtight Dutch Book"). Attempts to salvage unbounded utility pretty much always end up accepting certain Dutch books as rational, which means you've rejected the whole decision-theoretic justification of Bayesian probability theory. Now, the existence of bounds means that if you have a monotone utility function, then the limits will be well-defined.

So asymptotic reasoning about monotonically increasing harms is entirely legit, and you can't rule it out of bounds without giving up on either Bayesianism or rational preferences.

Larry D'anna:

You are dealing with an asymptote. There is a limit to how bad momentary eye-irritation can be, no matter how many people it happens to.

By positing that dust-speck irritation aggregates non-linearly with respect to number of persons, and thereby precisely exemplifying the scope-insensitivity that Eliezer is talking about, you are not making an argument against his thesis; instead, you are merely providing an example of what he's warning against.

You are in effect saying that as the number of persons increases, the marginal badness of the suffering of each new victim decreases. But why is it more of an offense to put a speck in the eye of Person #1 than Person #6873?

It's because something that's non-consequential is non-consequential

The dust specks are consequential; people suffer because of them. The further negative consequences of torture are only finitely bad.

Unknown: 10 years and I would leave the lever alone, no doubt. 1 day is a very hard call; probably I would pull the lever. Most of us could get over 1 day over torture in a way that is fundamentally different from years of torture, after all.

Perhaps you can defend one punch per human being, but there must be some number of human beings for whom one punch each would outweigh torture.

As I said, I don't have that intuition. A punch is a fairly trivial harm. I doubt I would ever feel worse about a lot of people (even 5^^^^^^5) getting punched than about a single individual being tortured for a lifetime. Sorry -- I am just not very aggregative when it comes to these sorts of attitudes.

Is that "irrational?" Frankly, I'm not sure the word applies in the sense you mean. It is inconsistent with most accounts of strict utilitarianism. But I don't agree that abstract ethical theories have truth values in the sense you probably assume. It is consistent with my attitudes and preferences, and with my society's attitudes and preferences, I think. You assume that we should be able to add those attitudes up and do math with them, but I don't see why that should necessarily be the case.

I think the difference is that you are assuming (at least in a very background sort of way) that there are non-natural, mind-independent, moral facts somehow engrafted onto the structure of reality. You feel like those entities should behave like physical entities, however, in being subject to the sort of mathematical relations we have developed based upon our interactions with real-world entities (even if those relations are now used abstractly). Even if you could make a strong argument for the existence of these sorts of moral rules, however, that is a far sight from saying that they should have an internal structure that behaves in a mathematically-tidy way.

You haven't ever given reasons to think that ethical truths ought to obey mathematical rules; you've just assumed it. It's easy to miss this assumption unless you've spent some time mulling over moral ontology, but it definitely animates most of the arguments made in this thread.

In short: unless you've grappled seriously with what you mean when you talk of moral rules, you have very little basis for assuming that you should be able to do sums with them. Is 6 billion punches for everyone "worse than" 50 years of torture for one person? It certainly involves the firing of more pain neurons. But the fact that a number of pain neurons fire is just a fact about the world; it isn't the answer to a moral question, UNLESS you make a large number of assumptions. I agree that we can count neuron-firings, and do sums with them, and all other sorts of things. I just disagree that the firing of pain and pleasure neurons is the sum total of what we mean when we say "it was wrong of Fred to murder Sally."

Ben, that's not about additivism, but indicates that you are a deontologist by nature, as everyone is. A better test: would you flip a lever which would stop the torture if everyone on earth would instantly be automatically punched in the face? I don't think I would.

Again, we return to the central issue:

Why must we accept an additive model of harm to be rational?

Thanks for the explanations, Bob.

Bob: The point of using 3^^^3 is to avoid the need to assign precise values... Once you accept the premise that A is less than B (with both being finite and nonzero), you need to accept that there exists some number k where kA is greater than B.

This still requires that they are commensurable though, which is what seeking a strong argument for. Saying that 3^^^3 dust specks in 3^^^3 eyes is greater harm than 50 years of torture means that they are commensurable and that whatever the utilities are, 3^^^3 specks divided by 50 years of torture is greater than 1.0. I don't see that they are commensurable. A < B < C < D doesn't imply that there's some k such that kA>D.

Consider: I prefer Bach to Radiohead (though I love both). That doesn't imply that there's some ratio of Bach to Radiohead, or that I think a certain number of Radiohead songs are collectively better than or more desirable than, for example, the d-minor partita. Even if I did in some cases believe that 10 Radiohead songs were worth 1 Bach prelude and fugue, that would just be my subjective feeling. I don't see why there must be an objective ratio, and I can't see grounds for saying what such a ratio would be. Likewise for dust-specks and torture.

Like Mitchell, I would like to see exactly how people propose to assign these ratios such that a certan number of one harm is greater than a radically different harm.