Circular Altruism

400 people die, with certainty.

Should that be 100?

1. 400 people die, with certainty.
2. 90% chance no one dies; 10% chance 500 people die.

ITYM 1. 100 people die, with certainty.

Care to test your skills against the Repugnant Conclusion? http://plato.stanford.edu/entries/repugnant-conclusion/

Whilst the your analysis of life-saving choices seems fairly uncontentious, I'm not entirely convinced that the arithmetic of different types of suffering add together the way you assume. It seems at least plausible to me that where dust motes are individual points, torture is a section of a contiuous line, and thus you can count the points, or you can measure the lengths of different lines, but no number of the former will add up to the latter.

I'm sorry, but I find this line of argument not very useful. If I remember correctly (which I may not be doing), a googolplex is larger than the estimated number of atoms in the universe. Nobody has any idea of what it implies except "really, really big", so when your concepts get up there, people have to do the math, since the numbers mean nothing. Most of us would agree that having a really really lot of people bothered just a bit is better than having one person suffer for a long life. That has little to do with math and a lot to do with our preception of suffering and a feeling that each of us has only one life. Worrying about discontinuities in this kind of discussion seems almost puerile.

A more interesting discontinuity that we run into quite frequently is our willingness to make great efforts and sacrifices to save the lives of children and then decide that at the age of 18, young men cease to be children and we send them off to war. What happens in our brains when young men turn 18? Sure these 18 year olds are all testosterone fired up and looking for a fight, but the discontinuity of the moral logic is strange. Have you talked about this at all?

(By the way, one of the saddest museums in the world is in Salta, Argentina, where they display mummies of children who were made drunk and buried alive to placate a now long forgotten god, but that is getting off the point.)

One can easily make an argument like the torture vs. dust specks argument to show that the Repugnant Conclusion is not only not repugnant, but certainly true.

More intuitively, if it weren't true, we could find some population of 10,000 persons at some high standard of living, such that it would be morally praiseworthy to save their lives at the cost of a googolplex galaxies filled with intelligent beings. Most people would immediately say that this is false, and so the Repugnant Conclusion is true.

Eliezer, I am skeptical that sloganeerings ("shut up and calculate") will not get you across this philosophical chasm: Why do you define the best one-off choice as the choice that would be prefered over repeated trials?

Can someone please post a link to a paper on mathematics, philosophy, anything, that explains why there's this huge disconnect between "one-off choices" and "choices over repeated trials"? Lee?

Here's the way across the philosophical "chasm": write down the utility of the possible outcomes of your action. Use probability to find the expected utility. Do it for all your actions. Notice that if you have incoherent preferences, after a while, you expect your utility to be lower than if you do not have incoherent preferences.

You might have a point if there existed a preference effector with incoherent preferences that could only ever effect one preference. I haven't thought a lot about that one. But since your incoherent preferences will show up in lots of decisions, I don't care if this specific decision will be "repeated" (note: none are ever really repeated exactly) or not. The point is that you'll just keep losing those pennies every time you make a decision.

1. Save 400 lives, with certainty.
2. Save 500 lives, with 90% probability; save no lives, 10% probability. What are the outcomes? U(400 alive, 100 dead, I chose choice 1) = A, U(500 alive, 0 dead, I chose choice 2) = B, and U(0 alive, 500 dead, I chose choice 2) = C.

Remember that probability is a measure of what we don't know. The plausibility that a given situation is (will be) the case. If 1.0A > 0.9B + 0.1*C, then I prefer choice 1. Otherwise 2. Can you tell me what's left out here, or thrown in that shouldn't be? Which part of this do you have a disagreement with?

Consider these two facts about me:

(1) It is NOT CLEAR to me that saving 1 person with certainty is morally equivalent to saving 2 people when a fair coin lands heads in a one-off deal.

(2) It is CLEAR to me that saving 1000 people with p=.99 is morally better than saving 1 person with certainty.

Models are supposed to hew to the facts. Your model diverges from the facts of human moral judgments, and you respond by exhorting us to live up to your model.

Why should we do that?

Torture vs dust specks, let me see:

What would you choose for the next 50 days:

1. Removing one mililiter of the daily water intake of 100,000 people.
2. Removing 10 liters of the daily water intake of 1 person.

The consequence of choice 2 would be the death of one person.

Yudkowsky would choose 2, I would choose 1.

This is a question of threshold. Below certain thresholds things don't have much effect. So you cannot simply add up.

Another example:

1. Put 1 coin on the head of each of 1,000,000 people.
2. Put 100,000 coins on the head of one guy.

What do you choose? Can we add up the discomfort caused by the one coin on each of 1,000,000 people?

Eliezer, can you explain what you mean by saying "it's the same gamble"? If the point is to compare two options and choose one, then what matters is their values relative to each other. So, 400 certain lives saved is better than a 90% chance of 500 lives saved and 10% chance of 500 deaths, which is itself better than 400 certain deaths.

Perhaps it would help to define the parameters more clearly. Do your first two options have an upper limit of 500 deaths (as the second two options seem to), or is there no limit to the number of deaths that may occur apart from the lucky 4-500?

Many were proud of this choice, and indignant that anyone should choose otherwise: "How dare you condone torture!" I don't think that's a fair characterization of that debate. A good number of people using many different reasons thought something along the lines of negligible "harm" * 3^^^3<50 years of torture. That many people spraining their ankle or something would be a different story. Those harms are different enough that it's by no means obvious which we should prefer, and it's not clear that trying to multiply is really productive, whereas your examples in this entry are indeed obvious.

"The primary thing is to help others, whatever the means. So shut up and multiply!"

Would you submit to torture for 50 years to save countless people? I'm not sure I would, but I think I'm more comfortable with the idea of being self-interested and seeing all things through the prism of self interest.

Similar problem: if you had this choice--you can die peacefully and experience no afterlife, or literally experience hell for 100 years if one was rewarded with an eternity of heaven, would you choose the latter? Calculating which provides the greatest utility, the latter would be preferable, but I'm not sure I would choose it.

Eliezer, as I'm sure you know, not everything can be put on a linear scale. Momentary eye irritation is not the same thing as torture. Momentary eye irritations should be negligible in the moral calculus, even when multiplied by googleplex^^^googleplex. 50 years of torture could break someone's mind and lead to their destruction. You're usually right on the mark, but not this time.

To get back to the 'human life' examples EY quotes. Imagine instead the first scenario pair as being the last lifeboat on the Titanic. You can launch it safely with 40 people on board, or load in another 10 people, who would otherwise die a certain, wet, and icy death, and create a 1 in 10 chance that it will sink before the Carpathia arrives, killing all. I find that a strangely more convincing case for option 2. The scenarios as presented combine emotionally salient and abstract elements, with the result that the emotionally salient part will tend to be foreground, and the '% probabilities' as background. After all no-one ever saw anyone who was 10% dead (jokes apart).

Eliezer's point would have been valid, had he chosen almost anything other than momentary eye irritation. Even the momentary eye-irritation example would work if the eye irritation would lead to serious harm (e.g. eye inflammation and blindness) in a small proportion of those afflicted with the speck of dust. If the predicted outcome was millions of people going blind (and then you have to consider the resulting costs to society), then Eliezer is absolutely right: shut-up and do the math.

GreedyAlgorithm, this is the conversation I want to have.

The sentence in your argument that I cannot swallow is this one: "Notice that if you have incoherent preferences, after a while, you expect your utility to be lower than if you do not have incoherent preferences." This is circular, is it not?

You want to establish that any decision, x, should be made in accordance w/ maximum expected utility theory ("shut up and calculate"). You ask me to consider X = {x_i}, the set of many decisions over my life ("after a while"). You say that the expected value of U(X) is only maximized when the expected value of U(x_i) is maximized for each i. True enough. But why should I want to maximize the expected value of U(X)? That requires every bit as much (and perhaps the same) justification as maximizing the expected value of U(x_i) for each i, which is what you sought to establish.

(I should say that I assumed that a bag of decisions is worth as much as the sum of the utilities of the individual decisions.)

I'm seconding the worries of people like the anonymous of the first comment and Wendy. I look at the first, and I think "with no marginal utility, it's an expected value of 400 vs an expected value of 450." I look at the second and think "with no marginal utility, it's an expected value of -400 vs. an expected value of -50." Marginal utility considerations--plausible if these are the last 500 people on Earth--sway the first case much more easily than they do the second case.

So we can keep doing this, gradually - very gradually - diminishing the degree of discomfort...

Eliezer, your readiness to assume that all 'bad things' are on a continuous scale, linear or no, really surprises me. Put your enormous numbers away, they're not what people are taking umbrage at. Do you think that if a googol doesn't convince us, perhaps a googolplex will? Or maybe 3^^^3? If x and y are finite, there will always be a quantity of x that exceeds y, and vice versa. We get the maths, we just don't agree that the phenomena are comparable. Broken ankle? Stubbing your toe? Possibly, there is certainly more of a tangible link there, but you're still imposing your judgment on how the mind experiences and deals with discomfort on us all and calling it rationality. It isn't.

Put simply - a dust mote registers exactly zero on my torture scale, and torture registers fundamentally off the scale (not just off the top, off) on my dust mote scale.

You're asking how many biscuits equal one steak, and then when one says 'there is no number', accusing him of scope insensitivity.

Eliezer - the way question #1 is phrased, it is basically a choice between the following:

1. Be perceived as a hero, with certainty.

2. Be perceived as a hero with 90% probability, and continue not to be noticed with 10% probability.

This choice will be easy for most people. The expected 50 extra deaths are a reasonable sacrifice for the certainty of being perceived as a hero.

The way question #2 is phrased, it is similarly a choice between the following:

1. Be perceived as a villain, with certainty.

2. Not be noticed with 90% probability, and be perceived as a villain with 10% probability.

Again, the choice is obvious. Choose #2 to avoid being perceived as a villain.

If you argue that the above interpretations are then not altruistic, I think the "Repugnant Conclusion" link shows how futile it is to try to make actual "altruistic decisions".

I don't think even everyone going blind is a good excuse for torturing a man for fifty years. How are they going to look him in the eye when he gets out?

The problem is not that I'm afraid of multiplying probability by utility, but that Eliezer is not following his own advice - his utility function is too simple.

It will be interesting to see if this is one of the mistakes Eliezer quietly retracts, or one of the mistakes that he insists upon making over and over no matter what the criticism.

I'm betting 10 credibility units on Yudkowsky publicly admitting that he was wrong on this one.

I think I understand the point of the recent series of posts, but I find them rather unsatisfying. It seems to me that there is a problem with translating emotional situations into probability calculations. This is a very real and interesting problem, but saying "shut up and multiply" is not a good way to approach it. Borrowing from 'A Technical Explanation' it's kind of like the blue tentacle question. When I am asked what would I do when faced with the choice between a googolplex of dust specks or 50 years of torture, my reaction is: But that would never happen! Or, perhaps, I would tell the psychopath who was trying to force me to make such a choice to go f- himself.

It seems a lot of people are willing to write off minimal discomfort and approximate that to 0 discomfort, I don't think thats fair at all.

If we are talking in terms of this 'discomfort' lets start out with two sets of K people out of a population of X >>> K people, with each set having the same 'discomfort' applied to them each, set A and set B. One set must bear with the discomfort, which set should we pick?.

Clearly at the start, both are defined to be the same. So we then double the number in set A while halving their discomfort.

One way to define an activity A to be 'half the discomfort' of B is to ask the average person how long will they take activity A for say... $100 and the same for B, if they are willing to take twice as long on A than B, lets call that half. There is no such thing as infinite discomfort because we are dealing with people here, double the number of people you double the discomfort.

Torturing two people for 50 years is twice as bad as torturing one person for fifty years, how do we work that out? well we have some non infinite of discomfort for "torturing for 50 years".

Eventually after many repetitions, we hit on some discomfort which 'suddenly' someone has arbitrary said is ~ 0 discomfort even though it is really some small discomfort. And since 0*K = 0, we can set the number of people in set A to be (X-K) (a bit unfair to have the guys in set B to be in set A too I think, give them a break) yet it will still be better to choose set A over set B. The sum of the discomforts is less in A than B.

Lets say that we are now that the discomfort of A is a speck of dust, and the discomfort of B is 50 years torture. Lets now crank up the discomfort of A, until we hit the precise point that you just about start to care about your discomfort (just before it changes from ~0 to some number). I reckon a stubbed toe would be a good point though I bet even more discomfort would be the true discontinuity point. K is now 1 person, and X is the entire human population of the planet. This is fine because its ~0*6.6 billion = 0, yet you take a stumble after you stub a toe, you lose .1 minutes of your life in a bad way, its not nice, if it was nice then the discomfort would be negative!

But we are all happy right? everyone stubs their toe, and a man (or woman) is saved from 50 years of torture. However, that comes to 1256 years of stubbed toes, that comes to a total of 1256 years of lost living, time spent wincing at your sore toe rather than looking the sky and so on. Is that still acceptable? double the people, 2512 years, still fine? keep on going cause to you (and people in general if your right), the discomfort is ~0.

Keep on doubling that number and watch those wasted pain filled years double and double. If you suddenly say 'ok thats enough, a trillion subbed toes is worse than 50 years torture!' then we simply double the number of people tortured, then half the population stub their toes for one guy, half for the other. Imagine the hundreds of thousands of years humanity has wasted with stubbed toes, and if you dont see that as bad you should wonder if your biased by scope insensitivity.

Mr. Yudkowsky, I'm not sure the duration/intensity of the torture is the only bad thing relevant here. A friend of mine pointed out that a problem with 50 years of torture is that it permanently destroys someone's life. (I think it was in one of the "fake altruism" family of posts that you pointed out that belief of utility != utility of belief.) So the utility curve would be pretty flat for the first couple thousand dust specks, beginning to slope down in proportion to the pain through a few minutes of torture. After that, it would quickly become steeper as the torture began to materially alter the person tortured. Another factor to consider is the difference between pain during which you can do other things, and pain during which you can't. So the 50-year-torturee's (or even a 1-minute torturee's) life is effectively shortened in a way that even a 1,000,000-dust-speck person's life is not. So I'm not sure people aren't implicitly including those factors sometimes, when they get mad about torture. I'd rather five years of chronic back pain than five minutes of permanently soul-crushing torture.

You might argue that it's still irrational, but it's not as obvious as you make it out to be.

This form of reasoning, while correct within a specified context, is dangerously flawed with regard to application within contexts sufficiently complex that outcomes cannot be effectively modeled. This includes much of moral interest to humans. In such cases, as with evolutionary computation, an optimum strategy exploits best-known principles synergisticly promoting a maximally-coherent set of present values, rather than targeting illusory, realistically unspecifiable consequences. Your "rationality" is correct but incomplete. This speaks as well to the well-known paradoxes of all consequentialist ethics.

I'm not sure I understand at what point the torture would no longer be justified. It's easy to say that it is preferable to a googolplex of people with dust specks is worse than one person being tortured, but there has to be some number at which this is no longer the case. At some point even your preferences should flip, but you never suggest a point where it would be acceptable. Would it be somewhere around 1.5-1.6 billion, assuming the dust specks were worth 1 second of pain? Is it acceptable if it is just 2 people affected? How many dust specks go into 1 year of torture? I think people would be more comfortable with your conclusion if you had some way to quantify it; right now all we have is your assertion that the math is in the dust speck's favor.

"I think people would be more comfortable with your conclusion if you had some way to quantify it; right now all we have is your assertion that the math is in the dust speck's favor."

The actual tipping point depends on your particular subjective assessment of relative utility. The actual tipping point doesn't matter; what matters is that there is crossover at some point, therefore such reasoning about preferences, like San Jose --> San Francisco --> Oakland --> San Jose is incoherent.

Roland, I'll take that bet.

The idea of an ethical discontinuity between something that can destroy a life (50 years of torture, or 1 year) and something that can't (1 minute of torture, a dust speck) has some intuitive plausibility, but ultimately I don't buy it. It very much seems like death must be in the same 'regime' as torture, but also that death is in the same regime as trivial harms, because people risk death for trivial benefit all the time - I imagine anyone here would drive across town for $100 or $500 or $1000, even though it's slightly more dangerous than staying at home. The life-destroying aspect means that the physical pain is only part (probably the smaller part) of the harm of prolonged torture, and that the badness of torture rises greater than linearly with duration, but doesn't necessarily make it incommensurable.

I think "Shut up and Multiply" would be a good tagline for this blog, and a nice slogan for us anti-bias types in general!

How come these examples and subsequent narratives never mention the value of floors and diminishing returns? Is every life valued the same? If there was a monster or disease that will kill everyone in the world there is a floor involved. Choice 1 of saving 400 lives ensures that humanity continues (assuming 400 people are enough to re-populate the world). While have a 90% chance of saving 500 leaves 10% chance that humanity on earth ends. Would you agree that floors are important factors that do change the value of an optimal outcome when they are one time events? In other words the marginal utility of a life is diminishing in this example.

The idea of saving someone life has a great value to the person who did the saving. They are a hero even if it is only one life. The subsequent individuals diminish in the utility they deliver because being a hero carries such great a return and only requires saving one person verse everyone. People who choose option 1 are: not doing the math or value life differently between individuals because of the effect it has on them.

The value placed on items is really what matters because we don’t value everything the same. The true question is why do we value them differently or are we really just miscalculating the expected value? Every equation has to be learned from 2+2=4 on and maybe we are just heading up that learning curve.

Save 400 lives, with certainty. Save 500 lives, with 90% probability; save no lives, 10% probability.

I'm surprised how few people are reacting to the implausibility of this thought experiment. When not in statistics class, God rarely gives out priors. Probabilities other than 0+epsilon and 1-epsilon tend to come from human scholarship, which is an often imperfect process. It is hard to imagine a non-contrived situation where you would have as much confidence in the 90/10 outcome as in the certain outcome.

Suppose the "90/10" figure comes from cure rates in a study of 20-year-old men, but your 500 patients are mostly middle-aged. You have the choice of disarming a bomb that will kill 400 people with probability 1-epsilon, or of taking that "90/10" estimate, really, really seriously; I know which choice I would make.

Your conclusion follows very clearly from the research results but it does not apply to the new situation. Doing the math is a false premise. Few people have personal experience of being tortured and more importantly no one who disagrees with you understands what you personally mean by the dust-speck. Perhaps if it was sawdust or getting pool water splashed in your eye, then it would finally register more clearly. Again, you (probably) haven't been tortured but you have gone through life without even conciously registering a dust speck in your eye. With a little adjustment above a threshold many people might switch sides. Pain is not linear.

what matters is that there is crossover at some point

But there isn't necessarily one. That's the point - Eliezer is presuming that dust speck harm is additive and that enough of such harms will equal torture. This presumption does not seem to have a basis in rational argument.

The comments on this post are no better than those on the Torture vs. Dust Specks post. In other words, simply bring the word "torture" into the discussion and people automatically become irrational. It's happened to some of the other threads as well, when someone mentioned torture.

It strongly suggests that not many of the readers have made much progress in overcoming their biases.

By the way, Eliezer has corrected the original post; anonymous was correct about the numbers.

Lee:

Models are supposed to hew to the facts. Your model diverges from the facts of human moral judgments, and you respond by exhorting us to live up to your model.

Be careful not to confuse "is" and "ought". Eliezer is not proposing an empirical model of human psychology ("is"); what he is proposing is a normative theory ("ought"), according to which human intuitive judgements may turn out to be wrong.

If what you want is an empirical theory that accurately predicts the judgements people will make, see denis bider's comment of January 22, 2008 at 06:49 PM.

I don't think even everyone going blind is a good excuse for torturing a man for fifty years. How are they going to look him in the eye when he gets out?

That's cold brother. Real cold....

The idea of an ethical discontinuity between something that can destroy a life (50 years of torture, or 1 year) and something that can't (1 minute of torture, a dust speck) has some intuitive plausibility, but...

Sorry, no. 'Torture' and 'dust speck' are not two different quantities of the same currency. I wouldn't even be confident trying to add up individual minutes of torture to equal one year. Humans do not experience the world like disinterested machines. They don't even experience a logarithmic progression of 'amount of discomfort.' 50 years of torture does things to the mind and body that one year (for 50 people) can never do. One year of torture does things one minute can never do. One minute of torture does things x dust specks in x people's eyes could never do. None of these things registers on each others' scales.

Cash, possessions, whatever, I'm with you and Eliezer. Pure human perception is different, even when you count neurons. And no, this isn't a blind irrational reaction to the key word 'torture'. This is how human beings work.

Something occurred to me reading through all this earlier. Do we put no weight on the fact that if you polled the 3^^^3 people and asked them whether they would all undergo one dust speck to save one person from 50 years of torture, they'd almost certainly all say yes? Who would say "no, look how many of us there are! Torture him!" I find this goes a long way to exploding the idea of 'cumulative discomfort'.

As was pointed out last time, if you insist that no quantity of dust-specks-in-individual-eyes is comparable to one instance of torture, then what is your boundary case? What about 'half-torture', 'quarter-torture', 'millionth-torture'? Once you posit a qualitative distinction between the badness of different classes of experience, such that no quantity of experiences in one class can possibly be worse than a single experience in the other class, then you have posited the existence of a sharp dividing line on what appears to be a continuum of possible individual experiences.

But if we adopt the converse position, and assume that all experiences are commensurable and additive aggregation of utility makes sense without exception - then we are saying that there is an exact quantity which measures precisely how much worse an instance of torture is than an instance of eye irritation. This is obscured by the original example, in which an inconceivably large number is employed to make the point that if you accept additive aggregation of utilities as a universal principle, then there must come a point when the specks are worse than the torture. But there must be a boundary case here as well: some number N such that, if there are more than N specks-in-eyes, it's worse than the torture, but if there are N or less, the torture wins out.

Can any advocates of additive aggregation of utility defend a particular value for N? Because if not, you're in the same boat with the incommensurabilists, unable to justify their magic dividing line.

Ben, according to your poll suggestion, we should forbid driving, because each particular person would no doubt be willing to drive a little bit slower to save lives, and ultimately having no one drive at all would save the most lives. But instead, people continue to drive, thereby trading many lives for their convenience.

Agreeing with these people, I'd be quite willing to undergo the torture personally, simply in order to prevent the dust specks for the others. And so this works in reverse against your poll.

Mitchell: "You're in the same boat with the incommensurabilists, unable to justify their magic dividing line." No, not at all. It is true that no one is going to give an exact value. But the issue is not whether you can give an exact value; the issue is whether the existence of such a value is reasonable or not. The incommensurabilists must say that there is some period of time, or some particular degree of pain, or whatever, such that a trillion people suffering for that length of time or that degree of pain would always be preferable to one person suffering for one second longer or suffering a pain ever so slightly greater. This is the claim which is unreasonable.

If someone is willing to make the torture and specks commensurable, it is true that this implies that there is some number where the specks become exactly equal to the torture. There is not at all the same intuitive problem here; it is much like the comparison made a while ago on Overcoming Bias between caning and prison time; if someone is given few enough strokes, he will prefer this to a certain amount of prison time, while if the number is continually increased, at some point he will prefer prison time.

I think this article could have been improved by splitting it into two; one of them to discuss the original problem (is it better to save 400 for sure than to gamble on saving 500 with certainty 90%), and the other to discuss the reasons why people pick the other one if you rephrase the question. They're both interesting, but presenting them at once makes the discussion too confused.

And the second half... specks of dust in the eye and torture can both be described as "bad things". That doesn't mean they're the same kind of thing with different magnitudes. That was mostly a waste of time to me.

Eliezer,

What do specks have to do with circularity? Where in last posts you explain that certain groups of decision problems are mathematically equivalent, independent on actual decision, here you argue for a particular decision. Note that utility is not necessarily linear of number of people.

It looks like there was an inferential distance problem resulting from the fact that many either haven't read or don't remember the original torture vs dust specks post. Eliezer may have to explain the circularity problem in more detail.

ultimately having no one drive at all would save the most lives

And ultimately no dust specks and no torture and lollipops all round would be great for everyone. Stick to the deal as presented. You have a choice to make. Speed is quantifiable. Death is very quantifiable. Pain - even physical pain - goes in the same category as love, sadness, confusion. They are abstract nouns because you cannot hold, measure or count them. Does N losing lottery tickets spread equally over N people equal one dead relative's worth of grief?

Reconsider my poll scenario: Wouldn't the opinions of 3^^^3 people, all willing to bear the brunt of a dust speck for you, sway your judgment one little bit? Are you that certain of your rationality? You are about to submit yourself to 50 years of torture, and you have 3^^^3 people screaming at you 'don't bother, it's okay, no single person has a problem with just blinking once, even those who would opt for torture in your place!' What do you reply? 'Stop being so damned irrational! Just insert the rods!'

Unknown,

such that a trillion people suffering for that length of time or that degree of pain would always be preferable to one person suffering for one second longer or suffering a pain ever so slightly greater.

As I wrote yesterday, a dust mote registers exactly zero on my torture scale, and torture registers fundamentally off the scale (not just off the top, off) on my dust mote scale. Torture can be placed, if not discretely quantified, on my torture scale. Dust motes can not. If it's a short enough space of time that you could convince me N dust motes would be worse, I'd say your idea of torture is different from mine.

Ben: the poll scenario might persuade me if all the people actually believed that the situation with the dust specks, as a whole, were better than the torture situation. But this isn't the case, or we couldn't be having this discussion. Each person merely thinks that he wouldn't mind suffering a speck as an individual in order to save someone from torture.

As for a speck registering zero on your torture scale: what about being tied down with your eyes taped open, and then a handful of sand thrown in your face? Does that register zero too? The point would be to take the minimum which is on the same scale, and proceed from there.

As for me, I don't have any specific torture scale. I do have a pain scale, and dust specks and torture are both on it.

My utility function doesn't add the way you seem to think it does. A googolplex of dusty eyes has the same tiny negative utility as one dusty eye as far as I'm concerned. Honestly. How could anyone possibly care how many people's eyes get dusty. It doesn't matter. Torture matters a lot. But that's not really even the point. The point is that a bad thing happening to n people isn't n times worse than a bad thing happening to one person.

Do we put no weight on the fact that if you polled the 3^^^3 people and asked them whether they would all undergo one dust speck to save one person from 50 years of torture, they'd almost certainly all say yes?

What if they each are willing to be tortured for 25 years? Is it better to torture a googolplex people for 25 years than one person for 50 years?

The assumption that harms are additive is a key part of the demonstration that harm/benefit calculations can be rational.

So, has it been demonstrated that one cannot be rational without making that assumption?

Caledonian, of course that cannot be demonstrated. But who needs a demonstration? Larry D'anna said, "A googolplex of dusty eyes has the same tiny negative utility as one dusty eye as far as I'm concerned." If this is the case, does a billion deaths have the same negative utility as one death?

To put it another way, everyone knows that harms are additive.

what about being tied down with your eyes taped open, and then a handful of sand thrown in your face

Unknown - this is called torture, and as such would register on my torture scale. Is it as bad as waterboarding? No. Do I measure them on a comparable scale? Yes. Can I, hence, imagine a value for N where N(Sand) > (Waterboarding)? Yes, I can. I stand by my previous assertion.

However, I'm beginning to see that this is a problem of interpretation. I am fully on board with Eliezer's math, I'm happy to shut up and multiply lives by probabilities, and I do have genuine doubts about whether I'm basing my decision on squeamishness. I hope not. But currently I see no reason to think I am.

Each person merely thinks that he wouldn't mind suffering a speck as an individual in order to save someone from torture.

Each person merely thinks? But you would retort, confidently, that they are in fact erroneous and irrational, you are rational and correct, and ask that the rods be inserted posthaste? To be honest mate, even if I did personally believe N dust motes 'added up to torture', if all those people said 'don't bother, we'll take the dust', I'd do so. If only because the perceived authority of that many people asserting something would (by Eliezer's own logic) amount to enormous evidence that my decision was wrong. And this is vindicated (for people like me at least) in that if I were one of the 3^^^3 and you were the unlucky one, I'd urge you to reconsider along with everyone else.

What if they each are willing to be tortured for 25 years? Is it better to torture a googolplex people for 25 years than one person for 50 years?

These are two different questions. The first is about people telling you what they're willing to do. The second is you deciding what gets done. The second is the scenario that we're confronted with, and my previous comment addresses that question.

Larry, you're not right. Two people getting dust motes in their eye is worse than one. Two people getting tortured is worse than one.

To put it another way, everyone knows that harms are additive.

Is this one of the intuitions that can be wrong, or one of those that can't?

Ben, I think you might not have understood what I was saying about the poll. My point was that each individual is simply saying that he does not have a problem with suffering a dust speck to save someone from torture. But the issue isn't whether one individual should suffer a dust speck to save someone, but whether the whole group should suffer dust specks for this purpose. And it isn't true that the whole group thinks that the whole group should suffer dust specks for this purpose. If it were, there wouldn't be any disagreement about this question, since I and others arguing this position would presumably be among the group. In other words, your argument from hypothetical authority fails because human opinions are not in fact that consistent.

Suppose that 1 person per google (out of the 3^^^3 persons) is threatened with 50 years of torture? Should each member of the group accept a dust speck for each person threatened with torture, therefore burying the whole group in dust?

After trying several ideas, I realized that my personal utility function converges, among its other features. And it's obvous in retrospect. After all, there's only so much horror I can feel. But while you call this nasty names like "scope insensitivity", I embrace it. It's my utility function. It's not good or bad or wrong or biased, it just is. (Scope insensitivity with regard to probabilities is, of course, still bad.)

I still think that one man should be tortured a lot instead of many being tortured slightly less, because higher individual suffering results in a higher point of convergence.

This also explains why our minds reject "Pascal's mugging".

OK, my final response on the subject, which has had me unable to think about anything else all day. Thanks to all involved for helping me get my thoughts in order on this topic, and sorry for hijacking.

therefore burying the whole group in dust

You've forgotten the rules of the game. There's no 'burying everyone in dust.' You either have a speck of dust in your eye and blink it away, or you don't. And that's for every individual in the group. Playing with the numbers doesn't change the scenario much either.

My #1 complaint is that no-one seems bothered by things like this:

So we then double the number in set A while halving their discomfort.

Halving their discomfort? Care to go into some more depth on that? Would that be half as many neurons firing 'pain!'? Rods inserted half as deep? Thumbs only halfway screwed?

And this:

We can keep doing this, gradually - very gradually - diminishing the degree of discomfort, and multiplying by a factor of a googol each time, until...

As far as I know, there is no reason why I should agree that you can do anything of the sort. You might be able to divide torture by N and get dust mote, and you might not. But you certainly can't take it for granted then tell me I'm irrational.

Once again we've highlighted the immaturity of present-day moral thinking -- the kind that leads inevitably to Parfit's Repugnant Conclusion. But any paradox is merely a matter of insufficient context; in the bigger picture all the pieces must fit.

Here we have people struggling over the relative moral weight of torture versus dust specks, without recognizing that there is no objective measure of morality, but only objective measures of agreement on moral values.

The issue at hand can be modeled coherently in terms of the relevant distances (regardless of how highly dimensional, or what particular distance metric) between the assessor's preferred state and the assessor's perception of the alternative states. Regardless of the particular (necessarily subjective) model and evaluation function, there must be some scalar distance between the two states within the assessor's model (since a rational assessor can have only a single coherent model of reality, and the alternative states are not identical.) Furthermore introducing a multiplier on the order of a googolplex overwhelms any possible scale in any realizable model, leading to an effective infinity, forcing one (if one's reasoning is to be coherent) to view that state as dominant.

All of this (as presented by Eliezer) is perfectly rational -- but merely a special case and inappropriate to decision-making within a complex evolving context where actual consequences are effectively unpredictable.

If one faces a deep and wide chasm impeding desired trade with a neighboring tribe, should one rationally proceed to achieve the desired outcome: an optimum bridge?

Or should one focus not on perceived outcomes, but rather on most effectively expressing one's values-complex: Ie, valuing not the bridge, but effective interaction (including trade), and proceeding to exploit best-known principles promoting interaction, for example communications, air transport, replication rather than transport...and maybe even a bridge?

The underlying point is that within a complex evolutionary environment, specific outcomes can't be reliably predicted. Therefore to the extent that the system (within its environment of interaction) cannot be effectively modeled, an optimum strategy is one that leads to discovering the preferred future through the exercise of increasingly scientific (instrumental) principles promoting an increasingly coherent model of evolving values.

In the narrow case of a completely specified context, it's all the same. In the broader, more complex world we experience, it means the difference between coherence and paradox.

The Repugnant Conclusion fails (as does all consequentialist ethics when extrapolated) because it presumes to model a moral scenario incorporating an objective point of view. Same problem here.

Ben, you are right. Two people with dusty eyes is worse than one. But it isn't twice as worse. It's not even nearly twice as worse. On the other hand I would say that two people being tortured is almost twice as bad as one, but not quite. I'm sure I can't write down a formula for my utility function in terms of number of deaths, or dusty eyes, or tortures, but I know one thing: it is not linear. There's nothing inherently irrational about choosing a nonlinear utility function. So I will continue to prefer any number of dusty eyes to even one torture. I would also prefer a very large number of 1-day tortures to a singe 50-year one. (far far more than 365 * 50). Am I being irrational? How?

Caledonian, of course that cannot be demonstrated.

Of course? It is hardly obvious to me that such a thing is beyond demonstration, even if we currently do not know.

But who needs a demonstration?

People interested in rational thinking who aren't idiots. At the very least.

So, which factor rules you out?

I think I'm going to have to write another of my own posts on this (hadn't I already?), when I have time. Which might not be for a while -- which might be never -- we'll see.

For now, let me ask you this Eliezer: often, we think that our intuitions about cases provide a reliable guide to morality. Without that, there's a serious question about where our moral principles come from. (I, for one, think that question has its most serious bite right on utilitarian moral principles... at least Kant, say, had an argument about how the nature of moral claims leads to his principles.)

So suppose -- hypothetically, and I do mean hypothetically -- that our best argument for the claim "one ought to maximize net welfare" comes by induction from our intuitions about individual cases. Could we then legitimately use that principle to defend the opposite of our intuitions about cases like this?

More later, I hope.

Some of us would prefer to kill them all, regardless.

Unknown: "There is not at all the same intuitive problem here; it is much like the comparison made a while ago on Overcoming Bias between caning and prison time; if someone is given few enough strokes, he will prefer this to a certain amount of prison time, while if the number is continually increased, at some point he will prefer prison time."

It may be a psychological fact that a person will always choose eventually. But this does not imply that those choices were made in a rationally consistent way, or that a rationally consistent extension of the decision procedures used would in fact involve addition of assigned utilities. Not only might decisions in otherwise unresolvable cases be made by the mental equivalent of flipping a coin, just to end the indecision, but what counts as unresolvable by immediate preference will itself depend on mood, circumstance, and other contingencies.

Similar considerations apply to speculations by moral rationalists regarding the form of an idealized personal utility function. Additivism and incommensurabilism both derive from simple moral intuitions - that harms are additive, that harms can be qualitatively different - and both have problems - determining ratios of badness exactly, locating that qualitative boundary exactly. Can we agree on that much?

I agree that as you defined the problems, both have problems. But I don't agree that the problems are equal, for the reason stated earlier. Suppose someone says that the boundary is that 1,526,216,123,000,252 dust specks is exactly equal to 50 years of torture (in fact, it's likely to be some relatively low number like this rather than anything like a googleplex.) It is true that proving this would be a problem. But it is no particular problem that 1,526,216,123,000,251 dust specks would be preferable to the torture, while the torture would be preferable to 1,526,123,000,253 dust specks would be worse than the torture: the point is that the torture would differ from each of these values by an extremely tiny amount.

But suppose someone defines a qualitative boundary: 1,525,123 degrees of pain (given some sort of measure) has an intrinsically worse quality from 1,525,122 degrees, such that no amount of the latter can ever add up to the former. It seems to me that there is a problem which doesn't exist in the other case, namely that for a trillion people to suffer pain of 1,525,122 degrees for a trillion years is said to be preferable to one person suffering pain of 1,525,123 degrees for one year.

In other words: both positions have difficult to find boundaries, but one directly contradicts intuition in a way the other does not.

My first reaction to this was, "I don't know; I don't understand 3^^^3 or a googol, or how to compare the suffering from a dust speck with torture." After I thought about it, I decided I was interpreting Eliezer's question like this: as the amount of suffering per person, say a, approaches zero but the number of people suffering, say n, goes to infinity, is the product a*n worse than somebody being tortured for 50 years?" The limiting product is undefined, though, isn't it? If a goes to zero fast enough, for example by ceasing to be suffering when it fall below the threshold of notice, then the product is not as bad as the torture. I think several other commentors are thinking about it the same way implicitly, and impose conditions so the limit exists. Andrew did this by putting a lower bound on a, so of course the product gets big, but it's not the same question. Even leaving aside the other contributions to utility like life-altering effects, I'm having trouble making sense of this question.

I've written and saved a(nother) response; if you'd be so kind as to approve it?

Any question of ethics is entirely answered by arbitrarily chosen ethical system, therefore there are no "right" or "better" answers.

Wrong, anon. If there are objective means by which ethical systems can be evaluated, there can be both better and right answers.

Unknown, there is nothing inherently illogical about the idea of qualitative transitions. My thesis is that a speck of dust in the eye is a meaningless inconvenience, that torture is agony, and that any amount of genuinely meaningless inconvenience is preferable to any amount of agony. If those terms can be given objective meanings, then a boundary exists and it is a coherent position.

I just said genuinely meaningless. This is because, in the real world, there is going to be some small but nonzero probability that the speck of dust causes a car crash, for example, and this will surely be considerably more likely than a positive effect. When very large numbers are involved, this will make the specks worse than the torture.

But the original scenario does not ask us to consider consequences, so we are being asked to express a preference on the basis of the intrinsic badness of the two options.

Caledonian, what is an objective standard by which an ethical system can be evaluated?

Mitchell, my sentiments exactly. Dust causing car crashes isn't part of the game as set up here - the idea is that you blink it away instantly, hence 'the least bad thing that can happen to you'.

The only stickler in the back of my mind is how I am (unconsciously?) categorising such things as 'inconvenience' or 'agony'. Where does stubbing my toe sit? How about cutting myself shaving? At what point do I switch to 3^^^3(Event) = Torture?

TGGP, are you familiar with the teachings of Jesus?

Anon wrote: "Any question of ethics is entirely answered by arbitrarily chosen ethical system, therefore there are no "right" or "better" answers."

Matters of preference are entirely subjective, but for any evolved agent they are far from arbitrary, and subject to increasing agreement to the extent that they reflect increasingly fundamental values in common.

TGGP, are you familiar with the teachings of Jesus?
Yes, I was raised Christian and I've read the Gospels. I don't think they provide an objective standard of morality, just the jewish Pharisaic tradition filtered through a Hellenistic lens.

Matters of preference are entirely subjective, but for any evolved agent they are far from arbitrary, and subject to increasing agreement to the extent that they reflect increasingly fundamental values in common.
That is relevant to what ethics people may favor, but not to any truth or objective standard. Agreement among people is the result of subjective judgment.

TGGP -- how about internal consistency? How about formal requirements, if we believe that moral claims should have a certain form by virtue of their being moral claims? Those two have the potential to knock out a lot of candidates...

Ben and Mitchell: the problem is that "meaningless inconvenience" and "agony" do not seem to have a common boundary. But this is only because there could be many transitional stages such as "fairly inconvenient" and "seriously inconvenient," and so on. But sooner or later, you must come to stages which have a common boundary. Then the problem I mentioned will arise: in order to maintain your position, you will be forced to maintain that pain of a certain degree, suffered by any number of people and for any length of time, is worse than a very slightly greater pain suffered by a single person for a very short time. This may not be logically incoherent but at least it is not very reasonable.

I say "a very slightly greater pain" because it is indeed evident that we experience pain as something like a continuum, where it is always possible for it to slowly increase or decrease. Even though it is possible for it to increase or decrease by a large amount suddenly, there is no necessity for this to happen.

Great New Theorem in color perception : adding together 10 peoples' perceptions of light pink is equivalent to one person's perception of dark red. This is demonstrable, as there is a continuous scale between pink and red.

Enough with the abstract. It's difficult to make a valid equation since dust=x, torture=y, and x=!y. So why don't you just replace dust in the equation with torture. Like a really small amount of torture, but still torture. Maybe, say, everybody gets a nipple pierced unwillingly.

Tcpkac: wonderful intuition pump.

Gary: interesting -- my sense of the nipple piercing case is that yes, there's a number of unwilling nipple piercings that does add up to 50 years of torture. It might be a number larger than the earth can support, but it exists. I wonder why my intuition is different there. Is yours?

Paul, is there a number of dust specks that add up to stubbing your toe - not smashing it or anything, but stubbing it painfully enough that you very definitely notice, and it throbs for a few seconds before fading?

The fact that you felt it desirable to ask that question means that the metaphor has failed. The message you attempted to send has been overwhelmed by its own noise.

1. In this whole series of posts you are silently presupposing that utilitarianism is the only rational system of ethics. Which is strange, because if people have different utility functions Arrow's impossibility theorem makes it impossible to arrive at a "rational" (in this blogs bayesian-consistent abuse of the term) aggregate utility function. So irrationality is not only rational but the only rational option. Funny what people will sell as overcoming bias.

2. In this particular case the introductory example fails, because 1 killing != - 1 saving. Removing a drowning man from the pool is obviously better then merely abstaining from drowning an other man in the pool.

3. The feeling of superiority over all those biased proles is a bias. In fact it is very obviously among your main biases and consequently one you should spend a disproportional amount of resources on overcoming.

What leads you to believe he expends any of his resources overcoming his biases? Past behavior suggests he's repeating his errors over and over again without correction.

The fact that Eliezer has changed his mind several times on Overcoming Bias is evidence that he expends some resources overcoming bias; if he didn't, we would expect exactly what you say. It is true that he hasn't changed his mind often, so this fact (at least by itself) is not evidence that he expends many resources in this way.

Eliezer -- no, I don't think there is. At least, not if the dust specks are distributed over multiple people. Maybe localized in one person -- a dust speck every 10th/sec for a sufficiently long period of time might add up to a toe stub.

The fact that Eliezer has changed his mind several times on Overcoming Bias is evidence that he expends some resources overcoming bias

No, he could simply be biased towards maintaining a high status by accepting the dominant opinions in his social groups. If looking bad in others' eyes is something you wish to avoid, you'll reject arguments that others reject whether you think they're right or not.

Eliezer's question for Paul is not particularly subtle, so I presume he won't mind if I give away where it is leading. If Paul says yes, there is some number of dust specks which add up to a toe stubbing, then Eliezer can ask if there is some number of toe stubbings that add up to a nipple piercing. If he says yes to this, he will ultimately have to admit that there is some number of dust specks which add up to 50 years of torture.

Rather than actually going down this road, however, perhaps it would be as well if those who wish to say that the dust specks are always preferable to the torture should the following facts:

1) Some people have a very good imagination. I could personally think of at least 100 gradations between a dust speck and a toe stubbing, 100 more between the toe stubbing and the nipple piercing, and as many as you like between the nipple piercing and the 50 years of torture.

2) Arguing about where to say no, the lesser pain can never add up to the slightly greater pain, would look a lot like creationists arguing about which transitional fossils are merely ape-like humans, and which are merely human-like apes. There is a point in the transitional fossils where the fossil is so intermediate that 50% of the creationists say that it is human, and 50% that it is an ape. Likewise, there will be a point where 50% of the Speckists say that dust specks can add up to this intermediate pain, but the intermediate pain can't add up to torture, and the other 50% will say that the intermediate pain can add up to torture, but the specks can't add up the intermediate pain. Do you really want to go down this path?

3) Is your intuition about the specks being preferable to the torture really greater than the intuition you violate by positing such an absolute division? Suppose we go down the path mentioned above, and at some point you say that specks can add up to pain X, but not to pain X+.00001 (a representation of the minute degree of greater pain in the next step if we choose a fine enough division). Do you really want to say that you prefer that a trillion persons (or a google, or a googleplex, etc) than that one person suffer pain X+.00001?

While writing this, Paul just answered no, the specks never add up to a toe stub. This actually suggests that he rounds down the speck to nothing; you don't even notice it. Remember however that originally Eliezer posited that you feel the irritation for a fraction of a second. So there is some pain there. However, Paul's answer to this question is simply a step down the path laid out above. I would like to see his answer to the above. Remember the (minimally) 100 gradations between the dust speck and the toe stub.

Ah, but Unknown, knowing it can be done in the abstract isn't the same as seeing it done.

So, Paul: Do enough dust specks - which by hypothesis, do produce a brief moment of irritation, enough to notice for a moment, so at least one pain neuron is firing - add up to experiencing a brief itch on your arm that you have to scratch? Also, do enough cases of feeling your foot come down momentarily on a hard pebble, add up to a toe stub that hurts for a few seconds?

How about listening to loud music blasting from a car outside your window - would enough instances of that ever add up to one case of being forced to watch "Plan Nine from Outer Space" twice in a row?

And can you swear on a stack of copies of "The Origin of Species" that you would have given the same answers to all those questions, if I'd asked you before you'd ever heard of the Dust Specks Dilemma?

Caledonian, offering an alternative explanation for the evidence does not imply that it is not evidence that Eliezer expends some resources overcoming bias: it simply shows that the evidence is not conclusive. In fact, evidence usually can be explained in several different ways.

Eliezer -- depends again on whether we're aggregating across individuals or within one individual. From a utilitarian perspective (see The Post That Is To Come for a non-utilitarian take), that's my big objection to the specks thing. Slapping each of 100 people once each is not the same as slapping one person 100 times. The first is a series of slaps. The second is a beating.

Honestly, I'm not sure if I'd have given the same answer to all of those questions w/o having heard of the dust specks dilemma. I feel like that world is a little too weird -- the thing that motivates me to think about those questions is the dust specks dilemma. They're not the sort of things practical reason ordinarily has to worry about, or that we can ordinarily expect to have well-developed intuitions about!

I don't think this is too difficult to understand. Both in both situations, the deciders don't want to be think of themselves as possibly responsible for avoidable death. In the first scenario, you don't want to be the guy who made a gamble and everyone dies. In the second, you don't want to choose for 100 people to die. People make different choices in the two situations because they want to minimize moral culpability.

Is that rational? Strictly speaking, mabye not. Is it human? Absolutely!

An AGI project would presumably need a generally accepted, watertight, axiom based, formal system of ethics, whose rules can reliably be applied right up to limit cases. I am guessing that that is the reason why Eliezer et al are arguing from the basis that such an animal exists.
If it does, please point to it. The FHI has ethics specialists on its staff, what do they have to say on the subject ?
Based on the current discussion, such an animal, at least as far as 'generally accepted' goes, does not exist. My belief is that what we have are more or less consensual guidelines which apply to situations and choices within human experience. Unknown's examples, for instance, tend to be 'middle of the range' ones. When we get towards the limits of everyday experience, these guidelines break down.
Eliezer has not provided us with a formal framework within which summing over single experiences for multiple people can be compared to summing over multiple experiences for one person. For me it stops there.

tcpkac, if a hundred people experiencing 49 years of torture is worse than one person experiencing 50 years, then yes, you can and must compare. Whether you extend this right down to 3^^^3 dust specks is another matter. There might not be a formal framework for something so subjective, but there are obvious inconsistencies with flat refusal to sum, even with something as abstract as 'pain'. Would an AGI need a formula for summing discomfort over multiple people/one person? Who gets to write that? Yeesh.

a brief moment of irritation, enough to notice for a moment, so at least one pain neuron is firing

I'm not a neurobiologist - is this how it works? Are there neurons whose specific job it is to deliver 'pain' messages? If we're reducing down to this level, can we actually measure pain? More importantly, even if we can, can we go on to assume that there is an ininterrupted progression in the neurological mechanism, all the way up this scale, from dust mote to torture? For me, it's not clear whether blinking away a dust mote falls under 'pain' or 'sensation'. Nipple piercing is much clearer, and hence I have no problem saying 3^^^3 Piercings > Torture.

Paul : "Slapping each of 100 people once each is not the same as slapping one person 100 times."

This is absolutely true. But no one has said that these two things are equal. The point is that it is possible to assign each case a value, and these values are comparable: either you prefer to slap each of 100 people once, or you prefer to slap one person 100 times. And once you begin assigning preferences, in the end you must admit that the dust specks, distributed over multiple people, are preferable to the torture in one individual. Your only alternatives to this will be to contradict your own preferences, or to admit to some absurd preference such as "I would rather torture a million people for 49 years than one person for 50."

Ben: as I said when I brought up the sand example, Eliezer used dust specks to illustrate the "least bad" bad thing that can happen. If you think that it is not even a bad thing, then of course the point will not be apply. In this case you should simply move to the least thing which you consider to be actually bad.

Caledonian, offering an alternative explanation for the evidence does not imply that it is not evidence that Eliezer expends some resources overcoming bias:

Of course it's not evidence for that scenario. There are alternative and simpler explanations.

If the data does not permit us to distinguish between A and ~A, it's not evidence for either state.

I think the argument is misguided. Why? The choice is not only hypothetical but impossible. There is not the remotest possibility of a googolplex persons even existing.
So I'll tone it down to a more realistic "equation", then I'll argue that it's not an equation after all.
Then I'll admit that I'm lost, but so are you... =)
Let's assume 1e7 people experiencing pain of a certain intensity for one second vs. one persion experiencing equal pain for 1e7 seconds (approx. 19 years).
Let's assume that every person in question has an expectancy of, say, 63 years of painless life. Then my situation is eqivalent to either extending the painless life expectency of 1e7 people from 63y-1s to 63y or to extend it for one person from 54y to 63y.
According to the law of diminishing returns, the former is definitely much less valuable than the latter.
But how much so? How to quantify this?
I have no idea, but I claim that neither do you... =)

regards, frank

p.s.
I have a hunch that you couldn't fit enough people with specks in their eyes into the universe to make up for one 50-year-torture.

Unknown: I didn't deny that they're comparable, at least in the brute sense of my being able to express a preference. But I did deny that any number of distributed dust specks can ever end up to torture. And the reason I give for that denial is just that distributive problem. (Well, there are other reasons too, but one thing at a time.)

I agree, you have to just multiply.

But your math is an attempt to abstract human harm to numbers, and the problem I have (and I suspect others intuitively have) is that the abstraction is wrong. You've failed to understand the lessons of the science of happiness: we forget small painful things quickly. The cost of a speck in the eye, let us imagine, is 1 unit of harm. But that's only true in the moment the speck hits the eye. In the hour the speck hits the eye, because of the human ability to ignore or forget small pains, the extended cost is 0. This is why a googol of specks is better than torture, because a googol 0s...

The real problem is defining the boundary between momentary (transient) harm and extendable harm. This is a psychological math problem.

I'm following a link from Pharyngula, and I don't have time to read the comments, my apologies if I'm repeating something

I think you're up against the sorites paradox, you are confusing apples and oranges in comparing torture to a dust speck and that there is no practical way to implement the computation you propose.

People who whine about the dust specks in their eyes will get an unsympathetic response from me - I care zero about it. People who have been tortured for a minute will have my utmost concern and sympathy. Somewhere along the line, one turns into the other, but in your example, a googleplex of zeroes is still zero.

Torture is qualitatively different from pain, say the pain of a debilitating disease. Torture involves the intentional infliction of suffering for the sake of the suffering, extreme loss of control, the absence of sympathy and empathy, extreme uncertainty about the future and so on. The mental impact of torture is qualitatively different from accidental pain.

Universal informed consent and shared risk would seem to my moral gut to be necessary preconditions to make me stomach this kind of utilitarian calculus.

So this large population that agrees that the occasional victim enhances the overall utility would share the risk of becoming the victim. In that scenario, how many people would accept the lifetime torture lottery ticket in exchange for a lifetime free of dust motes? Without knowing the answer to this question, they can't estimate their own risk.

MartinH:

See the follow-up here.

(If a dust speck is zero, you could substitute "stubbed toe".)

Incidentally, my own answer to the torture vs. dust specks question was to bite the other bullet and say that, given any two different intensities of suffering, there is a sufficiently long finite duration of the greater intensity such that I'd pick a Nearly Infinite duration of the lesser degree over it. In other words, yeah, I'd condemn a Nearly Infinite number of people to 50 years of slightly less bad torture to spare a large enough finite group from 50 years of slightly worse torture.

In real life, I consider myself lucky that questions like that one are only hypothetical.

I enjoyed the read, and it makes a lot of sense. however... it leaves me with a..
Hrm.
Well, I'm no mathematician, but between being a monkey and never multiplying and always feeling, and being a robot, always multiplying and never feeling, I think I'll stick with being human and do both.

With all due respect, but this post reminds me of why I find the expectation-calculation kind of rationality dangerous.

IMO examples such as the first, with known probabilities and a straightforward way to calculate utility, are a total red herring.

In more realistic examples, you'll have to do many judgment calls such as the choice of model, and your best estimate of the basic probabilities and utilities, which will ultimately be grounded on the fuzzy, biased intuitive level.

I think you might reply that this isn't a specific fault with your approach, and that everyone has to start with some axioms somewhere. Granted.

Now the problem, as I see it, is that picking these axioms (including quantitative estimates) once and for all, and then proceeding deductively, will exaggerate any initial choices (silly metaphor: A bit like going from one point to another by calculating the angle and then going in a straight line, instead of making corrections as you go. But (quitting the metaphor) I'm not just talking about divergence over time, but also along the deduction).

So now you have a conclusion which is still based on the fuzzy and intuitive, but which has an air of mathematical exactness... If the model is complex enough, you can probably reach any desired conclusion by inconspicious parameter twiddling.

My argument is far from "Omg it's so coldhearted to mix math and moral decisions!". I think math is an important tool in the analysis (incidentally, I'm a math student ;)), but that you should know its limitations and hidden assumptions in applying math to the real world.

I would consider an act of (intuitively wrongful) violence based on a 500-page utility expectation calculation no better than one based on elaborate logic grounded in scripture or ideology.

I think that, after being informed by rationality about all the value-neutral facts, intuition, as fallible as it is, should be the final arbiter.

I think these sacred (no religion implied) values you mention, and especially kindness, do serve an important purpose, namely as a safeguard against the subtly flawed logic I've been talking about.

You know, I have always said that the trolley problem in which you push the fat man onto the tracks to save several lives is immoral, because you are treating him as a means rather than an end.

I've just noticed that if I reframe it in such a way that it's not so personal, my intuition changes. For example, suppose it were a question of pushing a trolley containing one (unknown) person in front of another (empty) runaway trolley, in order to stop the runaway one from hitting a third trolley containing 4 people. Suddenly I'm actively killing the guy.

http://wiki.lesswrong.com/wiki/Shut_up_and_multiply The shut up and multiply article on the wiki (markup troubles...) taken in conjunction with the following out-of-context paragraph strongly implies to readers of the wiki that this post is about the moral imperative to reproduce:

You know what? This isn't about your feelings. A human life, with all its joys and all its pains, adding up over the course of decades, is worth far more than your brain's feelings of comfort or discomfort with a plan. Does computing the expected utility feel too cold-blooded for your taste? Well, that feeling isn't even a feather in the scales, when a life is at stake. Just shut up and multiply.

...is this intentional or unintentional subtext, and if the latter, do you intend to revise the word to "calculate" as some people quoting the post have done or not bother since apparently nobody but me noticed in the first place?

If that population of 400 or 500 people is all that's left of Homo Sapiens, then it's obvious to me that keeping 400 with probability 1 is better than keeping 500 with probability 0.9. Repopulating starting with 400 doesn't seem much harder than repopulating starting with 500, but repopulating starting with 0 is obviously impossible.

If we change the numbers a little bit, we get a different and still interesting example. I don't see an important difference between having 10 billion happy people and having 100 billion happy people. I can't visualize either number, and I have no reason to believe that having another 90 billion after the first 10 billion gives anything I care about.

Multiplying individual utility by number of people to get total utility is a mistake, IMO. I don't know what the correct solution is, but that's not it.

What's worse, stealing one cent each from 5,000,000 people, or stealing $49,999 from one person? (Let us further assume that money has some utility value.)

If we decide we can just add the diminished wealth together, the former is clearly one cent worse: $50,000 is stolen, as opposed to $49,999. But this doesn't take into account that loss of utility grows with each cent lost from the same person. Losing one cent won't bother me at all; everyone else who had a cent stolen would probably feel the same way. However, $49,999 from one person is enough to ruin their life: numerically, less was stolen overall, but the utility loss grows incredibly as it is concentrated.

Another case: is an eye-mote a second for a year (31,556,926 motes) in one person better than 31,556,927 motes spread out evenly among 31,556,927 people? The former case would involve serious loss of utilons, whereas a single mote is quickly fixed and forgotten: qualitatively different from constant irritation. The loss of utilons from dust motes can thus be concentrated and added, but not spread out and then added. (I think this may indicate time and memory plays a factor in this, since they do in the mechanism of suffering.)

In other words, a negligible amount of utility loss cannot be multiplied so that it is preferable to a concentrated, non-negligible utility loss. If none of the people involved in the negligible-group suffer individually, they obviously can't be suffering as a group, either (what would be suffering - a group is not an entity!).

However, I have read refutations of this that say "well just replace dust specks with something that does cause suffering." I have no problem with that; there may be "non-trivial" pain and "non-trivial" pleasure that can be added. So in the stubbed-toes example, it might be non-trivial, since it is concentrated enough to matter to the individual and cause suffering; and suffering is additive.

Perhaps there is such a line innately built into human biology, between "trivial" and "non-trivial". Eye-motes can't ever really degrade the quality of our lives, so cannot be used in examples of this kind. But in the case of one person being tortured slightly worse than ten people being tortured slightly less, the non-trivial suffering of the ten can be considered to be additive. This also solves this problem.

I, like others, can do the maths just fine, so what? How does it follow that circular preferences over very long chains of remotely possible pairs of choices should cause me to doubt strong moral intuition? Because I would, under carefully contrived conditions, lose against the allegedly optimal solution... As for grandstanding, hah! To presume to call this brand of consequentialism "rationality" is already quite rhetorical. Never mind warm fuzzies, bare swords, flames, and chimpanzees.

As already stated somewhere above, with or without "sacred" values humans invariably believe in thresholds where the expected negative utility jumps exponentially. If I believe that lengthy torture is a vastly different event (for the individual in question, and we clearly aren't considering any ripples) from a quickly and cleanly amputated limb, I'll still adjust my preferences accordingly. I'm only acting on my beliefs about human consciousness. That's not irrational in itself. Therefore... sorry, tried two intuitive therefores but neither one checks out. I'll get back on it.

Now that I have read (and commented on) the "Savage axiom" (http://lesswrong.com/lw/5te/a_summary_of_savages_foundations_for_probability/) thread, I would like to note here on this thread that there are no computable solutions to the Savage axioms.

Now, of course, in this universe, googolplexes are utterly irrelevant. If an AI could harness every planck volume of space in the observable universe to each perform one computations per planck time, all the stars would burn out long before it got anywhere close to 2^1024 computations, which is a long way off from a googolplex. So it seems to me "circular altruism" on this level is of absolutely no consequence.

Of course we might still cling to the "thought experiment" aspect of it. I don't see why we should, but even if we do, it doesn't help: ideal rationality, in the Savage sense, isn't even computable. No AI, even with unlimited time and space to make up its mind, can be rational, in the sense of always choosing the course that maximises some utility function with respect to some subjective probability distribution in all situations. So something still has to give. Of course there are lots of ways to do this. We can be "rational within epsilon" if you like, but this epsilon will matter when considering these googolplex circularity arguments. I'm skeptical that there is anything coherent here at all.

A googolplex is ten to the googolth power. That's a googol/100 factors of a googol. So we can keep doing this, gradually - very gradually - diminishing the degree of discomfort, and multiplying by a factor of a googol each time, until we choose between a googolplex people getting a dust speck in their eye, and a googolplex/googol people getting two dust specks in their eye.

Maybe the strange notation has me confused, but I don't see the contradiction here. Consider sneezes. One human sneezing N times in a row, where N>2, seems at least super-exponentially worse than N humans each sneezing once (assuming that no noticeable consequences for any of this last beyond the day). In fact, if we all sneeze simultaneously that would be pretty cool.

This next part doesn't directly address the original question. But if 3^^^3 humans know that by getting a dust speck in their eye they helped save someone from torture, the vast majority would likely feel happy about this and we wind up with a mountain of increased utility from Dust Specks relative to No Pain. Whereas an average-human torture victim who learns that the torture served to prevent dust specks might try to kill you bare-handed.

How about:

1. floor(3^(3^(3^(3 + sin(3^^^3))))) people are tortured for a day.

2. floor(3^(3^(3^(3 + cos(3^^^3))))) people are tortured for a day.

Choose.

Well, why are certain notations for large integers to be taken seriously but not others? Shut up and do trig!

(Mainly though I want to claim dibs to the name "a googolplex simultaneous sneezes")

50 years of torture is going to ruin someone's life. Dust specks and stubbed toes are not going to ruin anyone's life, which makes the number of people with dust specks and stubbed toes irrelevant. That's the threshold. You can't multiply one to get to the other.

The amount humanity loses to a dust speck in someone's eye is exactly 0, unless that person was piloting an aircraft or something and crashes because of it, which - based on my reading of the premise - doesn't seem to be the case. A stubbed toe might cost more, but even that is only true if you treat humanity as an amorpheous, hiveminded mass rather than a group of individuals.

I don't know if I understood your circular argument right, but you are basically saying that if 50 years of torture for one person (50yt1) < dustspeck for a googolplex (ds10^10^100) then 50yt1>49.9999999yt10^100>49.9999998yt10^200>...>ds10^10^100

if this is not what you are saying, then I don't understand your point and ask to elucidate it. if it is, then I think there is a serious flaw here: in the 50yt1 scenario, someone is suffering, i.e. feeling pain in the ds10^10^100 scenario, there is a mere annoyance. There has therefore to be a point in that sequence, where one can consistently argue X10^Y<X'10^2Y, where X is the last "pain", X' is the first mere annoyance, therefore interrupting the chain.

I hope this is understandable.

EDIT to avoid double post: I think the kind of reasoning you are using is very, very dangerous if you try a gradual transformation between two things with different quality not just quantity. It is clear that the two extremes of the sequence have a different quality, but you are assuming the only thing that changes is quantity.

Here's another word problem for you.

There is a disease - painful, but not usually life threatening - that is rapidly becoming a pandemic. Medical science is not going to be able to cure the disease for the next several decades, which means that many millions of people will have to endure it, and a few dozen will probably die. You can find a cure for the disease, but to do so you'll have to perform agonizing, ultimately lethal, experiments on a young and healthy human subject.

Do you do it?

Health professionals and consumers may change their choices when the same risks and risk reductions are presented using alternative statistical formats. Based on the results of 35 studies reporting 83 comparisons, we found the risk of a health outcome is better understood when it is presented as a natural frequency rather than a percentage for diagnostic and screening tests. For interventions, and on average, people perceive risk reductions to be larger and are more persuaded to adopt a health intervention when its effect is presented in relative terms (eg using relative risk reduction which represents a proportional reduction) rather than in absolute terms (eg using absolute risk reduction which represents a simple difference). We found no differences between health professionals and consumers. The implications for clinical and public health practice are limited by the lack of research on how these alternative presentations affect actual behaviour. However, there are strong logical arguments for not reporting relative values alone, as they do not allow a fair comparison of benefits and harms as absolute values do.

http://onlinelibrary.wiley.com/doi/10.1002/14651858.CD006776.pub2/abstract

This is awesome: Spin the risk!

I reject the idea that human suffering is a linear function. Once you accept such an idea, it's not too difficult too say that to avoid minor inconveniences of sufficiently large number of people we should torture one person for his whole life.

Here is a question to demonstrate:

Two people are scheduled to be tortured for no reason you know. One is to be tortured for two days, the other for three. You know that subjects are equally resistant to torture.

You have the choice:

• Reduce the time one subject is tortured from 3 to 2 days. Other is tortured for 2d.
• Reduce the time one subject is tortured from 2 to 1 day. Other is tortured for 3d.

Which choice would you make?

I certainly hope that most of so called utilitarians can see the importance of that choice. To grow infatuated with a small cold flame is to blind yourself to the possibility of being wrong in your estimates. Before you say that torture is preferable to dustspecks ask yourself how does human suffering scale from specks to torture.

Altruism isn't the warm fuzzy feeling you get from being altruistic. If you're doing it for the spiritual benefit, that is nothing but selfishness. The primary thing is to help others, whatever the means. So shut up and multiply!

That's how you get a warm and fuzzy feeling if you're a consequentialist. If you're a deontologist, you get it by obedience to the Rule, or often more easily by saying "Yay, Rule!"

How many units of physical pain per speck? How many units of perceived mistreatment per speck? How many instances of basic human rights infringements per speck?

I don't have a terminal value as following: "People should never experience an infinitesimally irritating dust speck hitting their eye"

I do have a terminal value as following: "People should never go through torture"

So in this case we can make another calculation which is: Googolplex of instances that are compatible with my terminal values vs a single event that is not compatible with my terminal values.

I'd like to add however that if these events are causally connected then dust specks would become the obvious choice. I'm sure there's a certain probability of getting into a car accident due to blinking etc, lots of other ways to make essentially the same argument. Anyway that aspect was not emphasized in either post so I take it was not intended either.

If the intial option 1 was written as "Save 400 lives with certainty, 100 people die with certainty" it would be less misleading. Because if you interpret the option 1 as no one dying, it actually is the correct choice, although it later becomes clear anyway.

You've officially given me the best example of the inherent flaw in the utilitarian model of morality. Normally, I use the example of a man who is the sole provider of an arbitrarily large family murdering an old homeless man. Utilitarianism says he should go free. The murder's family, of size X, will all experience disutility from his imprisonment. Call that Y. The homeless man, literally no one will miss. No family members to gain utility from exacting justice. Therefore, since X*Y > 0, the murderer should go back to providing for his family. I do not believe any rational person would consider that just, moral, or even reasonable.

I'm all for rational evaluations of problems, but rationality does not apply to moral arguments. Morality is an emotional response by its very nature. Rational arguments are fine when we're comparing large numbers of people. A plan that will save 400 lives vs. a plan that has a 90% chance to save 500 lives. That's not morality, that's rationality. It doesn't truly become about morality until it's personal. If you could save the lives of 3 people you've never met, would you let yourself be tortured? Would you torture someone? Regardless of your answer, it is easier said than done...

P.S. I'm not a psychologist, but I imagine if you had different answers to torturing vs. being tortured, that says something about you. Not sure what...

You are making assumption the feeling caused by having dust spec in your eye is in same category as feeling of being tortured for 50 years.

Would you rather have googolplex people drink a glass of water or have one person tortured for 50 years? Would you rather have googolplex people put on their underwear in the morning or have one person tortured for 50 years? If you put feeling of dust spec in same category as feelings arising from 50 years of torture, you can put pretty much anything in that category and you end up preferring one person being tortured for 50 years to to almost any physical phenomena that would happen to googolplex people.

And even if it's in same category? I bet that just having a thought causes some extremely small activity in brain areas related to pain. Multiply that by large enough number and the total pain value will be greater than pain value of person being tortured for 50 years! I would hope that there is no one who would prefer one person being tortured for 50 years to 3^^^3 persons having a thought...

It would be a very different kind of evaluation, but the importance would matter differently if it were the /last/ 500 humans we were talking about - and there was a 90% chance that all would live and a 10% chance that all would die on one pathway versus a guaranteed 100 dying on the other pathway. But since they are just /some group/ of 500 humans with presumedly other groups other places, it is worth the investment - gambling in this way pays out in less lives lost, on average.

In the torture vs dust specks comparison, it is important not to discard the disutilities of unfairness, nor of moral hazards. One cannot publicly acknowledge the superiority of "one guy tortured" vs " lots of people mildly inconvenienced" without others, including potentially our politicians, or enemies, deciding that this supports their use of actual torture on actual people "for the greater good". Accepting torture has a negative utility for many people.

Also we humans value fairness, and prefer that things be evenly distributed (fairness has positive utility). The disutility of even a tiny fraction of those people knowing that someone was tortured so as to spare them from dust specks, when added together, would probably exceed that of the person being tortured. The danger of "shut up and multiply" is that someone might be multiplying the wrong things.

Rejecting the principle that we can't, in general, sacrifice one person for the good of many, also has disutility. If we were to accept torturing someone to prevent a lot of dust specks, imagine how much time would have to be spent arguing whether we can take away this other guy's property for some greater good (which might fail to deliver, and might have been suggested for someone's self-interest).

Raise your hand if you (yes you, the person reading this) will submit to 50 years of torture in order to avert "least bad" dust speck momentarily finding its way into the eyes of an unimaginably large number of people.

Why was it not written "I, Eliezer Yudkowsky, should choose to submit to 50 years of torture in place of a googolplex people getting dust specks in their eyes"?

Why restrict yourself to the comforting distance of omniscience?

Did Miyamoto Musashi ever exhort the reader to ask his sword what he should want? Why is this not a case of using a tool as an end in and of itself rather than as a means to achieve a desired end?

Are you irrational if your something to protect is yourself...from torture?

Has anyone ever addressed whether or not this applies to the AGI Utility Monster whose experiential capacity would presumably exceed the ~7 billion humans who should rationally subserve Its interests (whatever they may be)?

It depends on the actual situation and my goal.

Imagine I were a ship captain assigned to try to If rescue a viable sample of a culture from a zone that was about to be genocided, I would be very likely to take the 400 peopleweights (including books or whatever else they valued as much as people) of evacuees, unless someone made a convincing case that the extra 100 people were vital cultural or genetic carriers. For definiteness, imagine my ship is rated to carry up to 400 peopleweight worth of passengers in almost any weather, but 500 people would overload it to the point of sinking during a storm of the sort that the weather experts predict 10 percent probable during voyage to safe harbor.

People are not dollars or bales of cotton to be sold at market. You can't just count heads and multiply that number by utilons per head and say "This answer is best, any other answer is foolish."

Well obviously you can do that, but the main reward for doing so is the feeling that you are smarter than the poor dumb fools who believe that the world is complex and situation dependent. That is, you can give yourself a sort of warm fuzzy feeling of smug superiority by defeating the straw man you constructed as your foolish competitor in the Intelligence Sweepstakes.

That being said, if there really is no other information available, I would take the same choice Eliezer recommends; I just deny that it is the only non foolish choice.

This applies to lottery tickets as well. A slim chance at escaping economic hell might be worth more than its nominal expected return value to a given individual. 100 million dollars might very well have a personal utility over a billion times the value of one dollar for example, if that person's deep goals would be facilitated mightily by the big win and not at all by a single dollar or any reasonable number of dollars they might expect to save over the available time. Also, if any entertainment dollar is not a foolish waste, then a dollar spent on a lottery ticket is worth its expected winning value plus its entertainment value, which varies /profoundly/ from person to person.

I myself prefer to give people $1 lottery tickets instead of $2.95 witty birthday cards. Am I wise or foolish in this? But posts here have branded all lottery purchases as foolish, so I must be a fool. I bow to the collective wisdom here and admit that I am a fool. There is a lot of other evidence that supports this conclusion :)

if you give yourself over to rationality without holding back, you will find that rationality gives to you in return.

I heartily agree, that's one reason I try to avoid trotting out applause lights to trigger other people into giving me warm fuzzies.

I am happy for one person to be tortured for 50 years to stave off the dust specks, as long as that person is me. In fact, this pretty much sums up my career in software development, it is not my favorite thing to do but I endured cubicle hell for many years in exchange for money in part, but also because of my deep belief that solving annoying little bugs and glitches that might inconvenience many many people was an activity important enough to override my personal preferences; I could easily have found other combinations of pay and fun that pleased me better, so I have actually been through this dilemma in muted form in real life and chose to personally suffer to hold off 'specks' like poorly designed user interfaces.

I do have great admiration for Eliezer but he claims to want to be more rational and to welcome criticism intended to promote his progress on The Way, so I thought it would be ok to be critical of this post, which irked me because paragraph four is a straw man "fool" phrased in second person, which seems like a sort of pre-emptive ad hominem against any reader of the post foolish enough to disagree with the premise of the writer. This seems like an extremely poor substitute for rational discourse, the sort of nonsense that could cost the writer Quirrell points, and none of us want that. I don't want to seem hostile, but since I am exactly the sort of fool who disagreed with the premise of paragraph 3, I do feel like I was being flamed a bit, and since I am apparently made of straw, flames make me nervous :)

This threshold thing is interesting. Just to make the idea itself solid, imagine this. You have a type of iron bar that can bend completely elastically (no deformation) if forces less than 100N is applied to it. Say they are more valuable if they have no such deformations. Would you apply 90N to 5 billion bars or 110N to one bar?

With this thought experiment, I reckon the idea is solidified and obvious, yes? The question that still remains, then, is whether dust specks in eyes is or is not affected by some threshold.

Though I suppose the issue could actually be dropped completely, if we now agree that the idea of threshold is real. If there is a threshold and something is below that threshold, then the utility of doing it is indeed zero, regardless of how many times you do it. If something is above the threshold, shut up (or don't) and multiply.

"Most people choose option 1." I find this hard to believe. Were they forced to answer quickly or under cognitive load, and without access to a calculator or pen and paper? I would appreciate it if you could edit the post to provide a citation.

I am truly confused. This post does not endorse either side.

I just would like to note something about my cognitive process here: in the "step by step" argument, what I seem to be thinking is "rigorously the same torture" and "for more people". The argument may be sound, but it does not seem to be hitting my brain in a sound way

Let's turn the argument on its head: if you could abolish torture at the cost of everybody getting a speck of dust in their eye, would you do it?

Next question: If you could stop the Holocaust at the cost of N people getting dust specks in their eye, what's the maximum value you'd permit for N? That is, is there a number N with the property that if N people get dust specks in their eye, you prevent the Holocaust, but if N+1 people get dust specks in their eye, then the Holocaust proceeds on schedule?

Arguments that begin with something benign and proceed by degree to silly conclusions have been around since ancient times. Dressing them up in the language of mathematics doesn't change their nature. The kind of utilitarian model presented here is not an accurate reflection of the real world. Locally you can get reasonable results if you decide to treat similar things on a linear scale, but for disparate things the linear approximation breaks down. You can still plug numbers into the model, but the answer is meaningless.

The problem here is that you don't KNOW that the probability is 90%. What if it's 80%? or 60%? or 12%? In real life you will only run the experiment once. The probabilities are just a GUESS. The person who is making the guess has no idea what the real probabilities are. And as Mr. Yudkowsky has pointed out elsewhere, people consistently tend to underestimate the difficulty of a task. They can't even estimate with any accuracy how long it will take them to finish their homework. If you aren't in the business of saving people's lives in EXACTLY this same way, on a regular basis, the estimate of 90% is probably crap. And so is the estimate of 100% probability of saving 400 lives. All you can really say, is that you see fewer difficulties that way, from where you are standing now. It's a crap shoot, either way, because, once you get started, no matter which option you choose, difficulties you hadn't anticipated will arise.

This reminds me of 'the bridge experiment', where a test subject is given the opportunity to throw a fat person off a bridge in front of a train, and thereby save the lives of 5 persons trapped on the tracks up ahead. The psychologists bemoaned the lack of rationality of the test subjects, since most of them wouldn't throw the fat person off the bridge, and thus trade the lives of one person, for five. I was like, 'ARE YOU CRAZY? Do you think one fat person would DERAIL A TRAIN? What do you think cow catchers are for, fool? What if he BOUNCED a couple of times, and didn't end up on the rails? It's preposterous. The odds are 1000 to 1 against success. No sane person would take that bet.'

The psychologists supposedly fixed this concern by telling the test subjects that it was guaranteed that throwing the fat person off the bridge would succeed. Didn't work, because people STILL wouldn't buy into their preposterous plan.

Then the psychologists changed the experiment so that the test subject would just have to throw a switch on the track which would divert the train from the track where the five people were trapped to a track where just one person was trapped (still fat by the way). Far more of the test subjects said they would flip the switch than had said they would throw someone off the bridge. The psychologists suggested some preposterous sounding reason for the difference, I don't even remember what, but it seemed to me that the change was because the plan just seemed a lot more likely to succeed. The test subjects DISCOUNTED the assurances of the psychologists that the 'throw someone off the bridge plan' would succeed. And quite rationally too, if you ask me. What rational person would rely on the opinion of a psychologist on such a matter?

When the 90%/500 or 100%/400 question was posed, I felt myself having exactly the same reaction. I immediately felt DUBIOUS that the odds were actually 90%. I immediately discounted the odds. By quite a bit, in fact. Perhaps that was because of lack of self confidence, or hard won pessimism from years of real life experience, but I immediately discounted the odds. I bet a lot of other people did too. And I wouldn't take the bet, for exactly that reason. I didn't BELIEVE the odds, as given. I was skeptical. Interestingly enough though, I was less skeptical of the 'can't fail/100%' estimate, than of the 90% estimate. Maybe I could easily imagine a scenario where there was no chance of failure at all, but couldn't easily imagine a scenario where the odds were, reliably, 90%. Once you start throwing around numbers like 90%, in an imperfect world, what you're really saying is 'there is SOME chance of failure'. Estimating how much chance, would be very much a judgement call.

So maybe what you're looking at here isn't irrationality, or the inability to multiply, but rather rational pessimism about it being as easy as claimed.

"My favorite anecdote along these lines - though my books are packed at the moment, so no citation for now - comes from a team of researchers who evaluated the effectiveness of a certain project, calculating the cost per life saved, and recommended to the government that the project be implemented because it was cost-effective. The governmental agency rejected the report because, they said, you couldn't put a dollar value on human life. After rejecting the report, the agency decided [i]not[/i] to implement the measure."

Does anyone know of a citation for this? Because I'd really like to be able to share it. I found this really, really, hilarious until I realized that, according to Eliezer, it actually happened and killed people. Although it's still hilarious, just simultaneously horrifying. It sounds like somebody misunderstood the point of their own moral grandstanding. (on the other hand, I suppose a Deontologist could in fact say "you can't put a dollar value on human life" and literally mean "comparing human lives to dollars is inherently immoral", not "human lives have a value of infinity dollars". To me as a consequentialist the former seems even stupider than the latter, but in deontology it's acceptable moral reasoning.)

Small inconveniences have consequences, and a googolplex is a very large number. A speck of dust in a googolplex people’s eye is a inconceivable bad thing., and I think most people would understand that if they thought what that entailed. What’s the chance that a momentary distraction will cause an accident? One in a billion? One in a quadrillion? Anyway you can be sure that a googolplex specks of dust will lead to large numbers of deaths and years of pain (much bigger than a googol). I suppose there is some minute way in which a speck of dust is more likely to cause a negative outcome than a positive - if that’s so then using a  “realistic” probability (say > 1e-100) the specks of dust seem by far the worse option. Shut up and multiply indeed!

I think the more interesting moral conclusion is that when you think about a probabilistic and uncertain world these minor inconveniences are not qualitatively different from major things like torture and death. The issue is that people don’t think about the variability in outcomes. I don’t think it’s a matter of “cold heartedly calculating”, but rather realizing that large numbers of small things have large consequences.

A more common example would be a traffic delay. Suppose you cause a 10 minutes delay to all traffic world-wide. What do you get? First it’s cost of some billions of dollars of lost work. Secondly some ambulances arrive to hospitals too late for the patients to survive. Maybe some police and firemen are delayed. 

But back to the original example. When you are talking about numbers like a googolplex I’m not sure there is any negative thing that is noticeable or could be described that wouldn’t multiply out to an obvious disaster which most people would consider far outweighs the torture (i.e. torture of far greater numbers for longer).

So maybe the problem is not that people view some things as sacred, but rather that they haven’t been explained the stakes? 

The use of torture in the example also muddies the issue I think. There are complicated reasons why people are against torture other than the pain inflicted. There is a (very imperfect) taboo against torture (and murder) and breaking this taboo is considered to possibly leading to more people tortured. So the taboo nature of torture interferes with the ability or desire to calculate.