What is sometimes called "the 1000 Sadists problem" is a classic "problem" in utilitarianism; this post is another version of it.
Here's another version, which apparently comes from this guy's homework:
Suppose that the International Society of Sadists is holding its convention in Philadelphia and in order to keep things from getting boring the entertainment committee is considering staging the event it knows would make the group the happiest, randomly selecting someone off the street and then torturing that person before the whole convention. One member of the group, however, is taking Phil. 203 this term and in order to make sure that such an act would be morally okay insists that the committee consult what a moral philosopher would say about it. In Smart's essay on utilitarianism they read that "the only reason for performing an action A rather than an alternative action B is that doing A will make mankind (or, perhaps, all sentient beings) happier than will doing B." (Smart, p. 30) This reassures them since they reason that the unhappiness which will be felt by the victim (and perhaps his or her friends and relatives) will be far outweighed by the happiness felt by the large crowd of sadists, especially since the whole thing will be kept strictly secret (as of course the whole convention has to be every year anyway). So they conclude that the best, indeed morally right, thing to do is go ahead and torture this person, and set off to do it.
Write a short paper in which you explain and critically evaluate what a defender of utilitarianism, for instance Smart’s version of act utilitarianism, could say about this example. Have the sadists misunderstood utilitarianism? Or will a defender of this view just have to accept the sadists' conclusion (and if so, what, if anything, does that say about the theory itself)?
That's a reverse version of the utility monster scenario.
Act utilitarianism always leads to these kind of paradoxes. I don't think it can be salvaged.
This is based on a discussion in #lesswrong a few months back, and I am not sure how to resolve it.
Setup: suppose the world is populated by two groups of people, one just wants to be left alone (labeled Jews), the other group hates the first one with passion and want them dead (labeled Nazis). The second group is otherwise just as "good" as the first one (loves their relatives, their country and is known to be in general quite rational). They just can't help but hate the other guys (this condition is to forestall the objections like "Nazis ought to change their terminal values"). Maybe the shape of Jewish noses just creeps the hell out of them, or something. Let's just assume, for the sake of argument, that there is no changing that hatred.
Is it rational to exterminate the Jews to improve the Nazi's quality of life? Well, this seems like a silly question. Of course not! Now, what if there are many more Nazis than Jews? Is there a number large enough where exterminating Jews would be a net positive utility for the world? Umm... Not sure... I'd like to think that probably not, human life is sacred! What if some day their society invents immortality, then every death is like an extremely large (infinite?) negative utility!
Fine then, not exterminating. Just send them all to concentration camps, where they will suffer in misery and probably have a shorter lifespan than they would otherwise. This is not an ideal solutions from the Nazi point of view, but it makes them feel a little bit better. And now the utilities are unquestionably comparable, so if there are billions of Nazis and only a handful of Jews, the overall suffering decreases when the Jews are sent to the camps.
This logic is completely analogous to that in the dust specks vs torture discussions, only my "little XML labels", to quote Eliezer, make it more emotionally charged. Thus, if you are a utilitarian anti-specker, you ought to decide that, barring changing Nazi's terminal value of hating Jews, the rational behavior is to herd the Jews into concentration camps, or possibly even exterminate them, provided there are enough Nazi's in the world who benefit from it.
This is quite a repugnant conclusion, and I don't see a way of fixing it the way the original one is fixed (to paraphrase Eliezer, "only lives worth celebrating are worth creating").
EDIT: Thanks to CronoDAS for pointing out that this is known as the 1000 Sadists problem. Once I had this term, I found that lukeprog has mentioned it on his old blog.