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.
Maybe you misunderstand the concept of lying. They would really believe that all Jews are dead if successfully lied to, so their stress would decrease just as much as as if they all were indeed dead.
This is more interesting. Here we go, the definitions:
Assumption: we assume that it is possible to separate overall personal happiness level into components (factors), which could be additive, multiplicative (or separable in some other way). This does not seem overly restrictive.
Definition 1: A component of personal happiness resulting from others being unhappy is called "malicious".
Definition 2: A component of personal happiness resulting from others being happy is called "virtuous".
Definition 3: A component of personal happiness that is neither malicious nor virtuous is called "neutral".
Now your suggestion is that malicious components do not count toward global decision making at all. (Virtuous components possibly count more than neutral ones, though this could already be accounted for.) Thus we ignore any suffering inflicted on Nazis due to Jews existing/prospering.
Does this sound right?
If this is the case then the Nazis do not really want to kill the Jews. What they really want to do is decrease their stress, killing Jews is just an instrumental goal to achieve that end. My understanding of the original thought experiment was that killing Jews was a terminal value for the Nazis, something they valued for its own sake regardless of whether it helped them achieve any other goals. In ... (read more)