(1) and (3) -- Actually my original thought was "a trillion in-group individuals (not existing yet) who like each other and hate the out-groups", but then I replaced it with trillion copies to avoid possible answers like: "if they succeed to kill all out-groups, they will probably split into subgroubs and start hating out-subgroups". Let's suppose that the trillion copies, after exterminating the rest of the universe, will be happy. The original mind may even wish to have those individuals created hard-wired to feel like this.
(2) -- What if someone else wants trillion copies too, but expresses their wish later? Let's assume there are two such hateful entities, let's call them A and B. Their copies do not exist yet -- so it makes sense to create trillion copies of A, and kill everyone else including (the single copy of) B; just as it makes sense to create trillion copies of B and kill everyone else including (the single copy of) A. Maybe the first one who expresses their wishes win. Or it may be decided by considering that trillion As would be twice as happy as trillion Bs, therefore A wins. Which could be fixed by B wishing for ten trillion copies instead.
But generally the idea was that calculations about "happiness for most people" can be manipulated if some group of people desires great reproduction (assuming their children will mostly inherit their preferences), which gradually increases the importance of wishes of given group.
Even the world ruled by utilitarian Friendly AI would allow fights between groups, where the winning strategy is to "wish for a situation, where it is utilitarian to help us and to destroy our enemies". In such world, the outside-hateful inside-loving hugely reproducing groups with preserved preferences would have an "evolutionary advantage", so they would gradually destroy everyone else.
(nods) I'm happy to posit that the trillion ViliamBur-clones, identical or not, genuinely are better off; otherwise of course the entire thing falls apart. (This isn't just "happy," and it's hard to say exactly what it is, but whatever it is I see no reason to believe it's logically incompatible with some people just being better at it than others. In LW parlance, we're positing that ViliamBur is much better at having Fun than everybody else. In traditional philosophical terms, we're positing that ViliamBur is a Utility Monster.)
...Their copies do
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.