There are lots of hippo-fighting things I could say here, but handwaving a bit to accept the thrust of your hypothetical... a strictly utilitarian FAI of course agrees to kill everyone else (2) and replace them with copies of you (1). As J_Taylor said, utility monsters are wily beasts.
I find this conclusion intuitively appalling. Repugnant, even, Which is no surprise; my ethical intuitions are not strictly utilitarian. (3)
So one question becomes, are the non-utilitarian aspects of my ethical intuitions something that can be applied on these sorts of scales, and what does that look like, and is it somehow better than a world with a trillion hateful Viliam_Burs (1) and nobody else?
I think it isn't. That is, given the conditions you've suggested, I think I endorse the end result of a trillion hateful Viliam_Burs (1) living their happy lives and the appalling reasoning that leads to it, and therefore the FAI should allow it. Indeed, should enforce it, even if no human is asking for it.
But I'm not incredibly confident of that, because I'm not really sure I'm doing a good enough job of imagining that hypothetical world for the things I intuitively take into consideration to fully enter into those intuitive calculations.
For example, one thing that clearly informs my intuitions is the idea that Viliam_Bur in that scenario is responsible (albeit indirectly) for countless deaths, and ought to be punished for that, and certainly ought not be rewarded for it by getting to inherit the universe. (4) But of course that intuition depends on all kinds on hardwired presumptions about moral hazard and your future likelihood to commit genocide if rewarded for your last genocide and so forth, and it's not clear that any such considerations actually apply in your hypothetical scenario... although it's not clear that they don't, either.
There are a thousand other factors like that.
Does that answer your question?
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(1) Or, well, a trillion something. I really don't know what I want to say about the difference between one identical copy and a trillion identical copies when it comes to their contribution to some kind of total. This is a major gap in my ethical thinking; I do not know how to evaluate the value of copies; it seems to me that distinctness should matter, somehow. But that's irrelevant here; your scenario retains its power if, instead of a trillian identical copies of you, the FAI is invited to create a group of a trillion distinct individuals who hate everyone outside that group.
(2) Assuming that nobody else also wants a trillion copies of them made and it can't just move us all to Canarsie and not tell you and etc. and etc. All of which is actually pretty critical in practice, and handwaving it away creates a universe fairly importantly different from the one we actually live in, but I accept it for the sake of peace with hippos.
(3) In particular, the identity issue raises its head again. Killing everyone and replacing them with a trillion distinct people who are in some way superior doesn't feel the same to me as replacing them with a trillion copies of one superior person. I don't know whether I endorse that feeling or not. For our purposes here, I can dodge that question as above, by positing a trillion not-quite-identical copies.
(4) I know this, because I'm far less appalled by a similar thought experiment in which you don't want everyone else dead, you plead for their continued survival despite knowing it makes you less happy, and the FAI ignores all of that and kills them all anyway, knowing that you provide greater utility, and your trillion copies cry, curse the FAI's name, and then go on about your lives. All of which changes the important parts of the scenario not at all, but sure does make me feel better about it.
(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) -- Wha...
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.