But this ignores actually doing the math! Suppose it is known that she would prefer abcdz's company to the other fellow's, and abcdz would prefer her company to no one's, and the other fellow would prefer her company to no one's, but his preference is smaller than theirs. The "stealing other people's partners is bad" is putting precedence above greatest good.* The claim that it's existentially risky is one that doesn't require utilitarianism; a selfish person is more concerned about those sorts of incentives than a utilitarian.

I am of the opinion that utilitarianism is wrong wrong wrong, but treating it as a moral decision procedure is even more wrong. If you're going to be a utilitarian, be a utilitarian at the meta level: think about what moral decision procedure will lead you (given your cognitive and other limitations) to maximize utility in the long run. I think there are many good reasons to believe that doing the math at every decision point will not be the optimal procedure in this sense. Of course, it would be if you were a fully informed, perfectly rational superbeing with infinite willpower and effectively infinite processing speed, but alas, even I cannot yet claim that status.

Given this unfortunate state of affairs, I suspect it is actually a better idea for most utilitarians to commit themselves to a policy like "Don't steal someone else's partner" rather than attempt to do the math every time they are faced with the decision. Of course, there may still be times when its just blindingly obvious that the math is in favor of stealing, in which case screw the policy.