The murderer wants to murder the victim, the victim doesn’t want to be murdered.
Murder isn’t a foundational desire. It’s only a means to some other end. And usually isn’t even a good way to accomplish its ultimate end! It’s risky, for one thing. So usually it’s a false desire: if they knew the consequences of this murder compared to all other choices available, and they were correctly thinking about how to most certainly get what they really ultimately want, they’d almost always see a better choice.
(But even if it were foundational, not a means to some other end, you could imagine some simulation of murder satisfying both the “murderer”’s need to do such a thing and everyone else’s need for safety. Even the “murderer” would have a better chance of satisfaction, because they would be far less likely to be killed or imprisoned prior to satisfaction.)
since the same act can increase one person’s utility and reduce anothers, there is no unambiguous way to label an arbitrry outcome.
Well first, in the most trivial way, you can unambiguously label an outcome as “good for X”. If it really is (it might not be, after all, the consequences of achieving or attempting murder might be more terrible for the would-be murderer than choosing not to attempt murder).
It works the same with (some? all?) other adjectives too. For example: soluble. Is sugar objectively soluble? Depends what you try to dissolve it in, and under what circumstances. It is objectively soluble in pure water at room temperature. It won’t dissolve in gasoline.
Second, in game theory you’ll find sometimes there are options that are best for everyone. But even when there isn’t, you can still determine which choices for the individuals maximize their chance of satisfaction and such. Objectively speaking, those will be the best choices they can make (again, that’s what it means for something to be a good choice). And morality is about making the best choices.
Re-read what I said. That’s not what I said.
First get straight: good literally objectively does mean desirable. You can’t avoid that. Your question about conflict can’t change that (thus it’s a red herring).
As for your question: I already generally answered it in my previous post. Use Game theory. Find the actions that will actually be best for each agent. The best choice for each party will always be the one that maximizes their chances of satisfying their true desires.
I might finish a longer response to your specific example, but that takes time. For now, Richard Carrier’s Goal Theory Update probably covers a lot of that ground.
http://richardcarrier.blogspot.ca/2011/10/goal-theory-update.html