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I was surprised to hear that you doubt that there are ever conflicts in desires.
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
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.
But, what if two different people have two conflicting desires? How do we objectively find the ethical resolution to the conflict?
Basically: game theory.
In reality, I'm not sure there ever are precise conflicts of true foundational desires. Maybe it would help if you had some real example or something. But the best choice for each party will always be the one that maximizes their chances of satisfying their true desire.
Missing the point. Ethics needs to sort good actors from bad--decisions about punishments and rewards depend on it.
(I'd say need to sort good choices from bad. Which includes the choice to punish or reward.) Discovering which choices are good and which are bad is a fact finding mission. Because:
1) it's a fact whether a certain choice will successfully fulfill a certain desire or not
And 2) that's what "good" literally means: desirable.
So that's what any question of goodness will be about: what will satisfy desires.
PS are you the same person as rkyeun? If not, to what extent are you on the same page?
No I'm not rkyeun. As for being on the same page...well I'm definitely a moral realist. I don't know about their first iff-then statement though. Seems to me that strong moral realism could still exist if supernaturalism were true. Also, talking in terms of molecules is ridiculously impractical and unnecessary. I only talked in those terms because I was replying to a reply to those terms :P
Even if it were true that under naturalism we could determine the outcome of various arrangements of particles, wouldn't we still be left with the question of which final outcome was the most morally preferable?
Yup.
But that's sort-of contained within "the positions of particles" (so long as all their other properties are included, such as temperature and chemical connections and so on...might need to include rays of light and non-particle stuff too!). The two are just different ways of describing the same thing. Just like every object around you could be described either with their usual names, ("keyboard:, "desk", etc) or with an elaborate molecule by molecule description. Plenty of other descriptions are possible too (like "rectangular black colored thing with a bunch of buttons with letters on it" describes my keyboard kinda).
How (under naturalism) do we objectively decide between your preferences and mine?
You don't. True preferences (as opposed to mistaken preferences) aren't something you get to decide. They are facts.