If you hoped that morality would be universalizable—sorry, that one I really can’t give back. Well, unless we’re just talking about humans. Between neurologically intact humans, there is indeed much cause to hope for overlap and coherence; and a great and reasonable doubt as to whether any present disagreement is really unresolvable, even it seems to be about “values”. The obvious reason for hope is the psychological unity of humankind, and the intuitions of symmetry, universalizability, and simplicity that we execute in the course of our moral arguments. (In retrospect, I should have done a post on Interpersonal Morality before this...)
If I tell you that three people have found a pie and are arguing about how to divide it up, the thought “Give one-third of the pie to each” is bound to occur to you—and if the three people are humans, it’s bound to occur to them, too. If one of them is a psychopath and insists on getting the whole pie, though, there may be nothing for it but to say: “Sorry, fairness is not ‘what everyone thinks is fair’, fairness is everyone getting a third of the pie”. You might be able to resolve the remaining disagreement by politics and game theory, short of violence—but that is not the same as coming to agreement on values. (Maybe you could persuade the psychopath that taking a pill to be more human, if one were available, would make them happier? Would you be justified in forcing them to swallow the pill? These get us into stranger waters that deserve a separate post.)
If I define rightness to include the space of arguments that move me, then when you and I argue about what is right, we are arguing our approximations to what we would come to believe if we knew all empirical facts and had a million years to think about it—and that might be a lot closer than the present and heated argument. Or it might not. This gets into the notion of ‘construing an extrapolated volition’ which would be, again, a separate post.
But if you were stepping outside the human and hoping for moral arguments that would persuade any possible mind, even a mind that just wanted to maximize the number of paperclips in the universe, then sorry—the space of possible mind designs is too large to permit universally compelling arguments. You are better off treating your intuition that your moral arguments ought to persuade others, as applying only to other humans who are more or less neurologically intact. Trying it on human psychopaths would be dangerous, yet perhaps possible. But a paperclip maximizer is just not the sort of mind that would be moved by a moral argument. (This will definitely be a separate post.)
Added a section on non-universalizability: