It may well be the case that there are multiple eventual equilibria that depend on the order in which one considers arguments

Another way to get several equilibria would be moral judgements whose "correctness" depends on whether other people share them. I find it likely that there would be some like that, since you get those in social norms and laws (like, on which side of the road you drive, or whether you should address strangers by their first or last name), and there's a bit of a fuzzy continuum between laws, social norms, and morality.