The model of morality that resonates the most with me comes from Jonathan Haidt. He posits that regardless of the behaviors a moral argument encourages, whether a behavior is considered moral or immoral depends on how society interprets five pillars of morality: care, fairness, loyalty, respect, and purity. (http://moralfoundations.org/)
Care is fairly universal: nearly everyone believes it is wrong to physically hurt other people under most circumstances, and that it is good to care for people who have difficulty caring for themselves, such as children and elders.
Nearly as universal is the moral foundation of fairness. On an individual level, this manifests as the golden rule: do for others as you would have them do for you. On a cultural level, this foundation can manifest in different ways, with one end of the political spectrum emphasizing equality of freedom, and the other emphasizing equality of opportunity.
The moral foundation of Loyalty tends to manifest as either an us-vs-them team mentality, or as a more generalized sense of duty to community, family, or humanity. Humans need to form groups, and swearing allegiance to a group can be a way of identifying ourselves, even if the groups are based on something silly, like sports or celebrity.
Respect for authority is both the most divisive moral pillar, and the hardest to violate. Revolutionaries throughout time have called for the overthrow of the powers that be, envisioning a society where everyone has an equal hand in the creation of a brighter future. Yet even as the head of one tyrant rolls from the chopping block, another steps up to take their place more often than not. We are pack animals. We can’t help but make leaders. Even anarchists have figureheads. At the end of the day, all we can do is hope that whatever process we have in place to seat or displace leadership is adequate, and work to ensure that the best person possible is in charge, and that there are sufficient limits to their power.
Purity may be the strangest of the moral pillars. It takes things universally acknowledged as good and fetishizes them creating compulsive and compulsory rituals one must perform to engage this good thing. In some worldviews, the obsession is with sexual purity. In others, it is with wholesome eating or exercise or sacrificing comfort for the sake of nature.
No matter how much we may disagree with how someone behaves in a moral context, we all seem to keep landing on one or more of these same moral foundations when we speak of morality as a premise.