Nice overview. But I found the ending part on why the Haidt calibration view doesn't imply relativism a bit shady—a bit Straussian even!
Pinker struck me as arguing that there are real external facts about human flourishing that help underpin the authority of the harm and reciprocity dimensions of the moral sense, whereas the new science of morality helps us to see that we are subject to all sorts of “illusions” when it comes to the authority, in-group, and purity dimensions.
Now, I agree about a trillion percent with what I imagine Pinker is going for here: improving real human well-being by establishing the cultural dominance of a distinctively liberal calibration of the moral sense. That is, in fact, the ticket. But I simply don't see how this stands as an adequate reply to someone who says that it is better that millions suffer and/or die for the greater glory of the tribe, or the Prophet, or to prevent the defilement of the blood of the Motherland. Yes, it is an objective fact of the world that if the well-being of each is our aim, then liberal morality, and its concomitant institutions, such as the extended order of market cooperation, are the necessary means. But, tragically, we do not all share this aim.
Must we? From the perspective of morality per se and not just from the perspective of one among many moralities? Is human flourishing of overriding importance–does it get greater weight than alternatives—because of it's very nature. Or are those of us with an already liberal moral sense simply willing to go to the mat for the idea? To my mind, Haidt's views do leave us with relativism. And the obviously correct thing to do is to fight and win a global culture war for a liberal morality. The ongoing fight against liberal morality is sometimes so savage because, well, because the people fighting it are not liberals for one thing, but also because the advantages of liberalism—greater wealth, better health, longer lives, more deeply satisfying individuation, etc.—are so attractive, so enticing, and therefore so dangerous to those whose sense of meaning is bound up in an illiberal calibration of the moral sense.
Why not just say that a more thoroughly liberal calibration of the moral sense will deliver a huge list of incredibly attractive goods for everyone in the world, and leave it at that? If some can't be persuaded to care about those goods, then their kids can be. And their happy, health, wealthy, long-lived kids will little lament the loss of their backwards ancestral codes.
My unpublished essay on Haidt and politics, here.