He calls values listed horizontally (harm, fairness, ingroup etc.) moral foundations. He measures how people, presumedly self-identified, with different political loyalties use these moral foundations in their moral reasoning. His point is that the Right and Left have differing moral compasses, and so they go in differing directions.
I couldn't even begin to make a rigorous critique of the social science involved here. I don't even know what the vertical axis is measuring. But I can tell what's bigger and what's smaller.
A couple of things stand out: liberals are more likely to be motivated by concerns about the harm to people in any situation; liberals are more likely to be concerned with fairness. They are less likely to be concerned about maintaining the boundaries between the ins and the outs, less concerned about authority and less motivated to maintain the purity codes that are the basis of the moral test of "ickiness".
I am especially confused about these last two categories of "lifestyle liberty" and "economic liberty" since they seem to be derivative of the other five values. If you are not concerned about the harm that might flow to others and you are not concerned about fairness, then "economic liberty" seems to follow logically, if you define "economic liberty" as the freedom to make and spend money as you wish.
I do not think that these moral preferences are determined by brain chemistry on an individual level. They are, I think, culturally produced. They are values handed down through families and reinforced through the culture, including religious institutions.
This graph connects with one of my concerns about Unitarian Universalism. Liberal Religion is not good at defining its pastoral mission on a social level. We get pastoral ministry on an individual and personal level, but on a social level, we are tongue-tied and reticent.
Where are we trying to take people? How are we proposing to change them? How are we proposing to "convert" people in any deeper sense than getting them to join one of our congregations?
This chart is as good an explanation as any, although differing language could be used, and there is one thing missing.
Here's the question: how would we bring people to operate out of the particularly liberal cluster of moral values: compassionate, fair, open, and less deferential to authority? How could we make them the moral foundations of our culture? We will not, of course, be entirely successful at this; we are one strand of culture among many. But this is who we are and what we stand for and it should be what we are trying to spread.
What tools do we have to do this work? We have congregations, and buildings and religious professionals. Most of work we do is the creation of worship experiences, mostly for ourselves, but theoretically for all. We have programs, including our work to try to shape the moral universe of our children. These are only our assets; but assets are not purposes.
To pull this together, the question that I have is this: How are we to use our ability to create worship experiences and to put together programs for children and adults to influence the people around us to count compassion and fairness more heavily than authority, tribal loyalty and "ickiness" in their moral reasoning?