Scott suggests that ranking morality is similar to ranking web pages. A quote:
Philosophers from Socrates on, I was vaguely aware, had struggled to define what makes a person “moral” or “virtuous,” without tacitly presupposing the answer. Well, it seemed to me that, as a first attempt, one could do a lot worse than the following:
A moral person is someone who cooperates with other moral people, and who refuses to cooperate with immoral people.
Proposed solution:
Just like in CLEVER or PageRank, we can begin by giving everyone in the community an equal number of “morality starting credits.” Then we can apply an iterative update rule, where each person A can gain morality credits by cooperating with each other person B, and A gains more credits the more credits B has already. We apply the rule over and over, until the number of morality credits per person converges to an equilibrium. (Or, of course, we can shortcut the process by simply finding the principal eigenvector of the “cooperation matrix,” using whatever algorithm we like.) We then have our objective measure of morality for each individual, solving a 2400-year-old open problem in philosophy.
He then talks about "eigenmoses and eigenjesus" and other fun ideas, like Plato at the Googleplex.
One final quote:
All that's needed to unravel the circularity is a principal eigenvector computation on the matrix of trust.
EDIT: I am guessing that after judicious application of this algorithm one would end up with the other Scott A's loosely connected components with varying definitions of morality, the Archipelago. UPDATE: He chimes in.
EDIT2: The obvious issue of equating prevailing mores with morality is discussed to death in the comments. Please read them first before raising it yet again here.
I'm broadly sympathetic to your point that Aaronson's algorithm is measuring something like conformity or group consensuses rather than morality, but the specific example you picked to garnish that point is dodgy. From Randall Collins's Violence: A Micro-sociological Theory, pages 425-426:
The last photo Collins refers to ("plate 97") sounds like it's your photo 2, and Collins's interpretation of it seems to me to fit better than the one you imply. I wouldn't go as far as to say that all of the "twenty-nine other visible faces range from somber to apprehensive", as a few of the people in the photo are evidently just trying to get a closer look, and a boy near the front seems more intrigued than anything else. Nonetheless, the crowd as a whole doesn't appear joyful or celebratory to me.
Turning to photo 1, I see perhaps ten spectators' faces clearly enough to make a guess at what they're expressing. Going from left to right, I see (1) thick-eyebrowed man in cap in background who looks as if he's whistling while thinking hard about something; (2) foreground man in white shirt with no tie with neutral-ish expression, but maybe happy; (3) man in middle distance with shorter man in front and a boater-wearer behind, the former gazing off to the photographer's right with a worried/pensive look; (4) smirking man in tie; (5) foreground woman in dress with irregular spots who looks surprised/wary; (6) another woman behind her with open mouth, who might be amused or surprised or scandalized; (7) cluster of three foreground women, where the nearest one's face is too blurry for me to interpret, but the two further back both look apprehensive; (8) foreground man with moustache, pointing as he stares intently; and (9) man at right edge with left eye not visible in photo, looking not especially happily to the photographer's right. As in photo 2, although there are happy-looking people present, they are a minority.
I don't believe it's accurate to use these scenes as examples of rightful celebration or joy. fubarobfusco's warning to exercise caution in how we read these photos may be well-advised.
Yes, I know these photos were analyzed quite substantially, but my point is really simple -- it's that the lynchings (and the witch burnings before them) were culturally normal. The were intense events and, of course, brought out a range of emotions, not just joy, but all I'm trying to say is that the majority of people did not see them as something to be ashamed of. It was OK, it was fine, it was moral.