I'm not sure if he's asking the wrong audience. We could address
a slightly different question, namely what are uses of
mathematics in social science, or potential uses, that
mathematicians would endorse. One example that comes to mind is
the site, FiveThirtyEight. For those who don't follow this as
closely, 538 is the number of electors in a US presidential
election. The main person at this site, Nate Silver, has hit 50
home runs in the subject of American political polling. (He
previously did baseball statistics.) He did this by using first-
year graduate statistics, which of course amounts to certain
parts of 18th and 19th century analysis. More importantly than
the specific formulas, Silver had a disciplined mindset. He also
has his ideology (he's liberal), but he wasn't slave to his
ideology. His reasoning is, here is a big set of measurements,
here are the results of multivariate regression, here is the
uncertainty in the results, here are possible systematic errors,
here is how we could learn more from