Another useful methodology often used in psychology -- less in social, more in cognitive -- is one alluded to here before, "multidimensional scaling" (MDS). MDS has only been used in a small number of legal analyses, but can be quite helpful in the right context.
As I describe in a forthcoming paper, "MDS is a procedure that helps researchers uncover 'hidden structures' in data by graphically plotting respondents' perceptions of perceived similarities (or dissimilarities) among various stimuli. When these stimuli are located on a plot based on such perceptions, underlying dimensions that respondents may have used (consciously or not) can be inferred."
So, for instance, a bunch of stimuli are identified -- crimes, Supreme Court opinions -- and every pairwise combination is created. Each pair is rated on how similar or close they are (though the researcher usually does not articulate the scale to be used, just asks "how similar"?). Those similarity ratings are then plotted to give the best fit to the data, yielding a "map" of the ratings that also reflects the perceived structural relationship of all those stimuli. Finally, by examining the map, one might be able to identify the dimensions that, implicitly or explicitly, underlay subjects' ratings (and also, interestingly, look at individual differences, e.g., do men and women or Republicans and Democrats come up with different maps or weight those dimensions differently?).
As a specific, somewhat prosaic example: subjects might be asked to rate the similarity of countries in the world, and a plot made of the countries based on those similarity ratings. The resulting map might look like a map of the world, which could suggest that subjects were, implicitly or not, using dimensions involving distance, in particular, dimensions of north/south and east/west. But the plot might line up the countries on a single axis going from largest to smallest, or richest to poorest, or most to least economically developed, suggesting that subjects used that single dimension in their ratings. Inferring which dimensions are important to respondents helps understand the way they see the world (literally, here), and what factors are important to them.
In the legal context, I used it in that paper to map people's perceptions of the seriousness of crimes. MDS is broadly useful for looking at lay intuitions about legal institutions, punishments, or cases; or to assess whether different punishments may have been proportionate; or any context in which (a) similarities among stimuli may be interesting or (b) we are interested in understanding what the basis might be for people's judgments or perceptions.