Background: I have a website where students vote on the attractiveness of their peers: they are presented with two images, and they must pick one (the "winner")- then the elo score for each is updated. A user can choose to vote globally (i.e. cross population, i.e. between all schools), or a user can vote within a single school (i.e. separate population). All students start with 1200 points, there is a minimum of 1000 points. It's easy to rank students individually: for example the most attractive person within school "x" is simply the one with the highest elo points.
Problem: I want to have a ranking for a group of students- in other words i want to say "here are the most attractive schools"
My idea (which I think is bad): Take an average of the elo points for all students. My thought is that since "every win also means there is a loss" the distribution curve for all schools should be relatively similar- so the average elo points for every school will be relatively similar. A wider distribution curve would simply mean there are greater numbers of both more attractive and less attractive students (I think?).
So does anyone have a (somewhat statistically significant) method of saying "this group of students is more attractive than that group of students?" I feel like I'm not collecting the proper metric- this would be easy if the users were ranking a single student on a 1-5 star scale, rather than my system where you're asked to pick between two students.
Any advice much appreciated, thank you.