I have data on the graduation rate, tuition, and average student income (a measure of accessibility) for about 7,000 colleges and universities in the U.S., and I'm trying to compose an interactive in which people can manipulate the importance of these three variables to create a ranking. Users drag three sliders to emphasize or deemphasize the importance of the variables:
I've standardized the variables through the usual means so that each value is the number of standard deviations from the mean. Each variable also has a weight assigned by the sliders, which add to 1. One user might give 50% weight to graduation rate and 25% to the other two; another might give 33% to all three, and so forth.
My first instinct was to just multiply the weight by the standardized value and add them together for each school's score. But this seems to overly reward outliers in one area, when the goal is to surface schools that perform well over all. Graduation rate is negatively correlated with accessibility and positively correlated to cost, FWIW.
Is there an accepted way to weight multivariate systems like this in a better way?