Suppose I have 3 columns and n rows. Each row represents a school and the columns represent variables of interest and have ordinal ranks (1,2,3,4....n; 1 being the best and n being the worst). Furthermore, the weight (significance) of each column is known - e.g. 0.25, 0.5, 0.25. The question is: for a given school, can the value of each column be multiplied by its respective weight in order to calculate a total rank for each school? I know that normally this should not be a problem with regular data but since the data is made up of ranks, how will this affect the calculations?
Multiplying the ranks by the column weights and then comparing the row sums for is one way to achieve this ranking.
Of course, that's assuming you want a ranking scheme such that rank 1 = 1 point, rank 2 = 2 points..., etc. That scoring scheme implicitly assumes that there amount of difference between each rank and the next is equal. Alternatively, another way you could do this is by coming up with an alternative score scheme (e.g. rank 1-5 = 1-5 points respectively, rank 6-10 = 6 points, rank 11-15 = 7 points, etc.) This would be useful if you thought there was a substantial difference between the top schools in each category, but not as much of a difference between schools with lower ranks in each category.
There are many other possibilities as well. Maybe someone with more experience analyzing rank data than myself could better explain the possible alternatives.