Problem: Suppose that $K$ different students are ranked based on $N$ different parameters (such as Physics marks, English marks, Biology marks, IQ etc). The rank under each parameter can be repetitive i.e. if two persons have the same IQ then they will have the same rank under the IQ parameter. I want to combine these $N$ individual ranks into a composite rank so we can find find the best overall student to the worst.
Known methods: There are several knows algorithms in literature for for combining individual ranks into a composite ranking. Most of these algorithms work by maximizing a function the $N$ correlations coefficient between the individual ranks under a parameter and the composite rank. Few algorithms maximize the sum of the squares of the individual correlations, other maximize the minima of these $N$ correlation coefficient etc.
I do not find the idea of maximizing a function of the correlation coefficient to create the composite rank to be logically convincing enough to make practical sense although it has statistical backing up. Is there a better way of coming up with a composite rank?