Is there interesting mathematics around ranking? (I mean ranking as reputation points here at mathoverflow.)
It looks obvious that there is no way to make adequate ranking --- is it a theorem, at least if the ranking is a function on the set of users?
On the other hand, one may imagine that ranking is a function of pairs of users, and it might take values in something more complicated. In this case there might be rig-proof ranking, but is it even defined?
This post was misunderstood by almost everyone, so let me try to clarify:
On one hand, a straightforward attempt to define ranking brings Arrow's theorem into the game that says --- it is impossible --- there is nothing better than dictatorship. On the other hand, let us take MO as an example, you want to rank users according to your own rule and use it to decide if a post worth investing your time. In this case, rank is a function on the edges of complete oriented graph on all users. But there is another problem --- a user cannot have a sufficient number of interactions to make such a decision --- so either you do not read most of the posts or read too many. We may take into account the ranking of users that have a good rank in your system. One possibility is that instead of a number you get a maximal subgraph formed by disjoint paths from A (you) to B (another user).
What is described is just one possible attempt. Was something like this used somewhere? Did you see other constructions that is impossible to fake?
Another request: please do not bring PageRank here again --- it can be faked easily (assuming you have enuf resources).