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).

rank aggregation problemorminimum feedback arc set$\endgroup$ – RobPratt May 1 at 1:0015more comments