# mathematics around ranking [closed]

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).

• PageRank is maybe one keyword here... – Sam Hopkins Apr 30 at 23:44
• rank aggregation problem or minimum feedback arc set – RobPratt May 1 at 1:00
• @AntonPetrunin That may be because the problem itself doesn't give much to go on. The first question - "Is there interesting mathematics around ranking? " - might be worth exploring (though I expect that it's more psychology than math), but the rest looks to me like underdefined statements with very little that can be answered. What do you think "adequate" means? Or "rig-proof"? – user44191 May 1 at 2:45
• I've read your revision (May 4th) but I do not understand what the goal of a ranking might be. What is a ranking, and what would it represent? – Ryan Budney May 4 at 21:26
• Hi Anton, it's still unclear to me what exactly you want to measure or define. It sounds like you have some sort of implied definition, using extrapolation from common-usage English language. I imagine most people want more to go on than that. Reputation in the MO sense is a fairly concrete (albeit, sometimes changing) algorithm. Reputation in an idealized English-language sense is purely subjective. Someone who is very reputable to me might mean nothing to someone else, or the reverse. This is sort of like university rankings. They're all different, and any one is likely justifiable. – Ryan Budney May 5 at 2:43