Cryptographically secure shaming
There is a very recent paper that solves this problem at a large scale using secure computation techniques:


  How to (not) share a password: Privacy preserving protocols for finding heavy hitters with adversarial behavior: Moni Naor, Benny Pinkas, Eyal Ronen


They motivate the problem from the point of view of passwords (they want to identify passwords that are too common), but it seems like the same problem you propose.