Incentive-Compatible Classification

We investigate the possibility of an incentive-compatible (IC, a.k.a. strategy-proof) mechanism for the classification of agents in a network according to their reviews of each other. In the $\alpha$-classification problem we are interested in selecting the top $\alpha$ fraction of users. We give upper bounds (impossibilities) and lower bounds (mechanisms) on the worst-case coincidence between the classification of an IC mechanism and the ideal $\alpha$-classification. We prove bounds which depend on $\alpha$ and on the maximal number of reviews given by a single agent, $\Delta$. Our results show that it is harder to find a good mechanism when $\alpha$ is smaller and $\Delta$ is larger. In particular, if $\Delta$ is unbounded, then the best mechanism is trivial (that is, it does not take into account the reviews). On the other hand, when $\Delta$ is sublinear in the number of agents, we give a simple, natural mechanism, with a coincidence ratio of $\alpha$.