Impartial selection addresses the problem of choosing one or more agents from a group based on nominations by other members of the group, in such a way that no agent can influence their own chance of being selected. Deterministic mechanisms for selecting a single agent face strong impossibilities. For example, Holzman and Moulin (Econometrica, 2013) showed that when each agent nominates one other agent, no impartial mechanism can simultaneously satisfy positive unanimity—that an agent nominated by everyone else is selected—and negative unanimity—that an agent with no nominations is not selected. In response to such negative results, subsequent work has explored relaxations of this setting, either by allowing randomization or by permitting the selection of a variable number of agents. In this talk, we will further motivate these relaxations by presenting a strengthening of Holzman and Moulin’s impossibility for the case where agents may nominate any number of peers, and we will cover some recent results on both relaxations. We will also discuss how the performance of impartial mechanisms can be improved if a prediction of the optimal set of agents is available.
