Impartial nomination correspondences

Among a group of selfish agents, we consider nomination correspondences that determine who should get a prize on the basis of each agent’s nomination. Holzman and Moulin (Econometrica 81:173–196, 2013) show that (i) there is no nomination function that satisfies the axioms of impartiality, positive unanimity, and negative unanimity, and (ii) any impartial nomination function that satisfies the axiom of anonymous ballots is constant (and thus violates positive unanimity). In this article, we show that \((\mathrm {i})^\prime \) there exists a nomination correspondence, named plurality with runners-up, that satisfies impartiality, positive unanimity, and negative unanimity, and \((\mathrm {ii})^\prime \) any impartial nomination correspondence that satisfies anonymous ballots is not necessarily constant, but violates positive unanimity.