Characterizing minimal impartial rules for awarding prizes

We study the problem of selecting prize winners from a group of experts when each expert nominates another expert for the prize. A nomination rule determines the set of winners on the basis of the profile of nominations; the rule is impartial if one's nomination never influences one's own chance of winning the prize. In this paper, we consider impartial, anonymous, symmetric, and monotonic nomination rules and characterize the set of all minimal such rules. We show that the set consists of exactly one nomination rule: a natural variant of the plurality correspondence called plurality with runners-up.