Ordinally consistent set-ranking methods for tournaments

•We study methods for ranking sets of items in a tournament.•We define a notion of ordinal consistency for such methods.•We construct two examples of ordinally consistent set-ranking methods.

A set-ranking method assigns to each tournament on a given set an ordering of the subsets of that set. Such a method is consistent if (i) the items in the set are ranked in the same order as the sets of items they beat and (ii) the ordering of the items fully determines the ordering of the sets of items. We describe two consistent set-ranking methods.