The implications of the ranking axiom for discrete cost sharing methods

In this paper, we study the Ranking property for discrete cost sharing methods. In the two‐agent model, we characterize the set of methods satisfying this axiom: the symmetry of the flow representing the method is necessary and sufficient for Ranking. In higher dimensions (n ≥ 3), we identify strong implications of the axiom; however, we prove that these conditions are not sufficient to characterize Ranking. For the so‐called elementary fixed flows, we derive a necessary and sufficient condition.