Simple random order methods to share costs

A simple random order method (SROM) is an extension of Weber's random order values (ROVs), which allows the convex weights on orderings of agents to depend on the set of agents with strictly positive demands. Thus, a SROM permits different coalitions of agents adopting exogenously different ROVs to take into account the differences in, for example, bargaining abilities, rights or status of the agents in a cost sharing problem. Within the family of additive methods satisfying the dummy axiom, we characterize SROMs by Measurement Invariance in the discrete cost sharing model where demands are indivisible, and Ordinality in the continuous model where demands are divisible, respectively.