Optimization based characterizations of cost sharing methods

We provide several new characterizations of well known cost sharing methods (CSMs) as maxima of linear (or convex) functionals. For the Shapley-Shubik method the characterization has an interpretation in terms of randomly ordered agents choosing their most preferred CSM, while the characterizations of the Aumann-Shapley and Serial methods have a very general character: any symmetric convex functional which uniquely characterizes a scale invariant CSM must characterize the Aumann-Shapley method, while the identical statement is true for the Serial method when scale invariance is replaced by demand monotonicity.