Priority rules and other asymmetric rationing methods

In a rationing problem, each agent demands a quantity of a certain commodity and the available resources fall short of total demand. A rationing method solves this problem at every level of resources and individual demands. We impose three axioms: Consistency-with respect to variations of the set of agents-Upper Composition and Lower Composition-with respect to variations of the available resources. In the model where the commodity comes in indivisible units, the three axioms characterize the family of priority rules, where individual demands are met lexicographically according to an exogeneous ordering of the agents. In the (more familiar) model where the commodity is divisible, these three axioms plus Scale Invariance-independence of the measurement unit-characterize a rich family of methods. It contains exactly three symmetric methods, giving equal shares to equal demands: these are the familiar proportional, uniform gains, and uniform losses methods. The asymmetric methods in the family partition the agents into priority classes; within each class, they use either the proportional method or a weighted version of the uniform gains or uniform losses methods.