In a rationing problem, each agent demands a quantity of a certain commodit
y and the available resources fall short of total demand. A rationing metho
d solves this problem at every level of resources and individual demands. W
e 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 axio
ms 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-character
ize 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 fa
mily partition the agents into priority classes; within each class, they us
e either the proportional method or a weighted version of the uniform gains
or uniform losses methods.