Parametric rationing methods

In a rationing problem, a single homogeneous good is allocated among agents with possibly complex characteristics, or types. When types are single positive numbers (agents' claims), Young's theorem says that in the presence of continuity, a method of rationing is consistent and symmetric if and only if it can be represented by a continuous parametric function. This theorem is generalized to all separable type spaces. Related results include a characterization of non-continuous parametric methods and a simple criterion for deciding when a two-agent method can be consistently extended to a multi-agent method. An application to the multi-category bankruptcy problem is described.