ABSTRACT

One large class of relations used in the measurement of social welfare and risk consists of relations induced by finitely generated cones. Within this class, we develop a general approach to investigate the ordering of distributions. We provide an equivalence between the statement that distributions x and y are ordered, and (1) the possibility of expressing as a positive combination of a subset of linearly independent vectors from the generators of the cone, (2) the existence of a relation defined on a simplicial cone such that x and y are ordered by this latter relation, (3) the existence of a generalized inverse G of the matrix whose columns generate the cone, such that the product of G and the vector results in a non-negative vector. We illustrate the results in the context of a discrete version of the cone of inframodular transfers.