Ordering distributions on a finitely generated cone
研究了由有限生成锥诱导的一类关系，用于社会福利和风险测量中的分布排序，给出了分布x和y有序的三种等价条件。
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 $$x-y$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>-</mml:mo> <mml:mi>y</mml:mi> </mml:mrow> </mml:math> 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 $$x-y$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>x</mml:mi> <mml:mo>-</mml:mo> <mml:mi>y</mml:mi> </mml:mrow> </mml:math> results in a non-negative vector. We illustrate the results in the context of a discrete version of the cone of inframodular transfers.