Asymmetric rules for claims problems without homogeneity

Abstract We introduce a general class of rules for claims problems, called the difference rules , and demonstrate that a rule satisfies composition down and composition up if and only if it is a difference rule. We show that these rules are very simple to describe when there are two agents. In a variable population framework, we introduce a family of rules satisfying consistency , composition down , and composition up , which we term the logarithmic-proportional rules . These rules satisfy neither symmetry nor homogeneity .