This paper is devoted to the study of claims problems. I characterize the family
of rules that satisfy both strong composition down (robustness with respect to reevaluations
of the estate) and consistency (robustness with respect to changes in the set
of agents). These are the fixed path rules, a generalization of the weighted constrained
equal awards rules. In addition, if strong composition down and consistency are combined
with homogeneity, only the weighted constrained equal awards rules survive. I
also prove that the constrained equal awards rule is the only rule that satisfies strong
composition down, consistency and equal treatment of equals.
Keywords: claims problem, strong composition down, fixed path rules, constrained equal
awards rule.
