constrained equal awards rules survive. We also prove that the constrained equal awards rule is the only rule that satisÞes strong … set of agents) together. Such a family is the Þxed path rules, which is a generalization of the weighted constrained equal … awards rules. In addition, once strong composition down and consistency are combined with homogeneity only the weighted …

equal awards rules. In addition, once strong composition down is combined with homogeneity only the weighted constrained … equal awards rules survive. We also prove that the constrained equal awards rule is the unique rules satisfying strong … set of agents) together. We call to that family the backbone family, which is a generalization of the weighted constrained …