Allocation of objects with conditional property rights

This paper considers the allocation of indivisible goods among members of a collective assuming that individuals are given the right to retain certain goods when some individuals alter the allocation problem. The assignment of rights is exhaustive in that, for every good x, either individual i can exercise a right over x against j or j against i. It is shown that the only Pareto efficient allocation rules satisfying these requirements are those having a hierarchy of diarchies.