Abstract
The allocation of indivisible objects is studied where individuals claim packages of them and a rule determines the number of each package to be allocated. There exists a rule satisfying feasibility, efficiency, and composition down (or composition up) if and only if the set of institutionally feasible packages is a hierarchy, i.e., for any pair of packages, either that they are disjoint or that one contains the other. Moreover, on a hierarchy, the unique rules satisfying the aforementioned properties are priority rules where a package has higher priority than another if it contains the other.
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