Consistency and unanimity in the house allocation problem I: Collective initial endowments∗

This paper studies allocation correspondences in house allocation prob-lems with collective initial endowments. We examine the implications of two axioms, namely “consistency ” and “unanimity. ” Consistency requires the al-location correspondence be invariant under reductions of population. Una-nimity requires the allocation correspondence respect unanimity, that is, it assigns to every agent the object that ranks best for him whenever possible. We prove that if an allocation correspondence satisfies these two axioms, then it is a subcorrespondence of the Pareto correspondence. Further, we give a characterization of the Pareto correspondence using a version of “converse consistency.” JEL Classification — C78, D70