This paper studies allocation correspondences in the house allocation problems with collective initial endowments. We examine the implications of two axioms, namely 'consistency' and 'unanimity.' Consistency requires the allocation correspondence be invariant under reductions of population. Unanimity 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.'
house allocation problem axiomatic characterization consistency unanimity Pareto efficiency