Revisiting Consistency in House Allocation Problems and the Computational Approach to the Axiomatic Method

How should we allocate a social endowment of objects among a group of agents when monetary compensation is not possible? Typical examples are the assignment of offices among faculty and the assignment of tasks among subalterns. We follow an axiomatic approach and impose two properties on rules: Pareto-efficiency and consistency. Previous research arrived at a “dictatorship” result imposing another property: neutrality (Ergin JME, 2000.) We identify Pareto-efficient and consistent rules that depart from this dictatorship and recover some fairness. Under the mild assumption that there are at least four objects, we characterize such a family of rules using minimal notions of Pareto-efficiency and consistency. We investigate the restrictions imposed by strategy-proofness on this family of rules. As a technical contribution, we develop a “computational” approach to the axiomatic method, which overcomes the challenges entailed in our main characte-