Order Symmetry: A New Fairness Criterion for Assignment Mechanisms

We introduce a new fairness criterion, order symmetry, for assignment mechanisms that match n objects to n agents with ordinal preferences over the objects. An assignment mechanism is order symmetric with respect to some probability measure over preference profiles if every agent is equally likely to receive their favorite object, every agent is equally likely to receive their second favorite, and so on. When associated with a sufficiently symmetric probability measure, order symmetry is a relaxation of anonymity that, crucially, can be satisfied by discrete assignment mechanisms. Furthermore, it can be achieved without sacrificing other desirable axiomatic properties satisfied by existing mechanisms. In particular, we show that it can be achieved in conjunction with strategyproofness and ex post efficiency via the top trading cycles mechanism (but not serial dictatorship). We additionally design a novel mechanism that is both order symmetric and ordinally efficient. The practical utility of order symmetry is substantiated by simulations on Impartial Culture and Mallows-distributed preferences for four common assignment mechanisms.

Economies with complex property rights

We discuss the exclusion core, a solution concept for object-allocation and object-exchange problems. The exclusion core is based on the right of exclusion and is especially useful for the analysis of economies with complicated property arrangements, such as those with shared ownership. The exclusion core coincides with the (strong) core in classic settings, and is closely related to the celebrated Top Trading Cycles algorithm.

Efficiency, Justified Envy, and Incentives in Priority-Based Matching

Top trading cycles (TTC) is Pareto efficient and strategy-proof in priority-based matching, but so are other mechanisms including serial dictatorship. We show that TTC minimizes justified envy among all Pareto-efficient and strategy-proof mechanisms in one-to-one matching. In many-to-one matching, TTC admits less justified envy than serial dictatorship in an average sense. Empirical evidence from New Orleans OneApp and Boston Public Schools shows that TTC has significantly less justified envy than serial dictatorship. (JEL C78, D61)

The Cutoff Structure of Top Trading Cycles in School Choice

This paper develops a tractable theoretical framework for the Top Trading Cycles (TTC) mechanism for school choice that allows quantifying welfare and optimizing policy decisions. We compute welfare for TTC and Deferred Acceptance (DA) under different priority structures, and find that the choice of priorities can have larger welfare implications than the choice of mechanism. We solve for the welfare-maximizing distributions of school quality for parametrized economies, and find that optimal investment decisions can be very different under TTC and DA. Our framework relies on a novel characterization of the TTC assignment in terms of a cutoff for each pair of schools. These cutoffs parallel prices in competitive equilibrium, with students’ priorities serving the role of endowments. We show that these cutoffs can be computed directly from the distribution of preferences and priorities in a continuum model, and derive closed-form solutions and comparative statics for parameterized settings. The TTC cutoffs clarify the role of priorities in determining the TTC assignment, but also demonstrate that TTC is more complicated than DA.