Top Trading Cycles in Large Markets: The Asymptotic Irrelevance of Priorities

Top Trading Cycles (TTC) is Pareto efficient and strategy-proof and explicitly uses agents’ priorities. Although TTC favors higher-priority agents in each round, we show that this priority advantage vanishes as the market grows large under a canonical random model of preferences and priorities. In the limit, TTC produces assignments with virtually the same incidence of justified envy as Random Serial Dictatorship (RSD) – a mechanism entirely blind to priorities. This stark asymptotic equivalence implies that TTC effectively fails to satisfy standard fairness criteria in large markets, casting significant doubt on its practical appeal for balancing efficiency and fairness.