We study the classical object reallocation problem under strict preferences, with a focus on characterizing "TTC domains" -- preference domains on which the Top Trading Cycles (TTC) mechanism is the unique mechanism satisfying individual rationality, Pareto efficiency, and strategyproofness. We introduce a sufficient condition for a domain to be a TTC domain, which we call the top-two condition. This condition requires that, within any subset of objects, if two objects can each be most-preferred, they can also be the top-two most-preferred objects (in both possible orders). A weaker version of this condition, applying only to subsets of size three, is shown to be necessary. These results provide a complete characterization of TTC domains for the case of three objects, unify prior studies on specific domains such as single-peaked and single-dipped preferences, and classify several previously unexplored domains as TTC domains or not.

翻译：我们在严格偏好下研究经典的对象再分配问题，重点在于刻画“TTC域”——即满足以下性质的偏好域：在该域上，顶级交易环（TTC）机制是唯一满足个体理性、帕累托效率和策略证明性的机制。我们引入了一个域成为TTC域的充分条件，称之为“前二条件”。该条件要求：在任何对象子集中，如果两个对象各自都能成为最受偏好的对象，那么它们也必须能成为前二最受偏好的对象（以两种可能的顺序）。我们证明了该条件的一个较弱版本——仅应用于大小为三的子集——是必要条件。这些结果为三个对象的情形提供了TTC域的完整刻画，统一了先前关于单峰偏好和单谷偏好等特定域的研究，并将多个先前未探索的域分类为TTC域或非TTC域。