We introduce balancedness a fairness axiom in house allocation problems. It requires a mechanism to assign the top choice, the second top choice, and so on, on the same number of profiles for each agent. This axiom guarantees equal treatment of all agents at the stage in which the mechanism is announced when all preference profiles are equally likely. We show that, with an interesting exception for the three-agent case, Top Trading Cycles from individual endowments is the only mechanism that is balanced, efficient, and group strategy-proof.

中文翻译：

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平衡房屋分配

我们在房屋分配问题中引入了平衡性公平公理。它需要一种机制来为每个代理分配相同数量的配置文件的首选、第二个首选等。当所有偏好配置文件都具有同等可能性时，该公理保证在宣布该机制的阶段对所有代理进行平等对待。我们表明，除了三代理案例的一个有趣的例外，来自个人禀赋的顶级交易周期是唯一平衡、有效和群体策略证明的机制。