Abstract We introduce a notion of efficiency, called Stepwise Ordinal Efficiency (SOE), and prove that it coincides with a fairness notion of interim favoring ranks, in the sense of Harless (2018). We also prove that SOE implies ordinal efficiency, while it is not compatible with rank efficiency. Then, we provide an impossibility result which states that no mechanism meets SOE, weak strategy-proof, and strong equal treatment of equals. Finally, we show that a modified eating algorithm satisfies SOE.

中文翻译：

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随机分配问题的逐步序数效率

摘要 我们引入了一个效率概念，称为逐步有序效率 (SOE)，并证明它与 Harless (2018) 意义上的临时优先级的公平概念一致。我们还证明了 SOE 意味着序数效率，而它与秩效率不兼容。然后，我们提供了一个不可能的结果，表明没有机制满足 SOE、弱策略证明和强平等对待。最后，我们表明修改后的饮食算法满足 SOE。