In this note, we study the envy-freeness and ordinal efficiency of the random serial dictatorship (RSD) rule on preference domains with a tier structure. Specifically, we obtain that the RSD rule is envy-free on restricted tier preference domains. For the ordinal efficiency axiom, we show that the almost-singleton condition is not sufficient for the RSD rule to be ordinally efficient. For assignment problems on the restricted tier preference domains, we characterize the condition under which the RSD rule is ordinally efficient.

中文翻译：

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层级结构偏好域随机序列专政的公平性与效率

在本文中，我们研究了具有层级结构的偏好域上的随机串行独裁（RSD）规则的无嫉妒性和顺序效率。具体来说，我们发现 RSD 规则在受限层偏好域上是无嫉妒的。对于序数效率公理，我们证明几乎单例条件不足以使 RSD 规则具有序数效率。对于受限层偏好域上的分配问题，我们描述了 RSD 规则通常有效的条件。