This paper establishes non-asymptotic convergence of the cutoffs in Random serial dictatorship in an environment with many students, many schools, and arbitrary student preferences. Convergence is shown to hold when the number of schools, $m$, and the number of students, $n$, satisfy the relation $m \ln m \ll n$, and we provide an example showing that this result is sharp. We differ significantly from prior work in the mechanism design literature in our use of analytic tools from randomized algorithms and discrete probability, which allow us to show concentration of the RSD lottery probabilities and cutoffs even against adversarial student preferences.

翻译：本文在包含大量学生、大量学校及任意学生偏好的环境中，建立了随机独裁制中截止线的非渐近收敛性。当学校数量$m$和学生数量$n$满足关系$m \ln m \ll n$时，收敛性被证明成立，我们提供了一个实例表明该结果是紧的。与机制设计文献中先前的研究不同，我们使用了来自随机算法和离散概率的分析工具，这使得我们即使在对抗性学生偏好下也能证明RSD彩票概率和截止线的集中性。