Shortlisting is a common and effective method for pre-selecting participants in competitive settings. To ensure fairness, a cut-off score is typically announced, allowing only contestants who exceed it to enter the contest, while others are eliminated. In this paper, we study rank-order contests with shortlisting and cut-off score disclosure. We fully characterize the equilibrium behavior of shortlisted contestants for any given prize structure and shortlist size. We examine two objective functions: the highest individual performance and total performance. For both objectives, the optimal contest is in a winner-take-all format. For the highest individual performance, the optimal shortlist size is exactly two contestants, but, in contrast, for total performance, the shortlist size does not affect the outcome, i.e., any size yields the same total performance. Furthermore, we compare the highest individual performance achieved with and without shortlisting, and show that the former is 4/3 times greater than the latter.

翻译：预选是竞争环境中筛选参赛者的常用且有效方法。为确保公平性，通常会公布一个分数线，仅允许得分超过该线的选手进入正式竞赛，其余选手则被淘汰。本文研究带有预选机制及分数线公开的排序竞赛。我们完整刻画了在任意给定奖项结构与预选规模下，入围选手的均衡行为。我们考察了两类目标函数：最高个体表现与总表现。对于这两类目标，最优竞赛均采用赢家通吃形式。就最高个体表现而言，最优预选规模恰好为两名选手；然而，对于总表现目标，预选规模不影响最终结果，即任意规模下获得的总表现均相同。此外，我们比较了采用与不采用预选机制时所能实现的最高个体表现，证明前者是后者的4/3倍。