FIFA世界杯分组抽签的公平性
The fairness of the group draw for the FIFA World Cup
AI总结：
本研究量化了2018年FIFA世界杯抽签的不公平性，发现官方抽签顺序虽优于其他23种，但仍使两国晋级概率扭曲超1个百分点，呼吁采用更公平的机制。
摘要：
一些体育赛事包含循环赛小组赛阶段，队伍在特定约束下被分配到不同小组。因此，组织者通常采用计算机辅助的随机抽签来避免任何死胡同，即剩余待抽队伍无法被分配到剩余空位的情况。已知该程序是不公平的：可行的分配并非等可能，即抽签不服从均匀分布。我们量化了2018年FIFA世界杯抽签所隐含的不公平性，并评估了其对每支国家队晋级淘汰赛阶段概率的影响。结果表明，在减少不良扭曲方面，Pot 1、Pot 2、Pot 3、Pot 4的官方抽签顺序明显优于其他23种抽签顺序。尽管如此，非均匀抽签仍使两个国家的晋级概率扭曲超过一个百分点。我们的研究结果呼吁关注抽签顺序的不可忽视作用，并使政策制定者能够决定是否采用更公平的抽签机制。
英文摘要：
Several sports tournaments contain a round-robin group stage where the teams are assigned to groups subject to some constraints. Hence, the organisers usually use a computer-assisted random draw to avoid any dead end, a situation when the teams still to be drawn cannot be assigned to the remaining empty slots. This procedure is known to be unfair: the feasible allocations are not equally likely, that is, the draw does not have a uniform distribution. We quantify the implied unfairness of the 2018 FIFA World Cup draw and evaluate its effect on the probability of qualification for the knockout stage for each national team. The official draw order of Pot 1, Pot 2, Pot 3, Pot 4 turns out to be a significantly better option than the 23 other draw orders with respect to the unwanted distortions. Nonetheless, the non-uniform draw distorts the probability of qualification by more than one percentage point for two countries. Our results call attention to the non-negligible role of draw order and make it possible for policymakers to decide whether using fairer draw mechanisms is justified.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
