Sortition, i.e., random appointment for public duty, has been employed by societies throughout the years, especially for duties related to the judicial system, as a firewall designated to prevent illegitimate interference between parties in a legal case and agents of the legal system. In judicial systems of modern western countries, random procedures are mainly employed to select the jury, the court and/or the judge in charge of judging a legal case, so that they have a significant role in the course of a case. Therefore, these random procedures must comply with some principles, as statistical soundness; complete auditability; open-source programming; and procedural, cryptographical and computational security. Nevertheless, some of these principles are neglected by some random procedures in judicial systems, that are, in some cases, performed in secrecy and are not auditable by the involved parts. The assignment of cases in the Brazilian Supreme Court (Supremo Tribunal Federal) is an example of such procedures, for it is performed by a closed-source algorithm, unknown to the public and to the parts involved in the judicial cases, that allegedly assign the cases randomly to the justice chairs based on their caseload. In this context, this article presents a review of how sortition has been employed historically by societies, and discusses how Mathematical Statistics may be applied to random procedures of the judicial system, as it has been applied for almost a century on clinical trials, for example. Based on this discussion, a statistical model for assessing randomness in case assignment is proposed and applied to the Brazilian Supreme Court in order to shed light on how this assignment process is performed by the closed-source algorithm. Guidelines for random procedures are outlined and topics for further researches presented.

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评估案件分配的随机性：巴西最高法院的案例研究

抽签，即随机任命公共职责，多年来一直被社会采用，特别是与司法系统相关的职责，作为指定的防火墙，以防止法律案件当事人与法律系统代理人之间的非法干预。在现代西方国家的司法制度中，主要采用随机程序来选择陪审团、法院和/或负责审理法律案件的法官，使其在案件进程中发挥重要作用。因此，这些随机程序必须遵守一些原则，如统计稳健性；完全可审计性；开源编程；以及程序、密码和计算安全。然而，其中一些原则被司法系统中的一些随机程序所忽视，即在某些情况下，秘密进行，相关部分不可审计。巴西最高法院（联邦最高法庭）的案件分配就是此类程序的一个例子，因为它是由公众和司法案件所涉部分未知的闭源算法执行的，据称该算法分配了根据案件数量随机将案件提交给司法主席。在此背景下，本文回顾了社会历史上如何使用抽签，并讨论了数理统计如何应用于司法系统的随机程序，因为它已应用于临床试验近一个世纪，例如. 基于这个讨论，提出了一种用于评估案件分配随机性的统计模型，并将其应用于巴西最高法院，以阐明闭源算法如何执行此分配过程。概述了随机程序的指南，并提出了进一步研究的主题。