贝叶斯制表审计：解释和扩展
Bayesian Tabulation Audits: Explained and Extended
摘要：
选举的制表审计提供了统计证据，证明所报告的竞选结果是“正确的”（意味着正确执行了选票的制表），否则制表审计确定了正确的结果。斯塔克为此提出了风险限制制表审计;这种审计是有效的，并开始在实践中使用。我们扩展了基于贝叶斯方法的选举审计研究，该方法由Rivest和Shen于2012年首次引入。(The斯塔克提出的风险限制审计本质上是“频率主义”而不是贝叶斯。）我们首先提供了一个简化的介绍贝叶斯制表审计。贝叶斯制表审计首先从比赛中的选票中随机抽取样本，并对这些选票进行统计。然后，它考虑了统计变化对比赛结果的影响。如果这些变化几乎总是产生先前报告的结果，则审计终止，接受报告的结果。否则，将使用扩大的样本重复审计。贝叶斯审计是有吸引力的，因为它们可以与任何确定获胜者的方法（如排名选择投票）一起使用。然后，我们将展示如何贝叶斯审计可以扩展到处理更复杂的情况下，如审计竞赛，\emph{span multiple jurisdictions}，或以其他方式“分层。“我们强调对这种多个司法管辖区的竞争进行审计，其中一些司法管辖区对每张纸质选票都有电子投票记录（CVR），而其他司法管辖区则没有。当一个州的一些县升级到新设备，而另一些县没有升级时，自然会出现这种复杂的情况。贝叶斯审计能够以简单的方式处理这种情况。我们还讨论了在实践中使用贝叶斯审计的好处和相关考虑。
英文摘要：
Tabulation audits for an election provide statistical evidence that a reported contest outcome is "correct" (meaning that the tabulation of votes was properly performed), or else the tabulation audit determines the correct outcome. Stark proposed risk-limiting tabulation audits for this purpose; such audits are effective and are beginning to be used in practice. We expand the study of election audits based on Bayesian methods, first introduced by Rivest and Shen in 2012. (The risk-limiting audits proposed by Stark are "frequentist" rather than Bayesian in character.) We first provide a simplified presentation of Bayesian tabulation audits. A Bayesian tabulation audit begins by drawing a random sample of the votes in that contest, and tallying those votes. It then considers what effect statistical variations of this tally have on the contest outcome. If such variations almost always yield the previously-reported outcome, the audit terminates, accepting the reported outcome. Otherwise the audit is repeated with an enlarged sample. Bayesian audits are attractive because they work with any method for determining the winner (such as ranked-choice voting). We then show how Bayesian audits may be extended to handle more complex situations, such as auditing contests that \emph{span multiple jurisdictions}, or are otherwise "stratified." We highlight the auditing of such multiple-jurisdiction contests where some of the jurisdictions have an electronic cast vote record (CVR) for each cast paper vote, while the others do not. Complex situations such as this may arise naturally when some counties in a state have upgraded to new equipment, while others have not. Bayesian audits are able to handle such situations in a straightforward manner. We also discuss the benefits and relevant considerations for using Bayesian audits in practice.
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