Risk-limiting audits (RLAs) are techniques for verifying the outcomes of large elections. While they provide rigorous guarantees of correctness, widespread adoption has been impeded by both efficiency concerns and the fact they offer statistical, rather than absolute, conclusions. We attend to both of these difficulties, defining new families of audits that improve efficiency and offer qualitative advances in statistical power. Our new audits are enabled by revisiting the standard notion of a cast-vote record so that it can declare multiple possible mark interpretations rather than a single decision; this can reflect the presence of ambiguous marks, which appear regularly on hand-marked ballots. We show that this simple expedient can offer significant efficiency improvements with only minor changes to existing auditing infrastructure. We establish that these Bayesian comparison audits are indeed risk-limiting in the formal sense of (Fuller, Harrison, and Russell, 2022). We then define a new type of post-election audit we call a contested audit. These permit each candidate to provide a cast-vote record table advancing their own claim to victory. We prove that these audits offer remarkable sample efficiency, yielding control of risk with a constant number of samples (that is independent of margin). This is a first for an audit with provable soundness. These results are formulated in a game-based security model that specify quantitative soundness and completeness guarantees. Finally, we observe that these audits provide a direct means to handle contestation of election results affirmed by conventional RLAs.

翻译：风险限制审核（RLAs）是验证大规模选举结果的技术方法。虽然它们提供了严格的正确性保证，但广泛采用受到效率问题以及其提供统计性（而非绝对性）结论这两方面因素的制约。我们致力于解决这两个难点，定义了新的审核族系，既能提升效率，又在统计效力上取得质的突破。我们的新审核方法通过重新审视选票记录的标准概念得以实现——这种记录可以声明多种可能的标记解释而非单一判断；这能够反映模糊标记的存在，而此类标记在手写选票中经常出现。我们证明，这种简单的变通方案只需对现有审核基础设施进行微小改动即可显著提升效率。我们验证了这些贝叶斯比较审核在形式意义上确实符合风险限制定义（Fuller, Harrison, and Russell, 2022）。随后我们定义了一种新型选举后审核——争议性审核。此类审核允许每位候选人提供支持自己胜选主张的选票记录表。我们证明这类审核具有卓越的样本效率，能以恒定数量的样本（与票数差距无关）实现风险控制。这是首个具备可证明正确性的审核方案。这些结果建立在基于博弈的安全模型框架中，该模型规定了量化的正确性与完备性保证。最后，我们指出这类审核为处理传统RLA确认选举结果争议提供了直接方法。