Risk-limiting audits (RLAs) are a significant tool in increasing confidence in the accuracy of elections. They consist of randomized algorithms which check that an election's vote tally, as reported by a vote tabulation system, corresponds to the correct candidates winning. If an initial vote count leads to the wrong election winner, an RLA guarantees to identify the error with high probability over its own randomness. These audits operate by sequentially sampling and examining ballots until they can either confirm the reported winner or identify the true winner. The first part of this work suggests a new generic method, called ``Batchcomp", for converting classical (ballot-level) RLAs into ones that operate on batches. As a concrete application of the suggested method, we develop the first ballot-level RLA for the Israeli Knesset elections, and convert it to one which operates on batches. We ran the suggested ``Batchcomp" procedure on the results of 22nd, 23rd and 24th Knesset elections, both with and without errors. The second part of this work suggests a new use-case for RLAs: verifying that a population census leads to the correct allocation of political power to a nation's districts or federal-states. We present an adaptation of ALPHA, an existing RLA method, to a method which applies to censuses. Our census-RLA is applicable in nations where parliament seats are allocated to geographical regions in proportion to their population according to a certain class of functions (highest averages). It relies on data from both the census and from an additional procedure which is already conducted in many countries today, called a post-enumeration survey.

翻译：风险限制审计（RLA）是提升选举结果准确性信心的重要工具。它由随机算法组成，用于检查投票制表系统报告的选举计票结果是否对应正确的获胜候选人。若初始计票得出错误的选举获胜者，RLA能以其自身随机性以高概率保证发现该错误。此类审计通过顺序抽样并检查选票，直到能够确认报告的获胜者或识别出真正的获胜者。本文第一部分提出了一种名为"Batchcomp"的新型通用方法，用于将传统的（选票级）RLA转换为在批次上运行的方法。作为所提出方法的具体应用，我们开发了首个针对以色列议会选举的选票级RLA，并将其转换为在批次上运行的方法。我们使用所提出的"Batchcomp"程序对第22届、第23届和第24届议会选举的结果进行了测试，包括无错误和有错误两种情形。本文第二部分提出了RLA的一个新用例：验证人口普查能否导致国家各地区或联邦州之间政治权力的正确分配。我们将现有的RLA方法ALPHA进行改编，使其适用于人口普查场景。我们的普查RLA适用于那些根据某类函数（最高均值法）按人口比例将议会席位分配给地理区域的国家。它依赖于人口普查数据以及许多国家目前已在开展的额外程序——事后盘点调查的数据。