More Style, Less Work: Card-style Data Decrease Risk-limiting Audit Sample Sizes
More Style, Less Work: Card-style Data Decrease Risk-limiting Audit Sample Sizes
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更多风格，更少工作：卡片式数据减少风险限制审计样本量
DOI：
10.1145/3457907
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发表时间：
2021
期刊：
影响因子：
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通讯作者：
Stark, Philip B.
中科院分区：
文献类型：
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作者：
Glazer, Amanda K.;Spertus, Jacob V.;Stark, Philip B.
美国的选举在很大程度上依赖于计算机，如选民登记数据库、电子民意调查簿、投票机、扫描仪、制表机和结果报告网站。这给选举结果带来了数字威胁。风险限制审计（RLA）通过手动检查选票卡的随机样本来减轻对其中一些系统的威胁。RLA有很大的机会纠正错误的结果（通过对可信的投票记录进行完全手动制表），但是当报告的结果正确时可以节省劳动力。当抽样不能针对包含审计中的竞赛的选票卡时，这种效率就会受到损害。如果样本是从所有投票卡中抽取的，那么RLA样本大小的比例就像包含审核中的竞赛的投票卡的分数的倒数。随着每张选票上卡片数量的增加，这一比例会缩小（即，当选举包含更多的竞争时）以及当包含竞争的选票的分数减少时（即，当较小比例的选民有资格在竞选中投票时）。在多卡选票上进行竞赛的RLA或小型竞赛的RLA的州可以通过使用关于哪些选票卡包含哪些候选人的信息-通过跟踪卡片式数据（CSD）来显著减少样本量。例如，CSD减少了75%的预期抽奖次数，以审计一个单一的县范围内的比赛对4卡选票。同样地，如果在一张4张牌的选票上有两个相同差额的比赛，而其中一个比赛在每张选票上，另一个比赛在10%的选票上，那么CSD会将预期的抽签次数减少95%或更多。在现实的例子中，节省可以是几个数量级。
U.S. elections rely heavily on computers such as voter registration databases, electronic pollbooks, voting machines, scanners, tabulators, and results reporting websites. These introduce digital threats to election outcomes. Risk-limiting audits (RLAs) mitigate threats to some of these systems by manually inspecting random samples of ballot cards. RLAs have a large chance of correcting wrong outcomes (by conducting a full manual tabulation of a trustworthy record of the votes), but can save labor when reported outcomes are correct. This efficiency is eroded when sampling cannot be targeted to ballot cards that contain the contest(s) under audit. If the sample is drawn from all cast cards, then RLA sample sizes scale like the reciprocal of the fraction of ballot cards that contain the contest(s) under audit. That fraction shrinks as the number of cards per ballot grows (i.e., when elections contain more contests) and as the fraction of ballots that contain the contest decreases (i.e., when a smaller percentage of voters are eligible to vote in the contest). States that conduct RLAs of contests on multi-card ballots or RLAs of small contests can dramatically reduce sample sizes by using information about which ballot cards contain which contests—by keeping track of card-style data (CSD). For instance, CSD reduce the expected number of draws needed to audit a single countywide contest on a 4-card ballot by 75%. Similarly, CSD reduce the expected number of draws by 95% or more for an audit of two contests with the same margin on a 4-card ballot if one contest is on every ballot and the other is on 10% of ballots. In realistic examples, the savings can be several orders of magnitude.