论文标题

更多样式,更少的工作:卡型数据降低风险限制的审核样本大小

More style, less work: card-style data decrease risk-limiting audit sample sizes

论文作者

Glazer, Amanda K., Spertus, Jacob V., Stark, Philip B.

论文摘要

美国的选举在很大程度上依赖于计算机,例如选民注册数据库,电子投票书,投票机,扫描仪,制表板和结果报告网站。这些引入了数字威胁到选举成果。风险限制审核(RLAS)通过手动检查投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(通过对可信赖的选票记录进行完整的手动制表),但是在报告结果正确时可以节省劳动。当不能将采样定位于包含审计中的比赛的投票卡时,这种效率就会受到侵蚀。如果样本是从所有铸件卡中绘制的,则RLA样本量尺寸比例像是在审核下包含比赛的投票卡的相互量表。随着每次选票的增加数量的增加(即,当选举包含更多竞赛)以及包含比赛的选票的一部分(即,当较小百分比的选民有资格参加比赛时投票时),这一部分缩小了。通过使用有关哪些选票卡包含哪些竞赛的信息,可以通过跟踪卡型数据(CSD)来大大减少竞赛的RLA竞赛或小型比赛。例如,CSD减少了在4张票投票中审核单一全县竞赛所需的预期抽奖数量,增加了75%。同样,对于两场比赛的审核,如果每次投票进行一项比赛,而另一场比赛的选票为10%,则CSD将预期的平局数量减少了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, 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 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 reduces the expected number of draws needed to audit a single countywide contest on a 4-card ballot by 75%. Similarly, CSD reduces 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.

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