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SaTC: CORE: Small: LESS DOUBT: Learning Efficiently form Statistical Samples-Demonstrating Outcomes Using Better Tests

SaTC：核心：小：更少怀疑：从统计样本中有效学习 - 使用更好的测试展示结果

基本信息

批准号：
2228884
负责人：
Philip Stark
金额：
$ 54.07万
依托单位：
University of California-Berkeley
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2022
资助国家：
美国
起止时间：
2022-10-01 至 2025-09-30
项目状态：
未结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2228884&HistoricalAwards=false
关键词：
SaTC CORE Small LESS DOUBT

项目摘要

It is important to bolster the integrity of and trust in U.S. elections. This project develops methods and software to simplify and reduce the cost of providing strong evidence that reported winners really won--or correcting the results if not. The key statistical tool is a risk-limiting audit (RLA) using a trustworthy paper record of the votes. This project increases the efficiency (reducing the legwork needed to confirm outcomes when outcomes are correct), flexibility (to accommodate constraints imposed by local laws, regulations, and technology), and applicability of RLAs (to accommodate more voting rules and to make it affordable to audit every contest in every election). The project builds and publishes open-source software implementing the improvements and is working with state and local election officials to pilot the methods.An RLA is any procedure with a known maximum chance (the risk limit) of not correcting a reported contest outcome if that outcome is wrong. RLAs correct outcomes by manually tabulating a trustworthy record of the validly cast votes. RLAs can be reduced to multiple instances of a core statistical problem: testing whether the mean of a bounded list of nonnegative numbers is less than or equal to 1/2. This project develops improved methods for sequential and batch-sequential tests of such hypotheses using simple random samples, cluster samples, stratified samples, and Bernoulli samples. The methods involve test statistics that are nonnegative supermartingales under the null. Tests that adapt by "learning" the true mean from the sample can improve efficiency substantially, as can adaptive stratified sampling designs that preferentially draw from strata where the null appears to be false--leading to a generalization of the multi-armed bandit problem.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

重要的是要加强美国选举的诚信和信任。该项目开发了一些方法和软件，以简化和降低提供有力证据的成本，这些证据表明报告的获奖者真的赢了，或者如果不是，则纠正结果。关键的统计工具是风险限制审计（RLA），使用可信的纸质投票记录。该项目提高了效率（减少了在结果正确时确认结果所需的跑腿工作），灵活性（以适应当地法律，法规和技术施加的限制）和RLA的适用性（以适应更多的投票规则，并使其能够负担得起每次选举中的每一场比赛）。该项目构建并发布了实现改进的开源软件，并与州和地方选举官员合作试点这些方法。RLA是任何已知的最大可能性（风险限制）的程序，如果结果是错误的，则不纠正报告的比赛结果。RLA通过手动将有效投票的可信记录制成表格来纠正结果。RLA可以简化为一个核心统计问题的多个实例：测试一个有界非负数列表的均值是否小于或等于1/2。本计画利用简单随机样本、群集样本、分层样本及伯努利样本，发展改良的序贯及批次序贯检验方法。该方法涉及的检验统计量是非负上鞅下的空。通过从样本中“学习”真实均值来适应的测试可以大大提高效率，同样，优先从空值似乎为假的地层中提取的自适应分层抽样设计也可以提高效率--从而导致多臂强盗问题的泛化。该奖项反映了NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。