BRAVO, the most widely tried method for risk-limiting election audits, cannot accommodate sampling without replacement or stratified sampling, which can improve efficiency and may be required by law. It applies only to ballot-polling audits, which are less efficient than comparison audits. It applies to plurality, majority, super-majority, proportional representation, and ranked-choice voting contests, but not to many social choice functions for which there are RLA methods, such as approval voting, STAR-voting, Borda count, and general scoring rules. And while BRAVO has the smallest expected sample size among sequentially valid ballot-polling-with-replacement methods when reported vote shares are exactly right, it can require arbitrarily large samples when the reported reported winner(s) really won but reported vote shares are wrong. ALPHA is a simple generalization of BRAVO that (i) works for sampling with and without replacement and Bernoulli sampling; (ii) increases power for stratified audits by avoiding the need to use a $P$-value combining function or to maximize $P$-values over nuisance parameters within strata, and allowing adaptive sampling across strata; (iii) works not only for ballot-polling but also for ballot-level comparison, batch-polling, and batch-level comparison audits, sampling with or without replacement, uniformly or with weights proportional to size; (iv) works for all social choice functions covered by SHANGRLA; and (v) in situations where both ALPHA and BRAVO apply, requires smaller samples than BRAVO when the reported vote shares are wrong but the outcome is correct--five orders of magnitude in some examples. ALPHA includes the family of betting martingale tests in RiLACS, with a different betting strategy parametrized as an estimator of the population mean and explicit flexibility to accommodate sampling weights and population bounds that vary by draw.
翻译:BRAVO是进行风险限制选举审计的最广泛尝试的方法,它无法在不进行更替或分层抽样的情况下进行取样,而这种抽样可以提高效率,而且可能是法律要求的。它只适用于投票投票审计,比比较审计效率低。它适用于多元性、多数、超多数、超多数、比例代表以及等级投票竞争,但不适用于许多社会选择功能,因为有RLA方法,如批准投票、STAR-voting、Borda 计数和一般评分规则等。尽管BRAVO在连续有效投票有效投票和替换方法中拥有最小的预期抽样规模,但在所报告的选票份额完全正确时,它可能要求任意大量抽样,如果所报告的获胜者(s)真正获胜,但所报告的选票份额是错误的。 ALPHA是一个简单概括的BRAVO(i),用于抽样和不替换的BERVO(ial)抽样测试包括(ioral-lical ) 和BERVA(ial-vo) 中,使用美元组合比值最小值,但以美元比值最高值最高值最高值的汇率比值的比值(SLIL),在SVIL 的比值上进行抽样和比值的比值的比值的比值) 的比值(SBVI) 和比值,用于所有的排序的排序的汇率的比值需要所有比例的比值) 的比值,并且进行所有比例的比值的比值的比值的比值,用于所有的比值的比值,用于所有的比。