2022/01/07 by Stark, Philip B. · 1 citation
#Computer Science and Game Theory (cs.GT) #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #Methodology (stat.ME)
paper · doi:10.48550/arxiv.2201.02707
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.