ALPHA: Audit that Learns from Previously Hand-Audited Ballots

Philip B. Stark

BRAVO is currently the most widely used method for risk-limiting election audits. However, it cannot accommodate sampling without replacement or stratified sampling, which can improve efficiency and are sometimes required by law. It applies only to ballot-polling, which is simple to implement but less efficient than comparison audits. It applies to plurality, majority, super-majority, proportional representation, and ranked-choice voting contests, but not to many other 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 the reported vote shares are exactly correct, BRAVO can require arbitrarily large samples when the reported reported winners really won but the reported vote shares are incorrect. ALPHA is a simple generalization of BRAVO that (i) works for sampling with and without replacement, (ii) can be used with stratified sampling in the SUITE approach, (iii) works for ballot-level and batch-level comparison audits and for all social choice functions covered by SHANGRLA, including approval voting, Borda count, and all scoring rules, and (iv) requires smaller samples than BRAVO--five orders of magnitude in some examples--when the reported vote shares are wrong but the outcome is correct, in situations where both ALPHA and BRAVO apply. ALPHA is also competitive with RiLACS. A Python implementation is provided.

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