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Counting votes is complex and error-prone. Several statistical methods havebeen developed to assess election accuracy by manually inspecting randomlyselected physical ballots. Two 'principled' methods are risk-limiting audits(RLAs) and Bayesian audits (BAs). RLAs use frequentist statistical inferencewhile BAs are based on Bayesian inference. Until recently, the two have beenthought of as fundamentally different.  We present results that unify and shed light upon 'ballot-polling' RLAs andBAs (which only require the ability to sample uniformly at random from all castballot cards) for two-candidate plurality contests, which are building blocksfor auditing more complex social choice functions, including some preferentialvoting systems. We highlight the connections between the methods and exploretheir performance.  First, building on a previous demonstration of the mathematical equivalenceof classical and Bayesian approaches, we show that BAs, suitably calibrated,are risk-limiting. Second, we compare the efficiency of the methods across awide range of contest sizes and margins, focusing on the distribution of samplesizes required to attain a given risk limit. Third, we outline several ways toimprove performance and show how the mathematical equivalence explains theimprovements.

A Unified Evaluation of Two-Candidate Ballot-Polling Election Auditing Methods