A Unified Evaluation of Two-Candidate Ballot-Polling Election Auditing Methods
This work addresses election integrity by providing insights into auditing methods, but it is incremental as it builds on prior mathematical equivalences.
The paper tackled the problem of evaluating and unifying two statistical methods for auditing two-candidate elections, showing that Bayesian audits can be risk-limiting and comparing their efficiency in terms of sample sizes across various contest conditions.
Counting votes is complex and error-prone. Several statistical methods have been developed to assess election accuracy by manually inspecting randomly selected physical ballots. Two 'principled' methods are risk-limiting audits (RLAs) and Bayesian audits (BAs). RLAs use frequentist statistical inference while BAs are based on Bayesian inference. Until recently, the two have been thought of as fundamentally different. We present results that unify and shed light upon 'ballot-polling' RLAs and BAs (which only require the ability to sample uniformly at random from all cast ballot cards) for two-candidate plurality contests, which are building blocks for auditing more complex social choice functions, including some preferential voting systems. We highlight the connections between the methods and explore their performance. First, building on a previous demonstration of the mathematical equivalence of classical and Bayesian approaches, we show that BAs, suitably calibrated, are risk-limiting. Second, we compare the efficiency of the methods across a wide range of contest sizes and margins, focusing on the distribution of sample sizes required to attain a given risk limit. Third, we outline several ways to improve performance and show how the mathematical equivalence explains the improvements.