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

TL;DR

This paper unifies and compares risk-limiting audits and Bayesian audits for two-candidate elections, demonstrating their mathematical connection, risk-limiting properties, and efficiency across various contest scenarios.

Contribution

It shows that Bayesian audits, when properly calibrated, are risk-limiting and provides a comprehensive comparison of their performance with traditional RLAs.

Findings

Bayesian audits can be risk-limiting when calibrated correctly.

The methods' efficiencies vary with contest size and margin.

Mathematical equivalence explains potential performance improvements.

Abstract

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.