Adaptive Risk-Limiting Comparison Audits

Risk-limiting audits (RLAs) are rigorous statistical procedures meant to detect invalid election results. RLAs examine paper ballots cast during the election to statistically assess the possibility of a disagreement between the winner determined by the ballots and the winner reported by tabulation. The design of an RLA must balance risk against efficiency: "risk" refers to a bound on the chance that the audit fails to detect such a disagreement when one occurs; "efficiency" refers to the total effort to conduct the audit.The most efficient approaches—when measured in terms of the number of ballots that must be inspected—proceed by "ballot comparison." However, ballot comparison requires an (untrusted) declaration of the contents of each cast ballot, rather than a simple tabulation of vote totals. This "cast-vote record table" (CVR) is then spot-checked against ballots for consistency. In many practical settings, the cost of generating a suitable CVR dominates the cost of conducting the audit which has prevented widespread adoption of these sample-efficient techniques.We introduce a new RLA procedure: an "adaptive ballot comparison" audit. In this audit, a global CVR is never produced; instead, a three-stage procedure is iterated: 1) a batch is selected, 2) a CVR is produced for that batch, and 3) a ballot within the batch is sampled, inspected by auditors, and compared with the CVR. We prove that such an audit can achieve risk commensurate with standard comparison audits while generating a fraction of the CVR. We present three main contributions: (1) a formal adversarial model for RLAs; (2) definition and analysis of an adaptive audit procedure with rigorous risk limits and an associated correctness analysis accounting for the incidental errors arising in typical audits; and (3) an analysis of efficiency.