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.