Doing More With Less: Mismatch-Based Risk-Limiting Audits

TL;DR

The paper proposes mismatch-based risk-limiting audits (RLAs) that evaluate whether the total number of CVR mismatches exceeds a lower bound on the CVR margin, $V^-$ (with $v^- = V^-/N$), within the SHANGRLA framework. It introduces the mismatch assorter $C(b_i) = rac{1 - 1_{b_i e c_i}}{2-2v'}$ and shows that a positive test of $ar{C} > 1/2$ implies $M( ablaC) < V$, certifying the outcome under a conservative audit. The study compares mismatch-based RLAs to card-level audits and other IRV/STV methods through simulations across various error models, highlighting when larger sample sizes are expected (notably as $m$ approaches $v$). It also discusses practical considerations such as the need for CVR linkage, privacy concerns, and potential improvements in estimators and multi-contest auditing strategies. Overall, the work clarifies when mismatch-based RLAs are advantageous and when more precise, function-specific methods are preferred.

Abstract

One approach to risk-limiting audits (RLAs) compares randomly selected cast vote records (CVRs) to votes read by human auditors from the corresponding ballot cards. Historically, such methods reduce audit sample sizes by considering how each sampled CVR differs from the corresponding true vote, not merely whether they differ. Here we investigate the latter approach, auditing by testing whether the total number of mismatches in the full set of CVRs exceeds the minimum number of CVR errors required for the reported outcome to be wrong (the "CVR margin"). This strategy makes it possible to audit more social choice functions and simplifies RLAs conceptually, which makes it easier to explain than some other RLA approaches. The cost is larger sample sizes. "Mismatch-based RLAs" only require a lower bound on the CVR margin, which for some social choice functions is easier to calculate than the effect of particular errors. When the population rate of mismatches is low and the lower bound on the CVR margin is close to the true CVR margin, the increase in sample size is small. However, the increase may be very large when errors include errors that, if corrected, would widen the CVR margin rather than narrow it; errors affect the margin between candidates other than the reported winner with the fewest votes and the reported loser with the most votes; or errors that affect different margins.