Sublinear Risk-Limiting Audits from Direct Ballot Selection and Statistical Ballot Manifests

2026-05-18

AI Summary

Traditional risk-limiting audits (RLAs) rely on accurate ballot manifests, yet in real-world elections, such manifests often contain errors that can invalidate audits or necessitate extensive manual correction. This work proposes two key innovations: first, a statistical mechanism that efficiently constructs a reliable manifest from an untrusted, coarse-grained list provided by election tabulation systems with sublinear effort; and second, a novel audit framework that directly selects ballots without requiring ordered ballot identifiers, thereby inverting the conventional comparison workflow. Experimental results demonstrate that, under a 3% margin, the overall audit time is reduced by more than an order of magnitude. In a Connecticut election with a 1% margin, the proposed method reduces the required ballot sample size by 55% compared to the Minerva approach.

Abstract

Risk-limiting audits (RLAs) are post-election auditing procedures that rigorously guarantee a specified maximum probability that an incorrect electoral outcome will not be detected. Aside from ready access to physical ballots, known RLAs require a software-independent accounting of the sizes of each ballot batch, called a ballot manifest. While typical electoral procedures automatically provide rough estimates for batch sizes, even slight inaccuracies (commensurate with the margin of the contest under audit) completely invalidate conventional RLAs (Lindeman et al., EVT 2012). Thus, establishing a sufficiently accurate manifest often requires handling every ballot and can be the dominant cost of conducting the RLA. We propose two new risk-limiting techniques: 1) A statistical mechanism for ensuring that the batch sizes reported by an untrusted tabulation are, in fact, an accurate manifest; this effectively bootstraps from a rough manifest to an accurate one with sublinear effort. 2) We propose a new class of RLAs called direct ballot selection. This method reverses the traditional comparison procedure and compares uniformly selected ballots against their cast vote records, requiring a new statistical test for identifier duplication but efficiently supporting elections without in order identifiers. These techniques reduce the complexity of RLAs across many elections. Our two main findings are as follows: 1) The time to create a manifest can be drastically reduced with a modest increase in the number of ballots sampled in the audit. At a 3% margin and a large population, there is a reduction in the overall audit time of at least an order of magnitude across methods. 2) Direct ballot selection improves over state-of-the-art polling for small margins. For Connecticut (29th in population) at a 1% margin, it beats Minerva (Security 2022) by 55% in ballot sample complexity.

Problem

• risk-limiting audits
• ballot manifest
• election auditing
• sublinear audit
• ballot sampling

Innovation

• risk-limiting audits
• ballot manifest
• direct ballot selection
• sublinear audit
• statistical verification