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

TL;DR

This paper introduces two innovative risk-limiting audit techniques that significantly reduce the effort and time required for election audits by ensuring accurate ballot manifests and enabling direct ballot selection, especially effective for small margins.

Contribution

The paper presents a statistical method for verifying untrusted batch sizes and a new direct ballot selection approach, reducing audit complexity and time in elections.

Findings

Reducing manifest creation time by at least an order of magnitude at 3% margin.

Direct ballot selection outperforms state-of-the-art polling for small margins, reducing sample complexity by 55%.

Techniques enable efficient, software-independent election audits with less effort.

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.