More style, less work: card-style data decrease risk-limiting audit sample sizes

TL;DR

This paper demonstrates that using card-style data (CSD) to identify which ballots contain specific contests significantly reduces the sample sizes needed for risk-limiting audits, especially in complex elections with multiple contests.

Contribution

It introduces the use of card-style data (CSD) to dramatically decrease RLA sample sizes by targeting ballots containing relevant contests, improving audit efficiency.

Findings

CSD reduces expected draws by 75% for single contests on 4-card ballots.

CSD reduces expected draws by over 95% for multiple contests with shared margins.

Savings in sample sizes can be several orders of magnitude in realistic election scenarios.

Abstract

U.S. elections rely heavily on computers such as voter registration databases, electronic pollbooks, voting machines, scanners, tabulators, and results reporting websites. These introduce digital threats to election outcomes. Risk-limiting audits (RLAs) mitigate threats to some of these systems by manually inspecting random samples of ballot cards. RLAs have a large chance of correcting wrong outcomes (by conducting a full manual tabulation of a trustworthy record of the votes), but can save labor when reported outcomes are correct. This efficiency is eroded when sampling cannot be targeted to ballot cards that contain the contest(s) under audit. If the sample is drawn from all cast cards, RLA sample sizes scale like the reciprocal of the fraction of ballot cards that contain the contest(s) under audit. That fraction shrinks as the number of cards per ballot grows (i.e., when elections contain more contests) and as the fraction of ballots that contain the contest decreases (i.e., when a smaller percentage of voters are eligible to vote in the contest). States that conduct RLAs of contests on multi-card ballots or of small contests can dramatically reduce sample sizes by using information about which ballot cards contain which contests -- by keeping track of card-style data (CSD). For instance, CSD reduces the expected number of draws needed to audit a single countywide contest on a 4-card ballot by 75%. Similarly, CSD reduces the expected number of draws by 95% or more for an audit of two contests with the same margin on a 4-card ballot if one contest is on every ballot and the other is on 10% of ballots. In realistic examples, the savings can be several orders of magnitude.