More style, less work: card-style data decrease risk-limiting audit sample sizes
This work provides a method to substantially reduce the labor and cost associated with conducting Risk-Limiting Audits for election officials, making these crucial audits more feasible and efficient, particularly in states with complex ballot structures or numerous small contests.
The paper addresses the problem of large sample sizes in Risk-Limiting Audits (RLAs) for U.S. elections, especially when auditing contests on multi-card ballots or small contests. By utilizing card-style data (CSD), which tracks which ballot cards contain which contests, the authors demonstrate significant reductions in sample sizes, such as a 75% reduction for a single countywide contest on a 4-card ballot and over 95% for two contests with different ballot coverage.
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.