Overstatement-Net-Equivalent Risk-Limiting Audit: ONEAudit

Abstract

A procedure is a risk-limiting audit (RLA) with risk limit $\alpha$ if it has probability at least $1-\alpha$ of correcting each wrong reported outcome and never alters correct outcomes. One efficient RLA method, card-level comparison (CLCA), compares human interpretation of individual ballot cards randomly selected from a trustworthy paper trail to the voting system’s interpretation of the same cards (cast vote records, CVRs). CLCAs heretofore required a CVR for each cast card and a “link” identifying which CVR is for which card—which many voting systems cannot provide. This paper shows that every set of CVRs that produces the same aggregate results overstates contest margins by the same amount: they are overstatement-net-equivalent (ONE). CLCA can therefore use CVRs from the voting system for any number of cards and ONE CVRs created ad lib for the rest. In particular:

• Ballot-polling RLA is algebraically equivalent to CLCA using ONE CVRs derived from the overall contest results.

• CLCA can be based on batch-level results (e.g., precinct subtotals) by constructing ONE CVRs for each batch. In contrast to batch-level comparison auditing (BLCA), this avoids manually tabulating entire batches and works even when reporting batches do not correspond to physically identifiable batches of cards, when BLCA is impractical.

• If the voting system can export linked CVRs for only some ballot cards, auditors can still use CLCA by constructing ONE CVRs for the rest of the cards from contest results or batch subtotals.

This works for every social choice function for which there is a known RLA method, including IRV. Sample sizes for BPA and CLCA using ONE CVRs based on contest totals are comparable. With ONE CVRs from batch subtotals, sample sizes are smaller than for BPA when batches are homogeneous, approaching those of CLCA using CVRs from the voting system, and much smaller than for BLCA: A CLCA of the 2022 presidential election in California at risk limit 5% using ONE CVRs for precinct-level results would sample approximately 70 ballots statewide, if the reported results are accurate, compared to about 26,700 for BLCA. The 2022 Georgia audit tabulated more than 231,000 cards (the expected BLCA sample size was $\approx$103,000 cards); ONEAudit would have audited $\approx$1,300 cards. For data from a pilot hybrid RLA in Kalamazoo, MI, in 2018, ONEAudit gives a risk of 2%, substantially lower than the 3.7% measured risk for SUITE, the “hybrid” method the pilot used.