What is a risk-limiting audit, and how few ballots can confirm a result?

A risk-limiting audit checks an election result by hand-examining a random sample of the paper ballots, and keeps going until the evidence is strong enough or until every ballot has been counted. It is a post-election procedure that can limit the risk that a reported outcome is incorrect. It requires voter-verified paper ballots, stored securely, and a statistical sample of them examined manually until enough evidence is gathered to meet the risk limit.

The idea is like tasting a pot of soup. If the winner's lead is wide, a small random sample is very unlikely to show the opposite, so a few ballots are enough. If the lead is narrow, the sample must be bigger. The sample size depends primarily on the margin of victory in the contest being audited.

How many ballots also depends on the method. Ballot polling counts a random sample of ballots and compares its percentages with the reported ones. Ballot comparison checks the computer's record of each sampled ballot against the paper ballot itself, and needs far fewer. In one worked example with 64,000 ballots, an 8% margin and a 10% risk limit, ballot comparison needs on average 80 ballots and ballot polling about 700. Sample sizes rise rapidly for narrow margins: in a county with 4,000 ballots, ballot comparison needs 300 ballots for a 2% margin and 3,000 for a 0.1% margin, while ballot polling would need a full hand count. Margins under 0.1% occur in one in sixty to one in 460 contests.

The risk limit sets how much risk is tolerated. With a 9% limit, as used in Colorado, if the initial results contain an erroneous winner, the audit will catch at least 91% of such cases and let up to 9% stay undetected. If the sample shows enough discrepancies, a larger sample is selected, until the original winner is confirmed or hand-counting all ballots determines a different winner.

In 2010 the American Statistical Association endorsed risk-limiting audits to verify election outcomes.