page_title: Risk-limiting audit
section_title: Sample size
hierarchical_section_title: Risk-limiting audit / Issues / Sample size
caption_attribution_description: English: Graph shows chance that election audit will find error, for different levels of error and sample sizes
context_page_description: A risk-limiting audit is one way of checking whether computers tallied an election accurately. It involves storing paper ballots securely until they can be checked,
  manually comparing a statistical sample of paper ballots to the computers' records for those same ballots,
  and checking whether all the computer records of ballots in the election were totalled correctly.
  Advantages of an RLA include: samples can be small and inexpensive if the margin of victory is large; there are options for the public to watch and verify each step;
  and errors found in any step lead to corrective actions, including larger samples, up to a 100% hand count if needed. Disadvantages include: the sample needs to be a large fraction of all ballots to minimize the chance of missing mistakes, if any contest is close; and it is hard to check computer totals publicly, except by releasing computer records to the public.
  If examining sampled ballots shows flaws in ballot storage, the usual approach cannot recover correct results,
  and researchers recommend a re-vote if the number of ballots held in flawed storage is enough to change winners.
context_section_description: Sample sizes rise rapidly for narrow margins of victory, with all methods. In a small city or county, with 4,000 ballots, method 1, ballot comparison, would need 300 ballots (300–600 minutes, as discussed in Cost below) for a contest with a 2% margin of victory. It would need 3,000 ballots (50-100 staff hours in the city or county) for a 0.1% margin of victory. Method 2 or 3, ballot polling or batch comparison, would need a full hand count of the 4,000 ballots (70-130 staff hours). Margins under 0.1% occur in one in sixty to one in 460 contests. Large numbers of contests on a ballot raise the chances that these small margins and large samples will occur in a jurisdiction, which is why no place does risk-limiting audits on all contests, leaving most local government races unaudited, though millions of dollars are at stake in local spending and land use decisions. Colorado picks contests with wider margins to avoid large samples.
  When Maryland evaluated audit methods, it noted that local boards of elections could not budget, or plan staffing, for risk-limiting audits, since the sample "is highly dependent on the margin of victory in any given audited contest... A very close margin of victory could... require days of staff work, possibly compromising the local certification deadline."
  An alternative to large samples is to audit an affordable sample size, and let the risk limit vary instead of the sample size. For a fixed sample, closer margins of victory would have more risk of letting erroneous winners take office, but any substantial sample would still have a known substantial chance of catching errors. Election managers would announce the level of confidence provided by the sample, and would have procedures to follow up if the sample finds one or more errors.
  The sample sizes presented will be enough to confirm a result, subject to the risk limit, when the apparent winner is the actual winner. If the sample does not confirm the win, more ballots are sampled, up to a 100% hand count to confirm a different winner.
caption: When sample sizes are limited by budget, they still have some likelihood of catching errors.
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