Machine-assisted election auditing
EVT'07 Proceedings of the USENIX Workshop on Accurate Electronic Voting Technology
CAST: Canvass audits by sampling and testing
IEEE Transactions on Information Forensics and Security - Special issue on electronic voting
Election audits using a trinomial bound
IEEE Transactions on Information Forensics and Security - Special issue on electronic voting
Risk-limiting postelection audits: conservative P-values from common probability inequalities
IEEE Transactions on Information Forensics and Security - Special issue on electronic voting
Implementing risk-limiting post-election audits in California
EVT/WOTE'09 Proceedings of the 2009 conference on Electronic voting technology/workshop on trustworthy elections
Single-ballot risk-limiting audits using convex optimization
EVT/WOTE'10 Proceedings of the 2010 international conference on Electronic voting technology/workshop on trustworthy elections
Single-ballot risk-limiting audits using convex optimization
EVT/WOTE'10 Proceedings of the 2010 international conference on Electronic voting technology/workshop on trustworthy elections
Computing the margin of victory in IRV elections
EVT/WOTE'11 Proceedings of the 2011 conference on Electronic voting technology/workshop on trustworthy elections
SOBA: secrecy-preserving observable ballot-level audit
EVT/WOTE'11 Proceedings of the 2011 conference on Electronic voting technology/workshop on trustworthy elections
Computing the margin of victory for various voting rules
Proceedings of the 13th ACM Conference on Electronic Commerce
A Bayesian method for auditing elections
EVT/WOTE'12 Proceedings of the 2012 international conference on Electronic Voting Technology/Workshop on Trustworthy Elections
BRAVO: ballot-polling risk-limiting audits to verify outcomes
EVT/WOTE'12 Proceedings of the 2012 international conference on Electronic Voting Technology/Workshop on Trustworthy Elections
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Simultaneous risk-limiting audits of a collection of contests have a known minimum chance of leading to a full hand count if the outcome of any of those contests is wrong. Risk-limiting audits are generally performed in stages. Each stage involves drawing a sample of ballots, comparing a hand count of the votes on those ballots with the original count, and assessing the evidence that the original outcomes agree with the outcomes that a full hand count would show. If the evidence is sufficiently strong, the audit can stop; if not, more ballots are counted by hand and the new evidence is assessed. This paper derives simple rules to determine how many ballots must be audited to allow a simultaneous risk-limiting audit to stop at the first stage if the error rate in the sample is sufficiently low. The rules are of the form "audit at least ρ/µ ballots selected at random." The value of ρ depends on the simultaneous risk limit and the amount of error to be tolerated in the first stage without expanding the audit. It can be calculated once and for all without knowing anything about the contests. The number µ is the "diluted margin": the smallest margin of victory in votes among the contests, divided by the total number of ballots cast across all the contests. The initial sample size does not depend on any details of the contests, just the diluted margin. This is far simpler than previous methods. For instance, suppose we are auditing a collection of contests at simultaneous risk limit 10%. In all, N ballots were cast in those contests. The smallest margin is V votes: The diluted margin is µ = V/N. We want the audit to stop at the first stage provided the fraction of ballots in the sample that overstated the margin of some winner over some loser by one vote is no more than µ/2 and no ballot overstates any margin by two votes. Then an initial sample of 15:2/µ ballots suffices. If the sample shows any two-vote overstatements or more than 7 ballots with one-vote overstatements, more sampling might be required, depending on which margins have errors. If so, simple rules that involving only addition, subtraction, multiplication, and division can be used to determine when to stop.