Probability
On auditing elections when precincts have different sizes
EVT'08 Proceedings of the conference on 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
Implementing risk-limiting post-election audits in California
EVT/WOTE'09 Proceedings of the 2009 conference on Electronic voting technology/workshop on trustworthy elections
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
Implementing risk-limiting post-election audits in California
EVT/WOTE'09 Proceedings of the 2009 conference on Electronic voting technology/workshop on trustworthy elections
OpenScan: a fully transparent optical scan voting system
EVT/WOTE'10 Proceedings of the 2010 international conference on Electronic voting technology/workshop on trustworthy elections
Super-simple simultaneous single-ballot risk-limiting audits
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
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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Postelection audits of a random sample of batches of ballots against a trustworthy audit trail can limit the risk of certifying an incorrect electoral outcome to, guaranteeing that--if the apparent outcome is wrong--the chance of a full hand count of the audit trail is at least 1- α. Risk-limiting audits can be built as sequential tests that audit more batches until either 1) there is strong evidence that the outcome is correct, given the errors found, or 2) there has been a complete hand count. The P-value of the hypothesis that the outcome is wrong is the largest chance, for all scenarios in which the outcome is wrong, that overstatements of the margins between winners and losers would be "no larger" than they were observed to be. Different definitions of "larger" give different P-values. A small P-value is strong evidence that the outcome is correct. This paper gives simple approaches to calculating a conservative P-value for several ways of summarizing overstatements and several ways of drawing the sample of batches to audit, emphasizing sampling with probability proportional to a bound up on the error in the pth audit batch (PPEB sampling). A P-value based on Markov's inequality applied to a martingale constructed from the data seems the most efficient among the methods discussed; there are plans to use it to audit contests in two California counties in November 2009.