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Election Certification by Statistical Audit of Voter-Verified Paper Ballots

43 Pages Posted: 4 Jan 2005  

Kenneth C. Johnson


Date Written: October 31, 2004


Voter-verified paper ballots can be used to provide a physical audit trail for electronic voting, but paper ballots present a conundrum: It may never be known whether an election result is valid unless the paper ballots are manually counted, but a full recount would not normally be justified unless there is sufficient cause to doubt the electronic count. A solution to this problem is to mandate a statistical audit as part of routine election certification processes, with the audit being based on a small, random sampling of ballots and employing robust statistical methods.

In a conventional statistical recount, a random sampling of paper ballots is manually counted to confirm the electronic result. But most of the recount effort goes into tedious counting and tallying operations that could be performed much more efficiently and accurately by computer, using an electronic ballot database, and which could be easily verified by auditors and anyone who has access to the database. All that is really needed to validate the election is to verify that the ballot database is an accurate representation of the paper ballots, i.e., the number of ballot recording errors should not be sufficient to change the election outcome.

This paper analyzes two election audit processes: a conventional statistical recount, and a statistical error count that detects discrepancies between ballot database records and corresponding paper ballots. The error-count method would have enormous advantages of efficiency and robustness. For example, considering a two-candidate election with 10,000,000 ballots and a 1% winning margin, a statistical recount would typically require approximately 70,000 ballots (and possibly many more) to verify the result with 99% confidence, whereas a statistical error count would require fewer than 1000. Moreover, a statistical recount would be very sensitive to audit error bias; for example, a 0.1% bias could require that the expected sample size be increased to 95,000 for the same 99% confidence level. By contrast, a statistical error count would be very insensitive to audit errors, e.g., the method could compensate for a 10% audit error rate by simply making the sample size approximately 10% larger. The error-count method's simplicity, efficiency, and insensitivity to audit errors would make it practical for use as a routine election certification procedure.

Keywords: Election audit, election recount, statistical recount, hypothesis testing, hypergeometric distribution

JEL Classification: C13, C67

Suggested Citation

Johnson, Kenneth C., Election Certification by Statistical Audit of Voter-Verified Paper Ballots (October 31, 2004). Available at SSRN: or

Kenneth C. Johnson (Contact Author)

Independent ( email )

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