Election Audit Mathematics

Election Audit Papers - How to Audit Elections to Ensure Correct Outcomes

New! Are election outcomes publicly-verifiably accurate? Eight Fundamentals of auditing vote tallies This is a one-pager suitable for a handout (to give to election officials and legislators?)

Checking Election Outcome Accuracy -- Post-Election Auditing Sampling This paper by Kathy Dopp makes significant improvements to existing post-election auditing sampling methods and provides an overview of sampling methods minimizing the risk of certifying incorrect election outcomes.

One-Page Concept Proposal for Election Reform Legislation, March 2007
Detailed comments on manual vote count audit amounts and procedures, auditable voting equipment, audit and recount committees; plus recommendations for ensuring election integrity

Mandatory Post-Election Vote Count Audit - A Short Legislative & Administrative Proposal (December 2008)

Post-Election Vote Count Audits -- Probability Proportional to Margin Error Bound (PPMEB) Method - How to determine initial audit sample size, and make random selections, to achieve any desired confidence (say 95% or greater) that any incorrect unofficial election outcome would be corrected before certification.

History of Confidence Election Auditing Development (1975 to 2008)& Overview of Election Auditing Fundamentals

Legislative Model Election Auditing Legislative Proposal This was written for Utah. (May 2006, updated last December 2008)

First U.S. Scientific Election Audit Reveals Voting System Flaws But Questions Remain Unanswered May 2007 Critique of the "Collaborative Public Audit" of Cuyahoga County Ohio's November 2006 Election

Response to California Secretary of State's Post-Election Audit Standards Working Group

California Secretary of State Debra Bowen's Election Requirements California is the first state to require measures that will make elections verifiably publicly accurate. Read the "Withdrawal of Approval.." documents to learn about these measures.

A Post Election Audit Working Group was formed by California Secretary of State Bowen. Here are notes of their first meeting.

The American Statistical Association Recommends 99% Confidence Level Election Audits in July 24th letter to House Leader Nancy Pelosi.

Federal Election Audit Proposals - Which is Best? Kathy Dopp, June 11, 2007

Federal Election Audit Costs, March 2007
Evaluates the cost and effectiveness of three audit proposals using federal election results from 2002 and 2004 US House and Senate elections

Fool Me Once: Checking Vote Count Integrity, March 2007

Shows how to evaluate the effectiveness of election audits by evaluating the tiered election audit proposal in 110th Congressional Session’s HR811, shows how to fix the HR811 audit to ensure higher probabilities, gives a better tiered audit, and shows how a calculated audit is more effective and efficient

Tiered Election Audits - Based on Margins between Candidates January 2007, Explains tiered election audits and gives a spreadsheet to help calculate tiered election audits that achieve any desired minimum success probability

How Big Should an Election Audit Be? Fixed Rate Audits Do Not Work For Elections, January 2007 Shows how to use a formula to slightly over-estimate the audit amounts necessary to ensure election outcome accuracy & provides a spreadsheet for calculating audit amounts.

The Election Integrity Audit Dopp and Stenger, September 2006 Shows how to exactly calculate the minimum amount of vote counts to audit in order to ensure election outcome accuracy to any desired certainty level; and shows how to exactly calculate the minimum number of corrupt vote counts that could alter election outcomes using precinct sizes; and makes recommendations for audit procedures

How Can Independent Paper Audits Ensure Election Integrity?
Dopp and Baiman, June 2005 (updated in July 2006) Gives fundamental formulas and spreadsheet formulas for calculating probabilities - first time the formula was given for determining how many corrupt (miscounted) vote counts could wrongly alter an election outcome

New Jersey Election Audit Legislative Proposal, June 5, 2007 p. 18

A Quick Primer on The Mathematics of Post-Election Audit Confidence Joseph Lorenzo Hall, March 20, 2007

On Estimating the Size and Confidence of a Statistical Audit by Aslam, Rivest, and Popa April 2007 Gives formulas for estimating the size of election audits and for the confidence levels of election audits that can be calculated with a calculator.

Utah's Election Audit and Recount Procedures Found Lacking October, 2006.

Critique of the Post-Election Auditing Recommendations of Verified Voting and the American Statistical Association


The Following are Currently Unavailable Online (Please email me if you need them. I have them someplace on my computers - kathy (dot) dopp (at) gmail (dot) com)

Mathematician Ousted from 2007 Post Election Audit Summit Hotel!

Other Articles & Projects

Humbolt County, CA Election Transparency Project

California Secretary of State Recount Proposals, December 2008 Note: Scientific, post-election audits would entirely replace the need for recounts by requiring manual recounts of from 1% to 100% of paper ballots automatically as necessary to ensure accurate election outcomes. Some of the recount procedures included in this document could be applied to post-election auditing.

Criticism of Connecticut Election Audit

California Secretary of State Debra Bowen leads the way by requiring public observation of elections. See required California County Election Observation Plans

Report and Feedback November 2007 Connecticut
Election Audit Observation
By The Connecticut Citizen Election Audit Coalition, January 16, 2008, www.CTElectionAudit.org

Verified Voting State by State Auditing Statutes Note: The Verified Voting State by State Auditing Statutes Document is inaccurate.

The Verified Voting (VV) auditing document provides useful information. However it merely repeats what was told to VV by State Election Officials regarding their own election auditing procedures, often mischaracterizing them.

Many state auditing procedures do *not* even compare the publicly reported vote counts to the manual counts. Many states do not audit any provisional or mail-in ballots. Many states conduct post-election machine testing that would not detect any deliberate tampering.

Except for New Mexico, current state post-election auditing procedures are self-audits by election administrators who check their own work. Some state election officials do not dutifully follow their state legislature's post-election auditing statutes, or use loopholes or imprecision in their statutes to avoid implementing the intent of the legislature.

For two examples, an Ohio county technician discovered that its Premier/Diebold central tabulators were dropping hundreds of votes from entire memory cards, a fact that would have been discovered years ago if Ohio had been conducting effective, scientific post-election audits. A Humbolt County, CA volunteer recounted the paper ballots with an open source program he had created and found that the Diebold central tabulator also drops the entire first batch of counted optical scan ballots (hundreds of votes) under common circumstances. Such programming errors would have been discovered years ago if states were conducting valid, scientific post-election audits.