A P ] 1 7 Ju l 2 00 9 Checking election outcome accuracy Post - election audit sampling Kathy

This article advances and improves existing post-election audit sampling methodology. Methods for determining post-election audit sampling have been the subject of extensive recent research. This article • provides an overview of post-election audit sampling research and compares various approaches to calculating post-election audit sample sizes, focusing on risklimiting audits, • discusses fundamental concepts common to all risk-limiting post-election audits, presenting new margin error bounds, sampling weights and sampling probabilities that improve upon existing approaches and work for any size audit unit and for single or multi-winner election contests, • provides two new simple formulas for estimating post-election audit sample sizes in cases when detailed data, expertise, or tools are not available, • summarizes four improved methods for calculating risk-limiting election audit sample sizes, showing how to apply precise margin error bounds to improve the accuracy and efficacy of existing methods, and • discusses sampling mistakes that reduce post-election audit effectiveness. Adequate post-election audit sampling is crucial because analyzing discrepancies found in too-small samples can determine little except that the sample size is inadequate. This article is one of three articles in a series Checking Election Outcome Accuracy. The other two articles discuss post-election auditing procedures and an algorithm for deciding whether to increase the sample or to certify the election outcome in response to any discrepancies found during a post-election audit.