On Estimating the Size and Confidence of a Statistical Audit

We consider the problem of statistical sampling for auditing elections, and we develop a remark-ably simple and easily-calculated upper bound for the sample size necessary for determining with probability at least c whether a given set of n objects contains b or more “bad ” objects. While the size of the optimal sample drawn with-out replacement can be determined with a com-puter program, our goal is to derive a highly ac-curate and simple formula that can be used by election officials equipped with only a simple cal-culator. We actually develop several formulae, but the one we recommend for use in practice is: U3(n, b, c