Efficient Post-Election Audits of Multiple Contests: 2009 California Tests
Philip B. Stark
University of California, Berkeley
August 3, 2009
CELS 2009 4th Annual Conference on Empirical Legal Studies Paper
Risk-limiting post-election audits have a pre-specified minimum chance of requiring a full hand count if the outcome of the contest is not the outcome that a full hand count of the audit trail would show. The first risk-limiting audits were performed in 2008 in California. Three refinements to increase efficiency were tested in Marin and Yolo counties, California, in November 2009. The first refinement is to audit a collection of contests as a group by auditing a random sample of batches of ballots and combining observed discrepancies in the contests represented in those batches in a particular way: the maximum across-contest relative overstatements (MACRO). MACRO audits control the familywise error rate (the chance that one or more incorrect outcomes fails to be corrected by a full hand count) at a cost that can be lower than that of controlling the per-comparison error rate with independent audits. A risk-limiting audit for the entire collection of contests can be built on MACRO using a variety of probability sampling schemes and ways of combining MACRO across batches. The second refinement is to base the test on the Kaplan-Markov confidence bound, drawing batches with probability proportional to an error bound (PPEB) on the MACRO. The Kaplan-Markov bound is especially well suited to sequential testing: After each batch is audited, a simple calculation--a product of fractions--determines whether to audit another batch or to stop the audit and confirm the apparent outcomes. The third refinement is to audit individual ballots rather than larger batches of ballots, comparing the cast vote record (the machine interpretation of the voter's marks on the ballot) to a human interpretation of the voter's intent. Such single-ballot audits can greatly reduce workload: When the outcome is correct, the number of ballots that must be audited to attain a given risk limit is roughly proportional to the number of ballots per batch. All three of these refinements can be used together, resulting in extremely efficient risk-limiting audits.
Number of Pages in PDF File: 23
Keywords: familywise error rate, Kaplan-Markov martingale confidence bound, nonnegative random variable, per-comparison error rate, probability proportional to size, sequential test, simultaneous test
JEL Classification: C12, C14, K39, M40
Date posted: August 7, 2009 ; Last revised: November 16, 2009
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