Limiting Risk by Turning Manifest Phantoms into Evil Zombies

Drawing a random sample of ballots to conduct a risk-limiting audit generally requires knowing how the ballots cast in an election are organized into groups, for instance, how many containers of ballots there are in all and how many ballots are in each container. A list of the ballot group identifiers along with number of ballots in each group is called a ballot manifest. What if the ballot manifest is not accurate? Surprisingly, even if ballots are known to be missing from the manifest, it is not necessary to make worst-case assumptions about those ballots--for instance, to adjust the margin by the number of missing ballots--to ensure that the audit remains conservative. Rather, it suffices to make worst-case assumptions about the individual randomly selected ballots that the audit cannot find. This observation provides a simple modification to some risk-limiting audit procedures that makes them automatically become more conservative if the ballot manifest has errors. The modification--phantoms to evil zombies (~2EZ)--requires only an upper bound on the total number of ballots cast. ~2EZ makes the audit P-value stochastically larger than it would be had the manifest been accurate, automatically requiring more than enough ballots to be audited to offset the manifest errors. This ensures that the true risk limit remains smaller than the nominal risk limit. On the other hand, if the manifest is in fact accurate and the upper bound on the total number of ballots equals the total according to the manifest, ~2EZ has no effect at all on the number of ballots audited nor on the true risk limit.