  U.S. elections rely heavily on computers such as voter registration
databases, electronic pollbooks, voting machines, scanners, tabulators, and
results reporting websites. These introduce digital threats to election
outcomes. Risk-limiting audits (RLAs) mitigate threats to some of these systems
by manually inspecting random samples of ballot cards. RLAs have a large chance
of correcting wrong outcomes (by conducting a full manual tabulation of a
trustworthy record of the votes), but can save labor when reported outcomes are
correct. This efficiency is eroded when sampling cannot be targeted to ballot
cards that contain the contest(s) under audit. If the sample is drawn from all
cast cards, RLA sample sizes scale like the reciprocal of the fraction of
ballot cards that contain the contest(s) under audit. That fraction shrinks as
the number of cards per ballot grows (i.e., when elections contain more
contests) and as the fraction of ballots that contain the contest decreases
(i.e., when a smaller percentage of voters are eligible to vote in the
contest). States that conduct RLAs of contests on multi-card ballots or of
small contests can dramatically reduce sample sizes by using information about
which ballot cards contain which contests -- by keeping track of card-style
data (CSD). For instance, CSD reduces the expected number of draws needed to
audit a single countywide contest on a 4-card ballot by 75%. Similarly, CSD
reduces the expected number of draws by 95% or more for an audit of two
contests with the same margin on a 4-card ballot if one contest is on every
ballot and the other is on 10% of ballots. In realistic examples, the savings
can be several orders of magnitude.
