  A collection of races in a single election can be audited as a group by
auditing a random sample of batches of ballots and combining observed
discrepancies in the races represented in those batches in a particular way:
the maximum across-race relative overstatement of pairwise margins (MARROP). A
risk-limiting audit for the entire collection of races can be built on this
ballot-based auditing using a variety of probability sampling schemes. The
audit controls 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. The approach is particularly efficient if batches are drawn with
probability proportional to a bound on the MARROP (PPEB sampling).
