  Risk-limiting audits (RLAs) are a significant tool in increasing confidence
in the accuracy of elections. They consist of randomized algorithms which check
that an election's vote tally, as reported by a vote tabulation system,
corresponds to the correct candidates winning. If an initial vote count leads
to the wrong election winner, an RLA guarantees to identify the error with high
probability over its own randomness. These audits operate by sequentially
sampling and examining ballots until they can either confirm the reported
winner or identify the true winner.
  The first part of this work suggests a new generic method, called
``Batchcomp", for converting classical (ballot-level) RLAs into ones that
operate on batches. As a concrete application of the suggested method, we
develop the first ballot-level RLA for the Israeli Knesset elections, and
convert it to one which operates on batches. We ran the suggested ``Batchcomp"
procedure on the results of 22nd, 23rd and 24th Knesset elections, both with
and without errors.
  The second part of this work suggests a new use-case for RLAs: verifying that
a population census leads to the correct allocation of political power to a
nation's districts or federal-states. We present an adaptation of ALPHA, an
existing RLA method, to a method which applies to censuses. Our census-RLA is
applicable in nations where parliament seats are allocated to geographical
regions in proportion to their population according to a certain class of
functions (highest averages). It relies on data from both the census and from
an additional procedure which is already conducted in many countries today,
called a post-enumeration survey.
