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Risk-limiting audits (RLAs) are a significant tool in increasing confidencein the accuracy of elections. They consist of randomized algorithms which checkthat an election's vote tally, as reported by a vote tabulation system,corresponds to the correct candidates winning. If an initial vote count leadsto the wrong election winner, an RLA guarantees to identify the error with highprobability over its own randomness. These audits operate by sequentiallysampling and examining ballots until they can either confirm the reportedwinner 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 thatoperate on batches. As a concrete application of the suggested method, wedevelop the first ballot-level RLA for the Israeli Knesset elections, andconvert it to one which operates on batches. We ran the suggested ``Batchcomp"procedure on the results of 22nd, 23rd and 24th Knesset elections, both withand without errors.  The second part of this work suggests a new use-case for RLAs: verifying thata population census leads to the correct allocation of political power to anation's districts or federal-states. We present an adaptation of ALPHA, anexisting RLA method, to a method which applies to censuses. Our census-RLA isapplicable in nations where parliament seats are allocated to geographicalregions in proportion to their population according to a certain class offunctions (highest averages). It relies on data from both the census and froman additional procedure which is already conducted in many countries today,called a post-enumeration survey.

New Algorithms and Applications for Risk-Limiting Audits