New Algorithms and Applications for Risk-Limiting Audits

Authors Bar Karov, Moni Naor

Thumbnail PDF


  • Filesize: 1.23 MB
  • 27 pages

Document Identifiers

Author Details

Bar Karov
  • Weizmann Institute of Science, Rehovot, Israel
Moni Naor
  • Weizmann Institute of Science, Rehovot, Israel

Cite AsGet BibTex

Bar Karov and Moni Naor. New Algorithms and Applications for Risk-Limiting Audits. In 4th Symposium on Foundations of Responsible Computing (FORC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 256, pp. 2:1-2:27, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


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 RLA for the Israeli Knesset elections, and convert it to one which operates on batches using "Batchcomp". We ran this suggested method on the real results of recent Knesset elections. The second part of this work suggests a new use-case for RLAs: verifying that a population census leads to the correct allocation of parliament seats to a nation’s federal-states. We present an adaptation of ALPHA [Stark, 2023], an existing RLA method, to a method which applies to censuses. This suggested census RLA 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.

Subject Classification

ACM Subject Classification
  • Applied computing → Voting / election technologies
  • Risk-Limiting Audit
  • RLA
  • Batch-Level RLA
  • Census


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. Michelle Blom, Jurlind Budurushi, Ronald L. Rivest, Philip B. Stark, Peter J. Stuckey, Vanessa Teague, and Damjan Vukcevic. Assertion-based approaches to auditing complex elections, with application to party-list proportional elections. In International Joint Conference on Electronic Voting, pages 47-62. Springer, 2021. Google Scholar
  2. Michelle Blom, Philip B Stark, Peter J Stuckey, Vanessa Teague, and Damjan Vukcevic. Auditing hamiltonian elections. In Financial Cryptography and Data Security. FC 2021 International Workshops: CoDecFin, DeFi, VOTING, and WTSC, Virtual Event, March 5, 2021, Revised Selected Papers, pages 235-250. Springer, 2021. Google Scholar
  3. United States Census Bureau. Historical households tables., 2022. Table HH-4.
  4. Giorgos Charalambous. The house of representatives. The Politics and Government of Cyprus. Oxford: Peter Lange, pages 143-168, 2008. Google Scholar
  5. Michael Gallagher. Proportionality, disproportionality and electoral systems. Electoral studies, 10(1):33-51, 1991. Google Scholar
  6. Tomer Grossman, Ilan Komargodski, and Moni Naor. Instance complexity and unlabeled certificates in the decision tree model. In 11th Innovations in Theoretical Computer Science Conference (ITCS 2020). Schloss Dagstuhl-Leibniz-Zentrum für Informatik, 2020. Google Scholar
  7. Guihua Hu, Ting Wen, and Yuhuan Liu. Determining the sample size of a post-enumeration survey: The case of china, 2020. Mathematical Population Studies, pages 1-31, 2022. Google Scholar
  8. The Knesset Lexicon. The distribution of knesset seats (bader-ofer method). This page wrongly states that the electoral threshold is 2.0%. It was since changed to 3.25%.
  9. Mark Lindeman and Philip B. Stark. A gentle introduction to risk-limiting audits. IEEE Security & Privacy, 10(5):42-49, 2012. Google Scholar
  10. Statistical Service of the Republic of Cyprus. Census of population and housing 2021: Preliminary results., 2022.
  11. Philip B. Stark. Sets of half-average nulls generate risk-limiting audits: Shangrla. In International Conference on Financial Cryptography and Data Security, pages 319-336. Springer, 2020. Google Scholar
  12. Philip B. Stark. Alpha: Audit that learns from previously hand-audited ballots. The Annals of Applied Statistics, 17(1):641-679, 2023. Google Scholar
  13. Department of Economics United Nations Secretariat and Statistics Division Social Affairs. Post enumeration surveys operational guidelines., 2010.
  14. Ian Waudby-Smith, Philip B. Stark, and Aaditya Ramdas. Rilacs: Risk limiting audits via confidence sequences. In International Joint Conference on Electronic Voting, pages 124-139. Springer, 2021. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail