k-Cut: A Simple Approximately-Uniform Method for Sampling Ballots in Post-election Audits

  • Mayuri SridharEmail author
  • Ronald L. Rivest
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11599)


We present an approximate sampling framework and discuss how risk-limiting audits can compensate for these approximations, while maintaining their “risk-limiting” properties. Our framework is general and can compensate for counting mistakes made during audits.

Moreover, we present and analyze a simple approximate sampling method, “k-cut”, for picking a ballot randomly from a stack, without counting. Our method involves doing k “cuts,” each involving moving a random portion of ballots from the top to the bottom of the stack, and then picking the ballot on top. Unlike conventional methods of picking a ballot at random, k-cut does not require identification numbers on the ballots or counting many ballots per draw. We analyze how close the distribution of chosen ballots is to the uniform distribution, and design mitigation procedures. We show that \(k=6\) cuts is enough for a risk-limiting election audit, based on empirical data, which provides a significant increase in sampling efficiency. This method has been used in pilot RLAs in Indiana and is scheduled to be used in Michigan pilot audits in December 2018.


Sampling Elections Auditing Post-election audits Risk-limiting audit Bayesian audit 


  1. 1.
    Baignères, T., Vaudenay, S.: The complexity of distinguishing distributions. Ph.D. thesis (2008). results also in Baigneères’Google Scholar
  2. 2.
    Banuelos, J.H., Stark, P.B.: Limiting risk by turning manifest phantoms into evil zombies (2012).
  3. 3.
    Bretschneider, J., et al.: Risk-limiting post-election audits: why and how? (ver. 1.1), October 2012.
  4. 4.
    Goggin, S.N., Byrne, M.D., Gilbert, J.E.: Post-election auditing effects of procedure and ballot type on manual counting accuracy, efficiency, and auditor satisfaction and confidence. Election Law J. 11, 36–51 (2012)CrossRefGoogle Scholar
  5. 5.
    Johnson, K.: Election verification by statistical audit of voter-verified paper ballots, 31 October 2004.
  6. 6.
    Lindeman, M., Halvorseon, M., Smith, P., Garland, L., Addona, V., McCrea, D.: Principle and best practices for post-election audits (2008).
  7. 7.
    Lindeman, M., Stark, P.B.: A gentle introduction to risk-limiting audits. IEEE Secur. Priv. 10, 42–49 (2012)CrossRefGoogle Scholar
  8. 8.
    Lindeman, M., Stark, P.B., Yates, V.S.: BRAVO: ballot-polling risk-limiting audits to verify outcomes. In: Halderman, A., Pereira, O. (eds.) Proceedings 2012 EVT/WOTE Conference (2012)Google Scholar
  9. 9.
    Miller, S.J., Nigrini, M.J.: The modulo \(1\) Central Limit Theorem and Benford’s law for products (2007).
  10. 10.
    Rivest, R.L.: Reference implementation code for pseudo-random sampler (2011).
  11. 11.
    Rivest, R.L.: Bayesian tabulation audits: explained and extended, 1 January 2018.
  12. 12.
    Rivest, R.L., Shen, E.: A Bayesian method for auditing elections. In: Halderman, J.A., Pereira, O. (eds.) Proceedings 2012 EVT/WOTE Conference (2012).
  13. 13.
    Stark, P.B.: Papers, talks, video, legislation, software, and other documents on voting and election auditing.
  14. 14.
    Stark, P.B.: Tools for ballot-polling risk-limiting election audits (2017).

Copyright information

© International Financial Cryptography Association 2020

Authors and Affiliations

  1. 1.Massachusetts Institute of TechnologyCambridgeUSA

Personalised recommendations