@InProceedings{RS12b,
  author =       { Ronald L. Rivest and Emily Shen },
  title =        { A Bayesian Method for Auditing Elections },
  url =          { https://www.usenix.org/system/files/conference/evtwote12/rivest_bayes_rev_073112.pdf },
  booktitle =    { Proceedings 2012 EVT/WOTE Conference },
  editor =       { J. Alex Halderman and Olivier Pereira },
  date =         { 2012-08-07 },
  eventtitle =   { EVT/WOTE'12 },
  eventdate =    { 2012-08-06/2012-08-07 },
  venue =        { Seattle, WA },
  OPTyear =      { 2012 },
  OPTmonth =     { August 6-7, },
  urla =         { <a href="https://www.usenix.org/conference/evtwote12">EVT/WOTE'12</a> },
  urlb =         { <a href="https://www.usenix.org/conference/evtwote12/bayesian-method-auditing-elections">video</a> },                  
  urlc =         { <a href="http://people.csail.mit.edu/rivest/bayes/">interactive implementation</a> },
  abstract =     {
                   We propose an approach to post-election auditing based on Bayesian
                   principles, and give experimental evidence for its efficiency and
                   effectiveness.  We call such an audit a ``Bayes audit''.  It aims to
                   control the probability of miscertification (certifying a wrong
                   election outcome).  The miscertification probability is computed using
                   a Bayesian model based on information gathered by the audit so far.
                   \par
                   A Bayes audit is a single-ballot audit method applicable to any voting
                   system (e.g.\ plurality, approval, IRV, Borda, Schulze, etc.)\ as long
                   as the number of ballot types is not too large.  The method requires
                   only the ability to randomly sample single ballots and the ability to
                   compute the election outcome for a profile of ballots.  A Bayes audit
                   does not require the computation of a ``margin of victory'' in order
                   to get started.
                   \par
                   Bayes audits are applicable both to ballot-polling audits, which work just
                   from the paper ballots, and to comparison audits, which work by
                   comparing the paper ballots to their electronic representations.  The
                   procedure is quite simple and can be described on a single page.
                   \par
                   The Bayes audit uses an efficient method (which may be based on the
                   use of gamma variates or on P\'{o}lya's Urn) for simulating a Bayesian
                   posterior distribution on the tally of a profile of ballots.  
                   \par
                   A Bayes audit is very similar to single-ballot risk-limiting audits.
                   However, since Bayes audits are based on different principles, the
                   precise relationship between risk-limiting audits and Bayes audits
                   remains open.
                   \par
                   We provide some initial experimental results indicating that Bayes
                   audits are quite efficient, requiring few ballots to be examined, and
                   that the miscertification rate is indeed kept small, even for very close
                   elections.
                 }                  
}