@misc{Riv18a,
author = { Ronald L. Rivest },
title = { Bayesian Tabulation Audits: Explained and Extended },
date = { 2018-01-01 },
OPTyear = { 2018 },
OPTmonth = { January 1, },
urla = { arXiv },
abstract = {%
Tabulation audits for an election provide statistical evidence that
a reported contest outcome is ``correct''
(meaning that the tabulation of votes was properly performed),
or else the tabulation audit determines the correct outcome.
\par
Stark
proposed \textbf{risk-limiting tabulation audits} for this purpose;
such audits are effective and are beginning to be used in
practice in Colorado and other states.
\par
We expand the study of election audits based on \textbf{Bayesian}
methods. Such Bayesian audits
use a slightly different approach first introduced by Rivest and Shen in
2012. (The risk-limiting audits
proposed by Stark are ``frequentist'' rather than Bayesian in
character.)
\par
We first provide a simplified presentation of
Bayesian tabulation audits.
Suppose an election has been run and the tabulation of votes
reports a given outcome.
A Bayesian tabulation audit begins by drawing a random sample of the votes
in that contest, and tallying those votes.
It then considers what effect statistical variations of this tally
have on the contest outcome.
If such variations almost always yield the previously-reported outcome,
the audit terminates, accepting the reported outcome.
Otherwise the audit is repeated with an enlarged sample.
\par
Bayesian audits are attractive because they work with \textbf{any}
method for determining the winner (such as ranked-choice voting).
\par
We then show how Bayesian audits may be extended to handle
more complex situations, such as
auditing contests that \emph{span multiple jurisdictions},
or are otherwise ``stratified.''
\par
We highlight the auditing of such multiple-jurisdiction contests
where some of the jurisdictions
have an electronic cast vote record (CVR) for each cast paper vote,
while the others do not.
Complex situations such as this may arise naturally when some counties
in a state have upgraded to new equipment, while others have not.
Bayesian audits are able to handle such situations
in a straightforward manner.
\par
We also discuss the benefits and relevant considerations for using
Bayesian audits in practice.
}
}