— To verify that vote-tallying inference from stratified samples,
machines are functioning properly sampling with probability pro-
portional to error bounds, mul-
—To provide for continuous
tiple testing, sequential testing,
improvement in the conduct
and combinatorially complex
of elections
games. Audit protocols must also
meet constraints of cost, time,
Statisticians can help. For exam-
complexity, and transparency
ple, they can do the following:
to diverse audiences—the pub-
lic, election integrity advocates,
— Characterize the distribu-
legislators, and election officials.
tion and nature of vote-counting
Because audits must work within
errors for different voting tech-
the practical limitations of elec-
nologies and different methods
tions and the legislative process,
of hand counting
statisticians should be prepared
— Develop and improve the
to collaborate across many disci-
efficiency of practical methods to
plines: political science, computer
control the risk that an incorrect
science, the social and behavioral
outcome will go undiscovered
sciences (usability studies and
survey research), forensics, and
— Estimate the cost and logis-
“usable security”—security that
tical requirements of various
is adequate to the task without
approaches to auditing and the
impairing usability. Statisticians
trade-offs among rigor, risk, time,
PhD student Luke Miratrix and Philip stark (right) audit
must “think outside the urn.”
the votes for Measure W in Yolo County, California, in
and cost
Methodological research in
November of 2008. Miratrix works with stark developing
— Inform policy when there are
election auditing is relevant to
risk-limiting methods.
competing risks and benefits—for
financial auditing, experimental
example, between the risk of dis-
design and analysis, and many
other fields in which one seeks
(VVPAT) can independently
enfranchisement and that of vote
to draw inferences about a finite
check the accuracy of machine
fraud, between cost and waiting
population that satisfies a priori
subtotals, typically subtotals by
time at the polls, between cost and
bounds, but for which para-
precinct. Vote-tabulation audits
accuracy of vote-count technology,
metric approximations could be
(also called post-election audits)
between security and ease of use
inaccurate. Preliminary results
that compare hand and machine
— Identify processes and technol- suggest that techniques recently
counts of a random sample of
ogies that can improve accuracy or developed for election auditing
subtotals can help ensure incor-
enable less painful compromises are more efficient than those cur-
rect outcomes are caught and
rently used in financial auditing.
corrected. Indeed, post-election
— Develop a knowledge base
audits uncovered many of the Risk-Limiting, Vote-
problems cited above.
The role of statisticians was
Tabulation Audits
Statisticians helped draft
discussed by David Marker, John
According to Principles and Best
Principles and Best Practices for
Gardenier, and Arlene Ash in the
Practices for Post-Election Audits,
Post-Election Audits (see http://
June 2007 issue of Amstat News.
a risk-limiting audit has a pre-
electionaudits.org/principles),
Here, we review recent progress,
specified, minimum chance of a
and the American Statistical
propose a road map for further
full manual count whenever the
Association Board of Directors
progress, and suggest ways for
outcome of the election is wrong.
endorsed its statistical content.
statisticians to contribute.
By definition, an outcome is
The document states the following
goals of vote-tabulation audits:
A Challenging
“wrong” if it disagrees with the
Statistical Problem
outcome a full hand count would
show. A risk-limiting audit is
— To deter fraud At first glance, election audit-
only as good as its audit trail.
ing appears to be a straightfor-
— To promote public confidence
No trail, no audit. Only with
ward sampling problem. In fact,
in elections
a complete and accurate audit
audits raise questions about non-
trail—ensured through a secure
— To find error, whether acci-
parametric tests for the mean of
chain of custody—can any audit
dental or intentional
nonstandard distributions, exact
provide real assurance.
38 AmstAt News JUNE 2009
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