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Abstract:
Automated counting processes make errors. How can we
determine whether the apparent winner of an election really won?
Could the margin be due to error—machine error, programming error,
processing error, voter error or even deliberate fraud? Post-election
audits—manual tallies of the votes in a random sample of
precincts—are designed to answer that question. I will try to convey
a feel for the logistical complexity of the election and election
auditing process and the tension between the need for efficiency
and the need for transparency. Confirming an election outcome
can be couched as a statistical hypothesis test. The null
hypothesis is that the apparent winner is not the true winner.
If the data allow us to reject that hypothesis with a small P-value,
we have high confidence in the election outcome. That is, we
have high confidence if, on the assumption that anybody other than
the apparent winner really won, the chance is tiny that the observed
miscount in the sampled precincts would be as small is it was
observed to be. How does confidence depend on the sample size,
the margin, the sizes of precincts in the race, and the observed
miscount? One method that seems politically and computationally
feasible is modelled on--you guessed it--drawing colored marbles
from an urn.
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