Bruce E. Hansen
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9/6/2001. Revised 11/2002
On the Reliability of Recounts from Undervotes: Evidence from the 2000 Presidential Election
Download Paper (PDF format)
The vote recount in the 2000 Presidential election (Broward, Miami-Dade and
Palm Beach Counties, Florida) is scrutinized for evidence of bias. A new
precinct-level dataset is carefully constructed, incorporating the
machine-vote tally, the recount vote tally, voter registration demographics,
and the ballot review by media sources. A new multivariate Beta-Logit model
is introduced, which allows the joint modeling of multivariate unobserved
latent probabilites, which is essential to the study of the recount vote. A
simple two-step estimator is proposed which approximates the joint maximum
likelihood estimator.
The parameter estimates are consistent with a strong hypothesis -- that the
recount vote tally was unbiased. Specifically, it is found that the
precinct-level machine-vote probability for a candidate is an unbiased
predictor for the hand recounted undervote probability. There is no evidence
of bias in the recount, and no evidence of differences between the three
counties which conducted the recounts.
11/28/00
Recount in Dade County? A Statistical Analysis
Complete Paper (PDF format)
A precinct-level statistical analysis of Miami-Dade County, Florida shows the following.
If the hand-count of ballots is completed, Vice-President Gore is expected to gain 254 votes relative to Governor Bush.
This includes both the 157 votes from the aborted hand-count of 135 precincts, plus an additional net 97 votes from a hand-count of the remaining 655 precincts.
A 95% confidence interval for the net gain is [172, 336].
A 95% confidence interval for the net gain from the uncounted 655 precincts is [15, 179].
The estimates are based on a Binomial model which allows voting probabilities to be precinct-specific. It is based on a "yield rate" of 20%, as obtained in the aborted hand-count, and on a canvassing board error rate of 8%, which is estimated from that data.
Revised 11/19/00
A NonParametric Analysis of UnderVotes in the Palm Beach Presidential Vote: Implications for a Recount
Complete Paper (PDF format)
A precinct-level nonparametric analysis of the November 2000 Presidential vote
in Palm Beach Florida shows that undervoting -- not marking the ballot
sufficiently for the counting machines to read -- cost Gore approximately
3104 more votes than Bush.
Our analysis also predicts that a hand recount will net approximately 294
votes for Gore, but the actual gain can range from 184 to 394.
Our estimates are conservative because they are based on the yield rate from the four-precinct hand recount. The Wednesday court ruling called for election officials to be more aggresive in their assessment of undervotes, and take into account so-called dimpled ballots, which were indented but not punched through. This will increase the yield rate, although the extent is unclear.
The estimates are based on a Binomial model which allows voting probabilities to vary nonparametrically. This methodology may be of general interest because it gives precise yet accurate confidence intervals using only precinct-level vote data.
Data and Programs (Zip format)
A Precinct-Level Demographic Analysis of Double-Punching in the Palm Beach Presidential Vote
A precinct-level demographic analysis of the November 2000 Presidential vote
in Palm Beach Florida shows that overvoting -- marking the ballot for two
different candidates -- cost Gore at least 4,270 more votes than Bush, and
possibly as many as 17,710. This result is highly statistically significant.
Our statistical analysis shows that:
(1) Overvoting is positively related to the percentage of registered
voters who are over the age of 65, Black, Hispanic, and Democrats, and is
negatively related to the percentage who voted for Bill Nelson (the
Democratic candidate for Senate). This equation accounts for 71% of the
variation in the percentage of overvotes.
(2) After controlling for the above variables, both Gore and Bush lost
votes due to overvoting. Our point estimate is that Gore lost 0.82% votes
for every 1% of overvoting, and Bush lost 0.24%.
(3) The impact of overvoting on the election is the effect on the
difference between Gore's votes and Bush's votes. This difference is
positively related to the percentage of registered Democrats and those
registered to third parties, and to the percentage of votes to Bill Nelson.
It is negatively related to the percentage of overvotes. This equation
accounts for 98% of the variation in the difference between Gore's and
Bush's votes.
(4) Our point estimate is that Gore lost 0.58% more votes than Bush
for every 1% of overvoting, holding demographic factors constant. A 99%
confidence interval for this impact is [-1.03,-0.13].
(5) Of the 19,000 ballots in Palm Beach lost due to overvoting, our point
estimate is that this cost Gore 15,580 votes, cost Bush 4560 votes, and the
effect was a net cost to Gore of 11,020 votes.
(6) A 99% confidence interval for this cost is [4270, 17710]. At a
high level of confidence, we conclude that Gore lost at least 4,270
votes due to overvoting.
Complete Paper (PDF format)
Data and Programs (Zip format)
Who Won Florida? Are the Palm Beach Votes Irregular?
A county-level demographic analysis of the November 2000 Presidential vote
in Florida shows that the Palm Beach vote is irregular. We can state with
99.9% confidence that 2058 of the 3407 votes cast for Patrick Buchanan are
inconsistent with the demographic characteristics of Palm Beach.
A 99.9% confidence interval for the correct Palm Beach vote is [251, 1349].
A vote outside this interval should be viewed as extremely unlikely and
irregular. In particular, the reported vote of 3407 should be dismissed as irregular.
An implication is that at least 2058 of the votes attributed to Buchanan are irregular.
Our demographic analysis shows precisely why we can make this claim. The
voting patterns of Florida counties show a strong relationship between the
votes cast for Buchanan and the demographic characteristics of the county.
Factors which contribute to low votes for Buchanan are high
percentages of elderly, Blacks, Hispanics, and college education, and median household income. Palm Beach has a high percentage of elderly
and college education, and a high median household income. Palm Beach is
therefore expected to have a low percentage vote for Buchanan. The
recorded high percentage vote is inconsistent with this prediction.
There have been an explosion of papers written on this subject in the past
few days. All of the analysis I have seen has looked only at the
relationship between the votes for the various candidates. The analysis
described here is the first I have seen which explores the Florida vote
using cross-sectional demographic variation. Hopefully this sheds
additional light on the subject.
Complete Paper (PDF format)
Data and Programs (Zip format)
email: bhansen@ssc.wisc.edu