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# 9/6/2001. Revised 11/2002

## On the Reliability of Recounts from Undervotes: Evidence from the 2000 Presidential Election

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