he never-ending presidential campaign of 2000, which stretched for 36 days beyond the traditional November end point, was one for the history books. And as such, it attracted the attention of a range of academics: law professors, historians, political scientists, and communications experts.

But another group of academics also found themselves riveted to the drama in Florida: statisticians. It led to a bonanza of interest among professional statisticians. In particular it led to discussions in many statistics classes, including my own, on the applications of sampling and other issues. A rash of articles and even web sites discussing the issues, appeared in the days following the election. Contrary to how the public felt, we statisticians found the debate and the delay incredibly interesting. As a matter of fact, many of us were sorry that it ended.

To recap briefly: On election night, the television networks, acting on estimates by the Voters News Service (VNS) prematurely said Democratic candidate Al Gore was the winner of Florida and its 25 electoral votes. That was at roughly 7:50 p.m. election night. Two hours later, they retracted this projection, stating that Florida was too close to call. Early the next morning, Republican candidate George W. Bush was named the winner of the Sunshine State and its crucial electors, which were enough to give him 271 electoral votes and the Presidency. About one hour and 40 minutes later this projection was retracted and once again Florida was too close to call. This led to the unprecedented and bizarre situation where the Democratic candidate, Gore, retracted his concession, made privately to Bush.

According to Warren Mitofsky, who was the founder and the former director of VNS, the reasons for these occurrences were as follows: the first projection, that Gore won Florida, was caused by statistical error. We have to remember that projections, based on exit polls, are subject to error with a low probability of being incorrect. Projection mistakes do occur and this was such a case. However, the second projection, that Bush won Florida, was caused by a data error in Daytona Beach, which is in Volusia county. Twenty thousand extra votes were mistakenly credited to Bush by VNS shortly after 2 a.m. on November 8, 2000. The county noted the correction before 3 a.m. that morning, decreasing Bush's lead by a total of 25,000 votes.

The next day, it was revealed that the actual margin was remarkably close, about 1,700 votes out of six million cast (or less than 0.03% of the total votes cast). Indeed, Florida’s election law required that if the margin of victory for any candidate was less than one half of one percent of the total votes cast, a recount would be mandatory. As the margin was much less than 1%, a machine recount had to be carried out. The recount was carried out, resulting in an even narrower gap of roughly 350 votes, with Bush still in the lead (without a count of an expected two to three thousand overseas absentee ballots).

he recount process was further complicated by several concurrent lawsuits, charges and countercharges of election-day shenanigans, ballot irregularities, and political bias. One of the issues was the confusing use of the butterfly ballots in Palm Beach County, which may have resulted in a large number of Gore voters mistakenly voting for Reform Party Candidate Patrick Buchanan. Buchanan received a much larger than expected number of votes in this county (approximately 2,500 more). As a result of these lawsuits, the public has been exposed to statisticians who have testified as expert witnesses in various court cases.

One of the key issues to be resolved was how to count the so-called undervote. The undervote represented the ballots which were cast but for which the machines, for one reason or another, did not record a vote for President. And here’s where the statisticians came in. One of the main questions was the use of probability and statistics to determine whether or not to carry out a hand count of the Florida undervote.

Apart from the complicated legal propositions, there were three statistical questions necessary to answer in order to establish whether a statewide recount in Florida should be undertaken. First, was there a substantial number of ballots cast for the presidency for which no vote was recorded by machine? Second, could a substantial percentage of these ballots be recovered, so as to classify ballots for which a vote for President was recorded? Third, was there a probability, however remote, that the election result in Florida could be affected by a full count of the votes?

n testifying for the Gore-Lieberman campaign in one of its Florida state lawsuits, Yale statistics professor Nicolas Hengartner weighed in on the subject. He demonstrated that the first two conditions were met. Arguing for a hand count of the ballots which were not counted by the machine in three Florida counties, Hengartner showed that there was an undercount, which ranged from an average of 1.5% in counties using old-style punch cards to an average of 0.3% in counties using more sophisticated optical scanning devices. Furthermore, he reported that varying percentages of these ballots (in the neighborhood of 25%) could be identified as votes for president by using hand counts, based on data obtained in the counties, which had already carried out hand counts. He did not testify on the third issue. However, the vote was so close that the probability of overturning the election of Florida, although difficult to determine, was not negligible. Cross-examination of Hengartner involved the issue of whether the undercount was machine related. In other words, did the punch card machine cause this undercount? This is a much more difficult question to answer. This issue is important to resolve in order to determine the future use of punch card ballots in elections. However, in this present situation, it is not relevant because the important issue is whether or not an undercount did occur and not the reasons for this occurrence. And the evidence did establish that there was an undercount.

Ultimately, the testimony of this statistician failed to carry the day. The Florida Supreme Court did rule that a statewide manual recount of all ballots should be undertaken. But the U.S. Supreme Court in December brought the counting to a stop, paving the way for Florida’s state government to bring the matter to a close and award the state’s electors to Bush.

To this statistician’s mind, a full statewide recount would have been the optimal solution. Any partial recount – i.e. recounting the votes in selected counties – could have been biased. And while a partial recount may have favored one candidate over the other, it would not have satisfactorily answered the vexing question as to who really won the popular vote in Florida. A hand recount may not have been a perfect solution. Uniform procedures as to how to classify the undervote as a vote may have been difficult to establish, but it was not impossible. And it is certainly preferable to ignoring the undercount.

A courtroom setting is not the ideal place to demonstrate the application of probability and statistics. Part of the problem is the fact that the concepts of statistics are difficult for the layperson to understand. The issues became even murkier in a courtroom where dueling attorneys raised questions on issues that are already confusing. The confusion, which the public must certainly have felt, is echoed by a famous quote by Benjamin Disraeli, a nineteenth century Prime Minister of England, who said: “There are three kinds of lies: lies, damned lies, and statistics.”

I will make two predictions. First, this issue will not go away. Currently, there are several groups counting the undervote under various criteria. Second, in future elections, the use of punch card balloting will disappear.

Aaron Tenenbein is professor of statistics and actuarial science at NYU Stern.