The Use of Statistics in Elections
By Andrew First

On the first Tuesday after the first Monday of November, every four years, Americans elect a new president. More often than not, the outcome of the election is unknown beforehand. Polls are taken in the weeks and months prior to an election, but those are merely a snapshot in time, reflecting the electorate’s opinion at that particular moment. The candidate that an undecided voter supports can change many times before the election, and some people are completely undecided until they step into the voting booth. In addition, slim margins can not be predicted beforehand due to sampling variability. While samples give a good idea of what voters are thinking, there is a margin of error in each poll that must be taken into account while analyzing the poll results.

After millions of dollars are spent on advertising, and candidates are on the campaign trail for many months, people are anxious to see the results of the elections. To get an accurate reflection of the way the populace cast their votes, one need not count every single vote right away. By taking exit polls, news organizations are able to predict the outcome of elections with remarkable accuracy. These results are available much faster than the official vote counts that are used to certify elections. These polls also tell us how different demographic groups voted for each specific candidate.

A presidential election is unique among elections in the world in how the winner is determined. Every state is allotted a specific number of electoral votes, corresponding to the number of Senators a state has plus the number of Congressmen the state sends to the U.S. House of Representatives. With the exception of Maine and Nebraska, these votes are awarded on a winner take all basis. When one casts a vote for the presidential race, it is actually a vote for a slate of electors chosen by the candidate, who will then cast the electoral vote for the candidate. In Maine and Nebraska, the winners of each congressional district receive one vote, while the winner of the state at-large is awarded two votes. In both of these states, however, the vote has never been split between two candidates. It is interesting to note that the electors are not bound by law to cast their vote for the candidate who they represent. In 1988, one elector from West Virginia cast his presidential vote for Lloyd Bentsen, the Democratic vice-presidential candidate, while the rest of the West Virginia electors cast theirs for Michael Dukakis. In 2004 a Minnesota elector cast his vote for John Edwards.

After these votes are tabulated, a candidate must have more than half of the total electoral votes cast in order to be named president-elect. A lot of the individual state results are known months ahead of time. California for example, was known far ahead of time that it would go Democratic in the 2004 election. By the same token Texas was known to be voting to reelect George Bush. Neither of these states disappointed, with Kerry receiving 54% of the vote in California, but only 38% in Texas.

Other states are too close to call. In polls taken before the election, if the numbers are within the margin of error, there is no way to predict who will win each state. These are known as battleground states. In the last few election cycles, Florida, Ohio and Pennsylvania have been the battleground states that represented the most electoral votes, so they in turn were the biggest prizes in the electoral race. The general consensus before November 2, 2004, was that whoever won two of the aforementioned states would also win the White House.

The procedure for electing a president leads to some interesting campaign strategies. Because Kerry had no reason to believe he could win in Texas, and Bush had no reason to believe he could lose in Texas, the both Kerry and Bush stayed out of these states almost completely, as winning a state with 70% of the vote has the same net effect on the electoral college as winning the state by one vote. Instead both candidates focused their time and money on campaigning in the battleground states such as Pennsylvania and Florida. Analyzing and predicting the election also shifts back to a statewide basis. The exit polls conducted on Election Day in 2004 can help show who voted for whom and why.

In 2004, Edison Media Research and Mitofsky International conducted exit polls that the six major news organizations used. In these, 250 precincts were randomly chosen throughout the country. The pollsters then asked voters leaving the polling place a series of questions. The important question was “Whom did you vote for?” They then asked questions such as the voters political affiliation, religious affiliation, income level, and if they were for or against the war in Iraq. The interval between respondents was determined by the population of the precinct, with the goal of interviewing approximately 100 voters per precinct.

The data collected by exit pollsters has raised some questions, because according to the polls John Kerry should have won the popular vote by well over two percent, however, the official results indicated that George Bush won by the same margin. In eleven key battleground states, Kerry was predicted to win nine of them based on the exit poll data. Bush ended up winning six of these (Freeman, 2004). Even in the states that Kerry won, the margin of victory was much smaller than what one may have predicted. In Pennsylvania, Kerry was predicted to win by a margin of 8.7%, while the official vote count was only 2.2%. In Ohio, exit polls indicated a 4.2% Kerry victory, while Bush ended up carrying the decisive state by 2.5%.

There was also a question about the timing of the release of exit poll numbers. The poll results cited above were released by CNN on election night. These numbers were the actual counts taken in the poll. If one were to look up these exit poll results today, the numbers would be different. The numbers are adjusted based on the assumption that the official results are correct (Freeman, 2005).

By breaking it down to individual precincts, the results are even more disturbing. In January 2006, a team of statisticians looked at the forty nine precincts polled in Ohio, and compared the uncalibrated results with the official vote count. Twenty of those forty nine had a discrepancy in favor of Bush that was outside of the margin of error, including “precinct 27”, in which official results showed Bush to carry the precinct with 62% of the vote, while exit poll data, received from 100 respondants, suggested that Kerry would win with 67%, a difference of 29% (Kennedy, 2006). To illustrate the improbability of these numbers, one would set up a null hypothesis that K=.38. The alternative hypothesis is K>.38. The sample size in precinct 27 was 100, and the sample K was .67. as n gets large, the distribution of sample K will asymptotically approach a normal distribution, and we can standardize this distribution thusly:

Z=(.67-.38)/sqrt(.38x.62/100)=5.97. Plugging this into a standard normal calculator, a p-value of 1.15x10-9 is obtained. Assuming a valid sampling technique, if Bush actually received 62% of the votes, these exit poll results would be obtained one time out of almost a billion samples.

Kerry supporters look at this data as evidence of fraud in the election. The chances of achieving the exit poll results if the official results are entirely accurate are very slim. That coupled with the fact that all of the software used to count votes is proprietary, and there is no actual paper record of whom each voter selected, makes it appear that something is amiss. Bush supporters point to alleged flaws in the polling methodology or random error to explain the discrepancy. There is also the possibility that Bush voters would be more reluctant to talk to pollsters. This, however, is merely a hypothesis. If this were indeed true, one would expect that to be the case nationally. John Zogby, a renowned pollster went so far as to call this hypothesis “preposterous”. The data collected actually suggested that Kerry supporters were more reluctant to complete the survey than Bush supporters. In areas where Bush won a substantial amount of the vote, 56% of the voters targeted completed the survey. In Kerry strongholds, only 53% of the voters answered the pollsters’ questions (Kennedy, 2006). Based on this, it would appear that the votes in the 2004 election were not counted correctly.

Less than three weeks after the United States election, on November 22, 2004, there was a runoff election in Ukraine for president. Viktor Yanukovych, the prime minister, was running against Viktor Yushchenko, a former prime minister himself, having served from 1999 until 2001. According to an exit poll conducted by Ukraine’s Social Monitoring Center, Yushchenko enjoyed a lead of 49.5% to 45.9%. Other exit polls, some of which were commissioned by the Bush administration indicated a larger lead for Yushchenko, some by 11%. When all of the results were officially counted, however, Yanukovych emerged with a victory of just less than 3%.

This discrepancy between official results and exit poll results caused world leaders to claim that the election results were invalid, including the Bush administration that only days earlier declared the methodology of exit polling to be flawed when it was Bush’s reelection that was the subject of debate. John Tefft, the deputy assistant secretary of state for European and Eurasian affairs, testified before the House Committee on International Relations on December 19, 2004, and stated that exit polls are one of the best ways to expose large scale fraud in elections. On election night, the city council of Kiev refused to accept the official results, and urged the Ukrainian parliament to do likewise. After a lawsuit filed by Yushchenko supporters reached the Ukrainian supreme court, the election held on November 22 was declared invalid, and another election was scheduled for December 26, which Yushchenko went on to win by a margin of 8%. An appeal by Yanukovych was rejected on January 20, 2005, and three days later, Yushchenko was inaugurated as Ukraine’s third president.

In 1990, Carlos Salinas de Gortari was elected to the Mexican presidency. After his election there were widespread allegations of fraud regarding the election. Between 1990 and 1994 Mexico instituted several reforms to their electoral process. Despite the reforms, a 1993 poll by Market Opinion Research Institute showed that 47% of Mexicans expected corruption in the upcoming national election, while only 28% expected them to be clean (Carter Center, 1994). With such widespread doubt on the validity of elections, there must be a way to instill confidence in the Mexican electorate as to the accuracy and fairness about its elections.

In 1994, on the eve of the election, The Chamber of Radio an TV, a Mexican media company, hired Warren Mitofsky to conduct exit polls on the presidential election. These exit polls were accurate to within a tenth of a percent, as to what the official results were. This accuracy has made Mexicans more confident in their electoral process, and in 2000, Vicente Fox won the presidency. This marked the first time in the history of the Institution Revolutionary Party that their candidate did not win. Fox’s victory was also the first time in Mexico’s history that a president followed a precedent that Americans take for granted. Outgoing president Ernesto Zedillo peacefully ceded power to a president-elect from an opposition party.

For over two hundred years, the United States of America has been seen throughout the world as the ideal example of what Democracy should be. In the last several decades, more and more countries have abandoned their old systems of aristocratic rule, and have adopted democratically elected governments. In the case of Ukraine, for over seventy years, they were under the control of the Soviet Union, and for the citizens there, memories of a totalitarian rule are all too fresh. For these fledgling Democracies, the people who fought to bring that Democracy there appreciate it and have a firmer grasp on what the alternative to that is. As Americans, it is easy to forget the hardships endured, and we take it for granted that our elections will be free of any corruption. In Ukraine, they went to great lengths to ensure that the man inaugurated was the one that the people chose. The statistical methods used in the 2004 presidential election could easily be applied to the United States. In Mexico, because there was widespread belief that the elections were fixed, statistics were used to mitigate citizens’ fears that the election reforms would not eliminate corruption. In both of these cases, statistics provided a check on the elections, and in turn instilled more confidence that the popularly chosen man ascended to the presidency, which is critical in a Democracy. In the United States, however, we have chosen to ignore these issues which would be huge red flags in any other country, thinking that it could not happen here. We Americans need to take a long hard look at our electoral process and make changes to ensure that all votes are counted correctly.

References:

Green, J., “Do Polls Still Work?”, Atlantic Monthly, 298, 4, 33, 2006.

Konner, J, “The Case for Caution”, Public Opinion Quarterly, 67, 1, 5-18, 2003.

“The Third Time Around”, Current Digest of the Post Soviet Press, 56, 52, 1, 2005.

Lipper, T, “Votes of Confidence”, Newsweek, 140, 20, 10, 2002.

Scheufele, D, “Recent Articles in the Field of Public Opinion Research”, International Journal of Public Opinion Research, 14, 1, 115-118, 2002.

Sudman, S, “Do Exit Polls Influence Voting Behavior?”, Public Opinion Quarterly, 50, 3, 331-339, 1986.

Freeman, S, The Unexplained Exit Poll Discrepancy, 2004

Kennedy, R, “Was the 2004 Election Stolen?”, Rolling Stone, 2006

The Carter Center, “Elections in Mexico: Third Report”, 1994