Who Won the 2000 U.S. Presidential Election?

Eric Schulman
Alexandria, Virginia

Abstract
In this paper we analyze the results of the 2000 United States
presidential election. We determined that Republican candidate
George W. Bush won the election at the 45.5% confidence level.
Democratic candidate Al Gore won the election at the 36.6%
confidence level. Green Party candidate Ralph Nader won the
election at the 6.40E-301 % confidence level. We were unable
to calculate the confidence level of Reform Party candidate Pat
Buchanan's victory.

1. Introduction
    On November 7, 2000, Americans held an election to determine who would be the next President of the United States. The four biggest vote getters were Democratic candidate Al Gore with 50.16 million votes, Republican candidate George W. Bush  with 49.82 million votes, Green Party candidate Ralph Nader with 2.78 million votes, and Reform Party candidate Pat Buchanan with 0.45 million votes. If Americans had chosen their President based on who got the most votes nationwide, Al Gore would have been elected.
    Instead, Americans choose their President based on who wins the electoral college. The winner of the popular vote in each state is awarded that state's electoral votes, which is equal to the number of Members of Congress that state has. The number of electoral votes currently ranges from 3 for low-population states like Wyoming to 54 for the most populous state, California. There are a total of 538 electoral votes, and a candidate must win a majority (270) in order to be declared President of the United States. If no candidate wins a majority of electoral votes, the winner is decided by the U.S. House of Representatives.
    In the 2000 election, the results were so inconclusive--in particular for the state of Florida--that the winner of the election was not finalized until December 13, 2000, when Al Gore conceded to George W. Bush. Even then, many Americans were not confident that this result was correct. In an attempt to boost the confidence of the electorate, we set out to analyze the election data to determine who really won.

2. Methods and Results
    We used six different methods to determine the winner based on the number of votes cast for the four major candidates in all fifty states plus the District of Columbia.
    The first method (listed as "current" in the table below) is that used today in the United States, where the winner of the popular vote in a state receives all the state's electoral votes. George W. Bush wins using this method with 271 electoral votes (1 more than necessary).
    In the next method ("popular"),  the 538 electoral votes are distributed according to how many votes each candidate received nationwide. No one achieved a majority (270 electoral votes) using this method.
    Many pundits expressed the opinion that votes for Ralph Nader resulted in Al Gore losing the election. To test this theory, we gave all of Nader's votes to Gore and all of Buchanan's votes to Bush ("two-way"). This resulted in Gore taking Florida and New Hampshire from Bush, giving Gore victory with a total of 296 electoral votes.
    A few pundits expressed the opinion that Pat Buchanan harmed George W. Bush's election chances. To test this theory, we gave all of Buchanan's votes to Bush but let Nader keep his votes ("three-way"). This resulted in Bush taking Iowa, New Mexico, Oregon, and Wisconsin from Gore, giving Bush a total of 301 electoral votes.
    Some pundits believe that the winner-take-all method of assigning a state's electoral votes is needlessly destabilizing. To test this, we apportioned a fraction of each state's electoral votes to each candidate, depending on the percentage of the popular vote each received ("fractional"). We then rounded each candidate's nationwide results to the nearest whole electoral vote. None of the candidates received a majority of the electoral votes using this method.
    The final method assigned two electoral votes to the winner of the popular vote in each state, and apportioned the other (whole) electoral votes to each of the candidates depending on their percentage of the vote in that state ("proportional"). Using this method, George W. Bush obtained 272 electoral votes, two more than necessary for victory.
 

Method
Gore
Bush
Nader
Buchanan
Winner
Millions of votes cast
50.16
49.82
2.78
0.45
Gore
Current
267
271
0
0
Bush
Popular
262
260
14
2
 
Two-Way
296
242
0
0
Gore
Three-Way
237
301
0
0
Bush
Fractional
260
261
15
2
 
Proportional
259
272
7
0
Bush
Mean±Sigma
263.5±19.0
267.8±19.5
6.0±7.1
0.7±1.0
 
Deviation (sigma)
-0.34
-0.11
-37.18
-269.30
 
Confidence
36.6%
45.5%
6.40E-301 %
*
 

    Since the six methods produced inconsistent results, we were forced to average the data in order to determine the real winner. This averaging gave 267.8±19.5 electoral votes to George W. Bush, 263.5±19.5 electoral votes to Al Gore, 6.0±7.1 electoral votes to Ralph Nader, and 0.7±1.0 electoral votes to Pat Buchanan. The deviation from the required 270 electoral votes was -0.11 sigma for Bush, -0.34 sigma for Gore, -37.18 sigma for Nader, and -269.30 sigma for Buchanan. We solved the normal error integral (also known as the error function) numerically in order to determine the confidence level that each of the candidates achieved the required 270 electoral votes. We lacked the computing resources to calculate the error function for Buchanan's -269.30 sigma deviation.

3. Conclusions
    In this paper we analyzed the results of the 2000 United States presidential election. Republican candidate George W. Bush won the election at the 45.5% confidence level. Democratic candidate Al Gore won the election at the 36.6% confidence level. Green Party candidate Ralph Nader won the election at the 6.40E-301 % confidence level. We were unable to calculate the confidence level of Reform Party candidate Pat Buchanan's victory.