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The table below is a '''list of United States presidential elections ordered by margin of victory''' in the '''[[United States Electoral College|Electoral College]] vote'''.
 
== Definition of the margin ==
 
===Informal definition===
In modern presidential elections, the margin of victory does '''not''' depend on the margin between the winner and his or her main rival.  If the “winner” doesn't get a majority of the electoral vote, the election is thrown into the House of Representatives where the candidate's rival may very well be chosen.  On the other hand, if a candidate does get a majority, he or she is guaranteed to have more votes than his or her rivals.  Thus, the margin of victory should be the candidate's margin of majority; that is, it should be the margin of votes above 50%.
 
Because the [[United States Electoral College|Electoral College]] has grown in size, the results are [[normalization constant|normalized]] to compensate. For example, take two elections, [[United States presidential election, 1848|1848]] and [[United States presidential election, 1968|1968]]. In the election of 1968 [[Richard Nixon]] got a majority by 32 votes. At first glance, the election of 1848 appears closer, because [[Zachary Taylor]] got a majority by only 18 votes.  But Nixon could have gotten as many as 269 votes above a majority (if he had won unanimously), while Taylor could only have gotten 145 votes above a majority.  Thus, we normalize the two elections to compare them.  We calculate Nixon's margin of victory by dividing the 32 by 269 to get 0.119.  We do the same with Taylor, dividing 18 by 145, to get 0.124.  And we find that Nixon's election was actually closer because a smaller fraction of the electors separated Nixon from a contingent election (For fair representation, in the 1972 election, Nixon was re-elected with a ratio of 0.926*, a landslide).
 
*On the basis of tables lower on the page, this ratio is 0.933, but I calculated it on the basis of these statistics (see http://en.wikipedia.org/wiki/United_States_presidential_election,_1972). Indeed, it is a lower ratio, but it certainly is necessary for fair representation.
 
Now, there's one more wrinkle.  The foregoing explanation applies to modern elections.  However, prior to the passage of the [[Twelfth Amendment to the United States Constitution|12th Amendment]], the winner of the presidential election was the person who got a majority of electors to vote for him '''and''' who got the most number of votes, because each elector cast two presidential votes.  Thus, for elections prior to 1804, if two candidates got above 50% of the electors, the margin of victory is the victorious candidate's margin over the other candidate who got above 50% of the electors.  As it happens, of the four elections prior to the 12th Amendment, two involved two candidates getting above 50% of the electors:  [[United States presidential election, 1792|1792]] and [[United States presidential election, 1800|1800]].
 
===Mathematical definition===
The margin of victory in the election is calculated as follows:
 
Let ''c'' be the total number of electors voting in the election.  Let ''w'' be the number of electoral votes cast for the candidate with the most electoral votes, and let ''r'' be the number of votes for the runner-up.
 
According to the [[United States Constitution|Constitution]], the electoral vote called a "draw" and sent into the [[United States House of Representatives|House of Representatives]] if the candidate with the most votes does not get a [[majority|simple majority]] of the electors voting. So, the margin of victory is the number of electoral votes over both the runner-up and half the electoral votes cast.  For elections after the passage of the [[Twelfth Amendment to the United States Constitution|12th Amendment]], the runner-up will always have less than half of the electoral votes cast, so the absolute margin of victory will be the difference of the winner's electoral votes and half the electoral votes cast.  To express this in mathematical formulae:
 
: <math>\mbox{absolute margin of victory} = \begin{cases}0; & w \le \frac{c}{2} \\ w - \max\{r, \frac{c}{2}\}; & w > \frac{c}{2} \end{cases}</math>
 
The minimum possible value for the margin of victory is clearly zero.  The maximum possible value of the margin of victory occurs in the case in which each elector casts a vote for the winning candidate and the runner-up gets no more than half of the vote.  In this case, the maximum margin of victory is ''c''/2.  In order to meaningfully compare election to election, we need that maximum margin to be constant from election to election.  Thus, we divide the absolute margin of victory by ''c''/2 to get a normalized margin of victory that ranges from 0 to 1:
 
: <math>\mbox{normalized margin of victory} = \begin{cases}0; & w \le \frac{c}{2} \\ \frac{w - \max\{r, \frac{c}{2}\}}{\frac{c}{2}}; & w > \frac{c}{2} \end{cases}</math>
 
==Table of election results==
 
Note that in the following table, the [[United States presidential election, 1824|election of 1824]] is ranked closer than the [[United States presidential election, 1800|election of 1800]] because the election of 1800 resulted in a two-way draw, while the election of 1824 resulted in a three-way draw.
 
Also note that the elections of 1789, 1792, 1796, and 1800 took place before the 12th Amendment and thus each elector had two votes (but had to vote for two separate people). For example, George Washington received the vote of every elector, but the second vote of each elector was split amongst other candidates.  Thus Washington is accounted to have received 100% of the possible electoral votes.
 
{| class="wikitable sortable"
! Rank
! Year
! Winner
! # of<br />Electors<br />(''c'')
! Votes cast<br />for winner<br />(''w'')
! Votes cast<br />for runner-up<br />(''r'')
! Normalized<br />margin of<br />victory
! Percentage
|-
| 1.
| [[United States presidential election, 1824|1824]]
| draw: [[Andrew Jackson]], [[John Quincy Adams]], [[William H. Crawford|William Crawford]] {{ref label|1824|a|a}}
| 261
| 84
| 99
| 0.000
| 32.18%
|-
| 2.
| [[United States presidential election, 1800|1800]]
| draw:  [[Thomas Jefferson]], [[Aaron Burr]] {{ref label|1800|b|b}}
| 138
| 73
| 73
| 0.000
| 52.90%
|-
| 3.
| [[United States presidential election, 1876|1876]]
| [[Rutherford B. Hayes]]
| 369
| 185
| 184
| 0.003
| 50.14%
|-
| 4.
| [[United States presidential election, 2000|2000]]
| [[George W. Bush]]
| 538
| 271
| 266
| 0.009
| 50.37%
|-
| 5.
| [[United States presidential election, 1796|1796]]
| [[John Adams]]
| 138
| 71
| 68
| 0.029
| 51.45%
|-
| 6.
| [[United States presidential election, 1916|1916]]
| [[Woodrow Wilson]]
| 531
| 277
| 254
| 0.043
| 52.17%
|-
| 7.
| [[United States presidential election, 2004|2004]]
| [[George W. Bush]]
| 538
| 286
| 251
| 0.063
| 53.16%
|-
| 8.
| [[United States presidential election, 1884|1884]]
| [[Grover Cleveland]]
| 401
| 219
| 182
| 0.092
| 54.61%
|-
| 9.
| [[United States presidential election, 1976|1976]]
| [[Jimmy Carter]]
| 538
| 297
| 240
| 0.104
| 55.20%
|-
| 10.
| [[United States presidential election, 1968|1968]]
| [[Richard Nixon]]
| 538
| 301
| 191
| 0.119
| 55.95%
|-
| 11.
| [[United States presidential election, 1848|1848]]
| [[Zachary Taylor]]
| 290
| 163
| 127
| 0.124
| 56.21%
|-
| 12.
| [[United States presidential election, 1960|1960]]
| [[John F. Kennedy]]
| 537
| 303
| 219
| 0.128
| 56.42%
|-
| 13.
| [[United States presidential election, 1948|1948]]
| [[Harry S. Truman]]
| 531
| 303
| 189
| 0.141
| 57.06%
|-
| 14.
| [[United States presidential election, 1836|1836]]
| [[Martin Van Buren]]
| 294
| 170
| 73
| 0.156
| 57.82%
|-
| 15.
| [[United States presidential election, 1880|1880]]
| [[James A. Garfield]]
| 369
| 214
| 155
| 0.160
| 57.99%
|-
| 16.
| [[United States presidential election, 1888|1888]]
| [[Benjamin Harrison]]
| 401
| 233
| 168
| 0.162
| 58.10%
|-
| 17.
| [[United States presidential election, 1856|1856]]
| [[James Buchanan]]
| 296
| 174
| 114
| 0.176
| 58.78%
|-
| 18.
| [[United States presidential election, 1812|1812]]
| [[James Madison]]
| 217
| 128
| 89
| 0.180
| 58.99%
|-
| 19.
| [[United States presidential election, 1860|1860]]
| [[Abraham Lincoln]]
| 303
| 180
| 72
| 0.188
| 59.41%
|-
| 20.
| [[United States presidential election, 1896|1896]]
| [[William McKinley]]
| 447
| 271
| 176
| 0.213
| 60.63%
|-
| 21.
| [[United States presidential election, 2012|2012]]
| [[Barack Obama]]
| 538
| 332
| 206
| 0.234
| 61.71%
|-
| 22.
| [[United States presidential election, 1844|1844]]
| [[James K. Polk]]
| 275
| 170
| 105
| 0.236
| 61.82%
|-
| 23.
| [[United States presidential election, 1892|1892]]
| [[Grover Cleveland]]
| 444
| 277
| 145
| 0.248
| 62.39%
|-
| 24.
| [[United States presidential election, 1900|1900]]
| [[William McKinley]]
| 447
| 292
| 155
| 0.306
| 65.32%
|-
| 25.
| [[United States presidential election, 1908|1908]]
| [[William Howard Taft]]
| 483
| 321
| 162
| 0.329
| 66.46%
|-
| 26.
| [[United States presidential election, 2008|2008]]
| [[Barack Obama]]
| 538
| 365
| 173
| 0.357
| 67.84%
|-
| 27.
| [[United States presidential election, 1828|1828]]
| [[Andrew Jackson]]
| 261
| 178
| 83
| 0.364
| 68.20%
|-
| 28.
| [[United States presidential election, 1992|1992]]
| [[Bill Clinton]]
| 538
| 370
| 168
| 0.375
| 68.77%
|-
| 29.
| [[United States presidential election, 1808|1808]]
| [[James Madison]]
| 175
| 122
| 47
| 0.394
| 69.71%
|-
| 30.
| [[United States presidential election, 1996|1996]]
| [[Bill Clinton]]
| 538
| 379
| 159
| 0.409
| 70.45%
|-
| 31.
| [[United States presidential election, 1904|1904]]
| [[Theodore Roosevelt]]
| 476
| 336
| 140
| 0.412
| 70.59%
|-
| 32.
| [[United States presidential election, 1924|1924]]
| [[Calvin Coolidge]]
| 531
| 382
| 136
| 0.439
| 71.94%
|-
| 33.
| [[United States presidential election, 1868|1868]]
| [[Ulysses S. Grant]]
| 294
| 214
| 80
| 0.456
| 72.79%
|-
| 34.
| [[United States presidential election, 1920|1920]]
| [[Warren G. Harding]]
| 531
| 404
| 127
| 0.522
| 76.08%
|-
| 35.
| [[United States presidential election, 1832|1832]]
| [[Andrew Jackson]]
| 286
| 219
| 49
| 0.531
| 76.57%
|-
| 36.
| [[United States presidential election, 1988|1988]]
| [[George H. W. Bush]]
| 538
| 426
| 111
| 0.584
| 79.18%
|-
| 37.
| [[United States presidential election, 1840|1840]]
| [[William Henry Harrison]]
| 294
| 234
| 60
| 0.592
| 79.59%
|-
| 38.
| [[United States presidential election, 1944|1944]]
| [[Franklin D. Roosevelt]]
| 531
| 432
| 99
| 0.627
| 81.36%
|-
| 39.
| [[United States presidential election, 1912|1912]]
| [[Woodrow Wilson]]
| 531
| 435
| 88
| 0.638
| 81.92%
|-
| 40.
| [[United States presidential election, 1872|1872]]
| [[Ulysses S. Grant]]{{ref label|1820-1872|e|e}}
| 352
| 286
| 42
| 0.639
| 81.95%
|-
| 41.
| [[United States presidential election, 1952|1952]]
| [[Dwight D. Eisenhower]]
| 531
| 442
| 89
| 0.665
| 83.24%
|-
| 42.
| [[United States presidential election, 1928|1928]]
| [[Herbert Hoover]]
| 531
| 444
| 87
| 0.672
| 83.62%
|-
| 43.
| [[United States presidential election, 1816|1816]]
| [[James Monroe]]
| 217
| 183
| 34
| 0.687
| 84.33%
|-
| 44.
| [[United States presidential election, 1940|1940]]
| [[Franklin D. Roosevelt]]
| 531
| 449
| 82
| 0.691
| 84.56%
|-
| 45.
| [[United States presidential election, 1852|1852]]
| [[Franklin Pierce]]
| 296
| 254
| 42
| 0.716
| 85.81%
|-
| 46.
| [[United States presidential election, 1956|1956]]
| [[Dwight D. Eisenhower]]
| 531
| 457
| 73
| 0.721
| 86.06%
|-
| 47.
| [[United States presidential election, 1932|1932]]
| [[Franklin D. Roosevelt]]
| 531
| 472
| 59
| 0.778
| 88.89%
|-
| 48.
| [[United States presidential election, 1964|1964]]
| [[Lyndon B. Johnson]]
| 538
| 486
| 52
| 0.807
| 90.33%
|-
| 49.
| [[United States presidential election, 1980|1980]]
| [[Ronald Reagan]]
| 538
| 489
| 49
| 0.818
| 90.89%
|-
| 50.
| [[United States presidential election, 1864|1864]]
| [[Abraham Lincoln]]
| 233
| 212
| 21
| 0.820
| 90.99%
|-
| 51.
| [[United States presidential election, 1792|1792]]
| [[George Washington]]
| 132
| 132
| 77
| 0.833*
| 100%
|-
| 52.
| [[United States presidential election, 1804|1804]]
| [[Thomas Jefferson]]
| 176
| 162
| 14
| 0.841
| 92.05%
|-
| 53.
| [[United States presidential election, 1972|1972]]
| [[Richard Nixon]]
| 538
| 520
| 17
| 0.933
| 96.65%
|-
| 54.
| [[United States presidential election, 1984|1984]]
| [[Ronald Reagan]]
| 538
| 525
| 13
| 0.952
| 97.58%
|-
| 55.
| [[United States presidential election, 1936|1936]]
| [[Franklin D. Roosevelt]]
| 531
| 523
| 8
| 0.970
| 98.49%
|-
| 56.
| [[United States presidential election, 1820|1820]]
| [[James Monroe]] {{ref label|1820|c|c}}{{ref label|1820-1872|e|e}}
| 235
| 231
| 1
| 0.991
| 99.57%
|-
| 57.
| [[United States presidential election, 1789|1789]]
| [[George Washington]] {{ref label|1789|d|d}}
| 69
| 69
| 34
| 1.000*
| 100%
|}
 
<nowiki>*</nowiki>''Unanimous; George Washington received the vote of every elector, but the 2nd vote of each elector was split among other candidates. Thus Washington is accounted to have received 100% of the possible electoral votes.''**
 
**contradiction. see http://en.wikipedia.org/wiki/United_States_presidential_election,_1789
 
*{{note label|1824|a|a}} None of the presidential candidates in 1824 received a majority of the electoral vote, so the presidential election was decided by the House of Representatives, who selected Adams.
*{{note label|1800|b|b}} Under the original procedure for the Electoral College, each elector had two votes and voted for two individuals. The candidate receiving the majority of votes became president and the candidate with the second highest number of votes became vice-president. While Jefferson had more electoral votes than his principal opponent, [[John Adams]], he was tied with his own vice-presidential running mate, [[Aaron Burr]], in electoral votes. Because of the tie, the 1800 presidential election was decided by the House of Representatives, who selected Jefferson as president. Subsequently the [[Twelfth Amendment to the United States Constitution]] was enacted in order to provide for the president and vice-president to be elected as a single [[Ticket (election)|ticket]].
*{{note label|1820|c|c}} There was a dispute as to whether [[Missouri]]'s electoral votes in 1820 were valid, due to the timing of its assumption of statehood. The figures listed include those votes.
*{{note label|1789|d|d}} Only ten of the thirteen states cast electoral votes in the first ever presidential election. [[North Carolina]] and [[Rhode Island]] were ineligible to participate since they had not yet ratified the [[United States Constitution]]. [[New York]] failed to appoint its electors before the appropriate deadline because of a deadlock in its state legislature.
*{{note label|1820-1872|e|e}} Votes which were not counted don't change the majority needed to win. Although there are only 232 counted votes in 1820, winner needed 118 (majority of 235) votes to win, same in 1872: By resolution of the House, 3 votes cast for Greeley were not counted (makes 349 counted votes) but 177 votes are still needed to win (majority of 352).
 
==See also==
* [[List of United States presidential elections by popular vote margin]]
 
== References ==
* [http://web.archive.org/web/20120825102042/http://www.mit.edu/~mi22295/elections.html How close were U.S. Presidential Elections?] - Michael Sheppard, Massachusetts Institute of Technology
{{Unreferenced|date=December 2006}}
 
{{U.S. presidential elections}}
{{Lists of US Presidents and Vice Presidents}}
 
{{DEFAULTSORT:List Of United States Presidential Elections By Electoral College Margin}}
<!--Categories-->
[[Category:Electoral College (United States)]]
[[Category:Lists of elections in the United States|United States presidential elections by Electoral College margin]]

Latest revision as of 02:10, 1 May 2014

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