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In
United States presidential election The election of the president and the vice president of the United States is an indirect election in which citizens of the United States who are registered to vote in one of the fifty U.S. states or in Washington, D.C., cast ballots not dir ...
s,
citizens Citizenship is a "relationship between an individual and a state to which the individual owes allegiance and in turn is entitled to its protection". Each state determines the conditions under which it will recognize persons as its citizens, and ...
who are registered to vote cast ballots for members of the Electoral College, who then cast electoral votes for
president President most commonly refers to: *President (corporate title) * President (education), a leader of a college or university * President (government title) President may also refer to: Automobiles * Nissan President, a 1966–2010 Japanese ...
and
vice president A vice president, also director in British English, is an officer in government or business who is below the president (chief executive officer) in rank. It can also refer to executive vice presidents, signifying that the vice president is on ...
. In order to be elected to office, a candidate must win an
absolute majority A supermajority, supra-majority, qualified majority, or special majority is a requirement for a proposal to gain a specified level of support which is greater than the threshold of more than one-half used for a simple majority. Supermajority r ...
of electoral votes. Since the Twenty-third Amendment gave citizens residing in the
District of Columbia ) , image_skyline = , image_caption = Clockwise from top left: the Washington Monument and Lincoln Memorial on the National Mall, United States Capitol, Logan Circle (Washington, D.C.), Logan Circle, Jefferson Memoria ...
the right to vote, this has meant winning at least 270 of the 538 electoral votes. Since the Twelfth Amendment in 1804, electors have cast separate votes for the president and vice president. Previously, each elector cast two votes for president, and the winner and runner-up became president and vice president, respectively.


Definition of the margin


Informal definition

The margin of victory in a
U.S. presidential election The election of the president and the vice president of the United States is an indirect election in which citizens of the United States who are registered to vote in one of the fifty U.S. states or in Washington, D.C., cast ballots not di ...
, with the exception below, is the difference between the number of Electoral College votes garnered by the candidate with an
absolute majority A supermajority, supra-majority, qualified majority, or special majority is a requirement for a proposal to gain a specified level of support which is greater than the threshold of more than one-half used for a simple majority. Supermajority r ...
of electoral votes (since 1964, it has been 270 out of 538) and the number received by the second place candidate (currently in the range of 2 to 538, a margin of one vote is only possible with an odd total number of electors or a faithless elector). The exception occurs if no candidate receives an absolute majority of votes in the Electoral College. In such a situation, the
House of Representatives House of Representatives is the name of legislative bodies in many countries and sub-national entitles. In many countries, the House of Representatives is the lower house of a bicameral legislature, with the corresponding upper house often c ...
holds a contingent presidential election. As prescribed by the
Constitution A constitution is the aggregate of fundamental principles or established precedents that constitute the legal basis of a polity, organisation or other type of entity and commonly determine how that entity is to be governed. When these pr ...
, the House chooses from among the three candidates who received the most electoral votes. (Thus, the winner could be a candidate who initially finished in third-place with one electoral vote.) Each state delegation votes ''en bloc'', with each state having a single vote. A candidate is required to receive an absolute majority of state delegation votes (currently 26 votes) in order for that candidate to become the president-elect. Because the Electoral College has grown in size, the results are normalized to compensate. For example, take two elections,
1848 1848 is historically famous for the wave of revolutions, a series of widespread struggles for more liberal governments, which broke out from Brazil to Hungary; although most failed in their immediate aims, they significantly altered the polit ...
and
1968 The year was highlighted by protests and other unrests that occurred worldwide. Events January–February * January 5 – " Prague Spring": Alexander Dubček is chosen as leader of the Communist Party of Czechoslovakia. * J ...
. In the election of 1968,
Richard Nixon Richard Milhous Nixon (January 9, 1913April 22, 1994) was the 37th president of the United States, serving from 1969 to 1974. A member of the Republican Party, he previously served as a representative and senator from California and was ...
won with a majority of 32 votes. At first glance, the election of 1848 appears closer, because
Zachary Taylor Zachary Taylor (November 24, 1784 – July 9, 1850) was an American military leader who served as the 12th president of the United States from 1849 until his death in 1850. Taylor was a career officer in the United States Army, rising to th ...
won with a majority of only 18 votes, however, Nixon could have received as many as 269 votes above a majority (if he had won unanimously), while Taylor could only have received 145 votes above the majority. Thus, the two elections must be normalized to each other to compare them: Nixon's margin of victory is calculated by dividing 32 by 269 to get 0.119. The same is done with Taylor by dividing 18 by 145, to get 0.124. Nixon's election was actually closer, because a smaller fraction of the electors separated Nixon from facing a contingent election in the House. While the above explanation applies to modern elections, initially the process was different. Prior to the ratification of the Twelfth Amendment in 1804, the winner of the presidential election was whoever received both a majority of electors to vote for them, and who received the most votes, because each elector cast two presidential votes. Thus, if two candidates had above 50% of the electors, the margin of victory is the victorious candidate's margin over the other candidate who had above 50% of the electors. Of the four elections prior to the 12th Amendment,
1792 Events January–March * January 9 – The Treaty of Jassy ends the Russian Empire's war with the Ottoman Empire over Crimea. * February 18 – Thomas Holcroft produces the comedy '' The Road to Ruin'' in London. * February ...
and 1800 both involved two candidates receiving above 50% of the electoral votes.


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. The
Constitution A constitution is the aggregate of fundamental principles or established precedents that constitute the legal basis of a polity, organisation or other type of entity and commonly determine how that entity is to be governed. When these pr ...
provides that if the candidate with the most votes does not receive a simple majority of the electors voting, the
House of Representatives House of Representatives is the name of legislative bodies in many countries and sub-national entitles. In many countries, the House of Representatives is the lower house of a bicameral legislature, with the corresponding upper house often c ...
chooses the president. 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 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: : \mbox = \begin0; & w \le \frac \\ w - \max\; & w > \frac \end 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: : \mbox = \begin0; & w \le \frac \\ \frac; & w > \frac \end


Table of election results

Under the procedure provided in Article II, Section 1, Clause 3 of the Constitution, by which the Electoral College functioned during the first four presidential elections (prior to ratification of the Twelfth Amendment), each elector cast two votes, one for president and one for vice president, but did not distinguish between them. The table's "runner-up" column shows the number of electoral votes for the candidate receiving the second highest number of combined electoral votes, and thus was elected vice president, for each of these elections except for the 1800 election, which ended in a tie between two candidates – the presidential and vice presidential candidates of the same party. The value in the "runner-up" column for 1800 is the number of electoral votes received by the presidential candidate of the other major political party (even though the two winning candidates each received more electoral votes than he did). The number in parentheses in the "Rank" column is the rank that would have been assigned to this election under the rules of the 12th Amendment. In the following table, the election of 1824 is ranked ''closer'' than the election of 1800 because the 1800 election resulted in a tie between the same party's candidates for president and vice president (as presidential and vice presidential electoral votes were not distinguished), while the election of 1824 resulted in the contingent election in the
House of Representatives House of Representatives is the name of legislative bodies in many countries and sub-national entitles. In many countries, the House of Representatives is the lower house of a bicameral legislature, with the corresponding upper house often c ...
selecting the candidate who had won the second highest number of electoral votes (out of the top three) since no candidate got a majority, 41 presidents have won a large total number of electoral votes, Franklin D. Roosevelt received the most total of electoral votes received by and candidate who was elected to the office of president due to him being the only on to serve more than 2 terms (1,876) and
John Adams John Adams (October 30, 1735 – July 4, 1826) was an American statesman, attorney, diplomat, writer, and Founding Fathers of the United States, Founding Father who served as the second president of the United States from 1797 to 1801. Befor ...
received the smallest (136).


See also

*
List of United States presidential elections by popular vote margin In a United States presidential election, the popular vote is the total number or the percentage of votes cast for a candidate by voters in the 50 states and Washington, D.C.; the candidate who gains the most votes nationwide is said to have ...
*
United States presidential elections in which the winner lost the popular vote There have been five United States presidential elections in which the successful presidential candidate did not receive a plurality of the popular vote, including the 1824 election, which was the first U.S. presidential election where the pop ...
*
National Popular Vote Interstate Compact MD, NJ, IL, HI, WA, MA, DC, VT, CA, RI, NY, CT, CO, DE, NM, OR MI, PA, TX The National Popular Vote Interstate Compact (NPVIC) is a proposed interstate compact among a group of U.S. states and the District of Columbia to award a ...


Notes


References


External links


How close were U.S. Presidential Elections?
- Michael Sheppard, Massachusetts Institute of Technology {{Lists of US Presidents and Vice Presidents United States Electoral College United States presidential elections by Electoral College margin