If there was more than one individual who received a vote from a majority of the electors, the House of Representatives would choose from amongst the two candidates. If no individual had a majority, then the House of Representatives would choose from the five individuals with the greatest number of electoral votes.
The choosing of the Vice President was a simpler process. Whichever candidate received the greatest number of votes, except for the one elected President, became Vice President. The Vice President, unlike the President, did not require the votes of a majority of electors. In the event of a tie for second place between multiple candidates, the Senate chose one of them to be Vice President. Each Senator cast one vote. It was not specified in the Constitution whether the sitting Vice President could cast a tie-breaking vote for Vice President under the original formula.
The 1800 election exposed a defect in the original formula in that if each member of the electoral college followed party tickets, there would be a tie between the two candidates from the most popular ticket. It also showed that the House of Representatives could end up taking multiple ballots before choosing a President.
In addition, it was becoming increasingly apparent that a situation in which the Vice President had been a defeated electoral opponent of the President impeded the ability of the two to effectively work together, and could provide motivation, at least in theory, for a coup d'état (since the Vice President would succeed to the office of the President upon the removal or death of the President). The Twelfth Amendment, in having the President and Vice President elected as a ticket eliminated this possibility.
The Twelfth Amendment, which applied to elections beginning in 1804, changed the process whereby the Electoral College, and if necessary the House of Representatives, chooses the President. It did not change the composition of the Electoral College.
Under the Twelfth Amendment, each elector must cast distinct votes for President and Vice President, instead of two votes for President. No elector may cast votes for Presidential and Vice Presidential candidates who both inhabit the same state as that elector (Habitation Clause). It is, however, possible for an elector to cast a vote for one candidate that is from the same state as that elector.
The Twelfth Amendment explicitly precluded those constitutionally ineligible to be President from being Vice President.
A majority of electoral votes is still required for one to be elected President or Vice President. When nobody has a majority, the House of Representatives, voting by states and with the same quorum requirements as under Article II, chooses a President. The Twelfth Amendment allows the House to consider no more than three candidates, compared to five under the original formula.
The Senate, similarly, may choose the Vice President if no candidate has received a majority of electoral votes. Its choice is limited to those with the "two highest numbers" of electoral votes. If multiple individuals are tied for second place, the Senate may consider all of them, in addition to the individual with the greatest number of votes. The Twelfth Amendment introduced a quorum requirement of two-thirds for the conduct of balloting. Furthermore, the Twelfth Amendment provides that the votes of "a majority of the whole number" of Senators are required to arrive at a choice.
In order to prevent deadlocks from keeping the nation leaderless, the Twelfth Amendment provided that if the House could not choose a President before March 4 (at that time the first day of a Presidential term), the individual elected Vice President would act as President, "as in the case of the death or other constitutional disability of the President." The Twelfth Amendment did not state for how long the Vice President would act as President, or if the House could still choose a President after March 4. Section 3 of the Twentieth Amendment replaced that provision of the Twelfth Amendment by changing the date for the commencement of Presidential terms to January 20 and permitting the Congress to direct, through legislation, "who shall then act as President" if there's no President-elect or Vice President-elect. It also clarified that if there's no President-elect on January 20, whoever acts as President does so until a person is "qualified" to occupy the Presidency.
Every Presidential election since the election of 1804 has been conducted under the Twelfth Amendment. Only once since that time has the House of Representatives chosen the President. In 1824, Andrew Jackson received 99 electoral votes, John Quincy Adams (son of John Adams) 84, William H. Crawford 41, and Henry Clay 37. All of the candidates were members of the Democratic-Republican Party (though there were significant political differences among them), and each had fallen short of the 131 votes necessary to win. In the less contested election for vice president, John C. Calhoun received 182 votes and was elected outright.
Since the House could only consider the top three candidates, Clay could not become President. Crawford's poor health following a stroke made his election by the House unlikely. Andrew Jackson fully expected that the House would vote for him, as he had won a plurality of the popular and electoral vote. Instead, the House elected Adams on the first ballot with 13 states, followed by Jackson with seven and Crawford with three. Clay had endorsed Adams for the Presidency; the endorsement carried additional weight because Clay was the Speaker of the House. When Adams later appointed Clay his Secretary of State, many — particularly Jackson and his supporters — accused the pair of making a "Corrupt Bargain." Others understood this to be a normal alliance in politics, as when presidential candidates name their running mates in order to strengthen their positions. Moreover, some historians have argued that Clay was closer ideologically to Adams than Jackson and that it was natural for Clay supporters to turn to Adams.
In 1836, the Whig Party nominated different candidates in different regions in the hopes of splintering the electoral vote and denying Martin Van Buren, the Democratic candidate, a majority in the Electoral College, thereby throwing the election into the Whig-controlled House. This strategy failed, however, with Van Buren winning majorities of both the popular and electoral vote, and there have been no further attempts by a major U.S. party to adopt the strategy of running regional candidates for national office since that time. In that same election no candidate for Vice President secured a majority in the electoral college as Democratic Vice Presidential nominee Richard Mentor Johnson did not receive the electoral votes of Democratic electors from Virginia, because of his relationship with a former slave. As a result Johnson received 147 electoral votes, one vote short of a majority; to be followed by Francis Granger with 77, John Tyler with 47 and William Smith with 23. This caused the Senate to choose whether Johnson or Granger would be the new Vice President. Johnson won with 33 votes, with Granger receiving 17.
In modern elections, a running mate is often selected in order to appeal to a different set of voters. The issue arose during the 2000 presidential election contested by George W. Bush (alongside running-mate Dick Cheney) and Al Gore (alongside Joe Lieberman). It was alleged that Cheney and Bush were both inhabitants of Texas, and that the Texas electors therefore violated the Twelfth Amendment in casting their ballots for both. Bush's residency was unquestioned, as he was Governor of Texas at the time. Cheney and his wife had moved to Dallas five years earlier when he assumed the role of chief executive at Halliburton. Cheney grew up in Wyoming and had represented it in Congress. A few months before the election, he switched his voter registration and driver's license to Wyoming and put his home in Dallas up for sale. Three Texas voters challenged the election in a federal court in Dallas and then appealed the decision to the Fifth Circuit Court of Appeals where it was dismissed.
In addition, the following states rejected the amendment: