The presidential election of 1800, the fourth presidential election in United States' history, was one of the first to show the flaws of the U.S. Electoral College system. The election was between Thomas Jefferson and John Adams, and as such, was something of a redux of the presidential election of 1796, which had been decided in John Adams' favor. But according to the U.S. Electoral College system of the time, in the 1796 election Thomas Jefferson had become Vice President. This was because the U.S. Electoral College system at the time involved electors voting for only Presidential candidates, but still receiving two votes. The candidate with absolute majority would become President and the candidate with the next highest amount of electoral votes would become Vice President.
Thus, the 1796 presidential election had resulted in a President and a Vice President who were political opponents from two different parties. This problem of determining the President and Vice President through the U.S. Electoral College would characterize the presidential election of 1800.
Though John Adams was soundly defeated, Thomas Jefferson and Aaron Burr actually received the same number of votes in the U.S. Electoral College. This meant that neither could be definitively called the victor. Under Article 2 of the Constitution, the House of Representatives would cast a vote to decide the election if there was a tie in the voting of the U.S. Electoral College. This meant that the House of Representatives now had the power to determine who was President, which changed the race significantly.The political parties involved in the presidential election of 1800 were the Federalists, of whom John Adams was a major representative, and the Democratic-Republicans. Both Jefferson and Burr belonged to the Democratic-Republicans. Though elections had been held to change Representatives and Senators in Congress, the lame duck Congress at the time of the presidential election was primarily Federalist. As such, the party which was opposed to both of the potential candidates would get to decide which of those two candidates won the presidential election thanks to the tie in the U.S. Electoral College.
Most of the Federalists would have preferred to vote for Aaron Burr, as Thomas Jefferson had been the opponent of the Federalist Party since that party's inception. This was especially strange given that the Democratic-Republicans had clearly intended for Jefferson to be the presidential candidate, while he should have been the vice-presidential candidate. Thanks to the U.S. Electoral College system of the time, however, there was no functional difference and the Federalists could choose the so-called vice-presidential candidate over the presidential candidate for the winner of the presidential election.
Burr might have thus become the President of the United States if it hadn't been for Alexander Hamilton. Hamilton, a major leader in the Federalist Party, used his significant influence to push for Jefferson's election over Burr. Hamilton believed that it was better for Jefferson to win the presidential election because Jefferson was simply wrong, but was honest, while Burr was a dangerous liar. (Hamilton and Burr would of course go on to have the most famous duel in American history, in which Burr would kill Hamilton.) As a result, Jefferson just barely garnered more votes from the House of Representatives than did Burr, and Jefferson won the election with Burr becoming his Vice-President.
This election's primary effect upon America was the creation of the Twelfth Amendment, which reworked the U.S. Electoral College. The Twelfth Amendment was only passed in 1804, but it importantly altered the U.S. Electoral College to allow electors to vote for both a President and a Vice-President in a presidential election, instead of voting for two different presidential candidates, or the same presidential candidate twice.
The Twelfth Amendment established further systems to help prevent any problems as occurred in this election, but the key point was that the ticket system of presidential elections, in which a President and Vice-President would run for office together, became the system of America thanks to the confusion of the election of 1800.