DIRECTIONS-- READ THE LINKED ARTICLE. COMPARE WHAT REALLY HAPPENED IN THE ELECTION OF 1800 TO LYRICS “THE ELECTION OF 1800”.

Much of the climax of Lin-Manuel Miranda's musical Hamilton hinges on the outcome of the presidential election of 1800. As Miranda tells the story, the main candidates are Thomas Jefferson and "Aaron Burr, with his own faction." Jefferson and Burr end up in a tie, "the delegates" have to choose the winner, and, at Hamilton’s urging, they end up backing Jefferson over Burr.

It's a dramatic and effective number that brings several plot threads together — Hamilton's return to politics, his longtime rivalry with Jefferson, his fear of Burr's ambition — and sets the course for the fatal showdown between the two lead characters.
Yet the actual election of 1800 was far more complex and dramatic — it brought the nation to a constitutional crisis and even, some thought, the brink of open violence.
And Burr's real-life conduct was even more opportunistic and duplicitous than it was in the musical (which features, overall, a toned-down version of the man who'd later be accused of trying to seize American territory to create a new empire for himself). Because Burr was in fact Jefferson's running mate, who was understood by practically everyone to be truly running for vice president.
Until, that is, he saw an opportunity.
Badly flawed constitutional design made the crisis possible
The odd constitutional flaw that led to the electoral crisis of 1800-'01 was a simple one: There was no way the electoral college could distinguish between candidates for president and candidates for vice president.
The way the system initially worked, each state's electors (members of the electoral college) got to cast two votes. When all the votes were in, the person with the most electoral votes would become president (if he had the support of a majority of electors), and the person with the second highest number of votes would become vice president (as Burr notes in "The Adams Administration").
The system was created without any expectation or understanding that organized parties would soon dominate US politics. So once the first parties started putting up both presidential and vice presidential candidates, it quickly became clear that there was a huge potential problem.
Namely: Even if a presidential candidate won a majority of electors, if his vice presidential running mate got those same electors' votes, they'd technically end up in a tie.
And in that case, the election would be thrown to the House of Representatives. Not a newly elected House, mind you, but the lame-duck House already sitting. Additionally, rather than voting in the normal way, in this situation the House is supposed to vote by state, with the large and small states' votes counting equally.
When Jefferson and Burr tied, the Federalists plotted to throw the election to Burr
All this created ample opportunity for mischief, and that’s exactly what ensued in 1800. Jefferson and Burr — the Democratic-Republican Party's choices for president and vice president — got 73 votes each. This was a majority over John Adams's Federalist ticket, but also an outcome that technically counted as a "tie" that had to be resolved by the House (which would have to choose between them, with the runner-up becoming vice president). And many Federalists — who loathed Jefferson and feared his potential presidency — got the idea that they could throw the election to Burr instead.
Now, Burr could have thrown cold water on this scheme by letting it be known he wouldn't accept the presidency (or that he'd resign from it if the House installed him, thus making vice president Jefferson the president). Indeed, when asked during the campaign what he'd do in case of a tie vote, Burr had said he wouldn't stand in Jefferson's way.
But once the electoral tie was apparent, Ron Chernow writes in Hamilton, "Burr changed his mind." Though he wouldn't publicly seek or even privately lobby for the presidency (so far as we know), Burr very conspicuously refused to state that he'd turn it down if the House handed it to him.
Some historians characterize this as merely a "passive" move, but it sure looks nakedly ambitious to me. Burr effectively sent the message that he was willing to go along with his longtime rivals' scheme to deny his own party's candidate the presidency, just so he could be president instead.
All this threw the country into a serious constitutional crisis, in which it looked like the obvious rightful winner of the presidency might be denied the office due to his enemies' intrigues.
This created a major crisis for the new nation — and violence seemed possible
In the case of a tie, the (lame duck) House of Representatives was to vote on who became president. But again, each state delegation, not each member, got one vote. And a majority of all the state delegations was necessary to win.
At the time, there were 16 states — so Jefferson needed to win nine state delegations to become president.
Yet when the first vote was taken in February 1801, he only came up with eight. All seven state delegations controlled by Jefferson's party voted for him — and Georgia's delegation (which was just one Federalist) joined them. But six other Federalist-controlled state delegations went ahead with their plot to vote for Burr. And two more delegations were each split between the parties and therefore between Jefferson and Burr, so they couldn't cast a vote at all. With the House divided 8-6-2, nobody was elected president.
As the two sides dug in, 34 more rounds of balloting over the next five days kept producing the exact same outcome. It looked like the Federalists could theoretically stall the installation of a new president until past the scheduled inauguration day of March 4. No one knew what would happen then. Would some sort of interim president be installed somehow? Would outgoing president John Adams decide to stay put rather than stepping down?
A violent crisis seemed quite possible. "Republican newspapers talked of military intervention," Gordon Wood writes in Empire of Liberty. "The governors of Virginia and Pennsylvania began preparing their state militias for action. Mobs gathered in the capital and threatened to prevent any president from being appointed by statute."
A backroom "understanding" led to a peaceful resolution
All this time, Hamilton did in fact frantically lobby the Federalists to choose Jefferson over Burr — in even stronger terms than he uses in the musical. Per Chernow, he called Burr "wicked enough to scruple nothing" and "one of the worst men in the community," and said that Burr once suggested using the new army to "demolish" the "miserable Constitution." (It is also possible that Hamilton feared a Burr-Federalist alliance would block his own hoped-for political comeback.)
It wasn't Hamilton who saved the day in the end, though. Credit goes to Rep. James Bayard, a Federalist from Delaware — who was lucky enough to be his state's only House representative, and therefore in full control of his delegation's vote.
Though Jefferson would always strongly deny making any deal for the presidency, Bayard got backchannel assurances from Jefferson's allies that Jefferson would "preserve Hamilton’s financial system, maintain the navy, and retain Federalist bureaucrats below cabinet level," Chernow writes.
So finally, enough Federalist House members finally abandoned their support of Burr on the 36th ballot, and Jefferson was elected president. Soon afterward, the Constitution would be amended to prevent another near-disaster like this — electors would now vote separately for the offices of president and vice president.
As for Burr, he was installed as Jefferson's vice president, but having proven himself untrustworthy, he was frozen out of any influence in the new administration, and was dropped from the ticket in 1804.
Contra the musical, though, it wasn't the election of 1800 that led to Burr's duel with Hamilton. Miranda has simplified the timeline by mixing that election with Burr’s 1804 attempt to revive his political career by being elected governor of New York. Burr lost that bid, became furious at reports that Hamilton had privately slandered him during the campaign, and eventually challenged him to the fatal duel.
A few years later, Burr was charged with treason for allegedly trying to take over American territory to start a new country
A footnote on Burr: Hamilton the musical leaves out perhaps the most bizarre part of his story. After his vice presidency was over and both parties considered him a pariah, Burr traveled in the West and South, where he got up to some mischief. There are many competing claims about what, exactly, Burr intended to do ... but it sure looked to a whole lot of people like Burr was plotting to treasonously take over parts of American territory and found a new country that would be run by him. That's one way to get back into the room where it happens.
For his part, Burr claimed his main aim was to conquer Spanish-controlled territory so he could add it to the US. President Jefferson didn't buy it, and had him arrested and tried for treason. The trial was judged by Supreme Court Chief Justice John Marshall, who found Burr not guilty in an extremely controversial decision. So, the killing of Hamilton wasn't the only reason that Burr became the villain in our history.

According to Hamilton, what happened in the Election of 1800?

According to Hamilton, in the Election of 1800, Thomas Jefferson and Aaron Burr tied in the electoral college, causing the election to be thrown to the House of Representatives. Hamilton urged the delegates to vote for Jefferson, which resulted in Jefferson becoming the president.

According to the musical Hamilton, the election of 1800 ended in a tie between Thomas Jefferson and Aaron Burr. The delegates had to choose the winner, and Alexander Hamilton urged them to back Jefferson over Burr, setting the course for the fatal showdown between the two lead characters.

According to the musical Hamilton, the Election of 1800 ended in a tie between Thomas Jefferson and Aaron Burr. As a result, the decision of who would become president was left to the delegates. Alexander Hamilton, who had a rivalry with Jefferson but feared Burr's ambition, convinced the delegates to back Jefferson over Burr. This decision sets the stage for the fatal showdown between Hamilton and Burr.