In the musical Hamilton there is a song near the end that focuses on and is titled The Election of 1800. The song talks about how Burr and Jefferson ran against each other which is true, but it leaves out the fact that they ran together at the beginning of the election and only when they both got the same number of votes did they become rivals. Jefferson eventually won the election like it says in the song, but unlike what the song says it was not completely up to Hamilton though he did play a large role in Jefferson's victory. What it doesn't tell us is that Burr came very close to winning the election due to backing from the Federalist party though Hamilton eventually was able to sway most of the Federalists to Jefferson's side. I think the reason Miranda does this is because it is more about the fact that Hamilton was one of the deciding factors in the election of 1800. The song ends with Jefferson and Madison talking about how it is crazy that the candidate with the second most votes gets to be vice president and that they should change that. The reason for this was that there was a flaw in the constitution that made both the Vice President run on the same ballot so who ever got the most votes became president and the guy after him became the vice-president. Eventually the 12th amendment solved this problem by having people vote for either president or vice-president. I feel that the reason Miranda had Madison and Jefferson joke about it at the is because it would eventually happen. Part of the song is about people asking Hamilton who he will vote for and we know who he eventually chooses, but the question I would like to ask is that even though he tells us that he doesn't vote for Burr because he doesn't have beliefs why do you think he chose Jefferson over Burr since he hated both of them?
https://www.law.cornell.edu/constitution/amendmentxii
http://history1800s.about.com/od/19th-Century-Presidents/tp/Early-American-Vice-Presidents.htm