Poor W (aka Nicholas Hubbard) - he got the whole affair up and running and then was denied his right share of the infamy.

I didn't want to go too far down the Madison rabbit hole in order to keep the focus on the Election, but I agree that Madison's political views are a bit more complicated and nuanced than that he shifted from a federalist ideology to anti-federalist. A few good books for folks interested in diving into more of Madison's ideology are Richard K Matthews's If Men Were Angels: James Madison and the Heartless Empire of Reason; Noah Feldman's The Three Lives of James Madison: Genius, Partisan, President; and Kevin Gutzman's James Madison and the Making of America. To be fair to Mr. Adams, there was no precedent for how a defeated incumbent should involve themselves in a constitutional crisis, and Adams had been attacked for four years by a sizable portion of his own party. That said, I think he was very much in his feelings about the matter and shifted his focus to anything but the election mess. For Burr's part, I don't know that it crossed his mind to involve himself in the matter except to put forward that he thought Jefferson should rightfully be president. Samuel Smith of MD approached Burr about dropping out of the contest, but that would have meant that Adams would have become Vice President instead of him (though Adams likely would have declined and then it would have been down to Charles Cotesworth Pinckney). Burr, had he been chosen as president by the House, would have served, but I think he knew that was a bad scenario and would have lead to a miserable four years in office with no path to reelection. Better to serve as VP under Jefferson and use the opportunity to get close to him, the administration, and other leaders in DC to set him up for a future run. Little did he know at the time that this fluke desperate scheme by the Federalists would end up being the closest he would ever come to the presidency.