An old post of mine:
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Usually, the "Burr wins" scenarios here have been about his winning in the House (if Hamilton didn't convince enough Federalists to oppose him). But suppose he wins in the Electoral College? Two scenarios:
(1) For some reason, one Democratic-Republican elector dislikes Jefferson and prefers Burr, so he votes for Burr and some other D-R.
(2) Some Federalist elector hates Jefferson (of course) but also hates Adams--even more than Hamilton did. And he doesn't share Hamilton's antipathy to Burr--or at least he feels that the opportunist Burr is a lesser evil than the "fanatical" Jefferson. So he votes for Pinckney (whom he sincerely hopes will win) but also for Burr...
The Jeffersonians of course are going to be very angry. Besides the Twelfth Amendment as in OTL, may we see some sort of constitutional amendment prohibiting faithless electors?
As for why Burr would accept the presidency under such circumstances--with both parties disliking him--rather than yielding to Jefferson and hoping for the Democratic-Republican presidential nomination in 1808 or even 1804 (after all, as John E. Ferling once noted in *Adams vs. Jefferson: The Tumultuous Election of 1800,* p. 183, Jefferson had shown a "penchant for retiring to Monticello--he had done so in 1776, 1781, and 1793"
https://books.google.com/books?id=j0wB9SX1VrEC&pg=PA183), Ferling observes,
"While the odds were good that Burr would live another twenty years, dying young was not uncommon in the eighteenth century. In fact, Burr's mother and father had died at ages twenty-seven and forty-two, respectively, while his wife, Theodosia, had passed away at forty-seven. Furthermore, Burr like every other activist, was all too aware of the vagaries of politics. Any politician who attempted to plan career moves eight or even four years down the road was on shaky ground. Any veteran of the American Revolution would have known as much, having seen the political landscape turn topsy-turvy by the overthrow of British rule and the demise of the Articles of Confederation. For that matter, within a six-month span in 1798 the Federalist Party had fallen from the giddy heights of supremacy to division and despair, and in two years John Adams had gone from being hailed as the equal of Washington in popularity to a defeated president who was being sent packing."
Of course it may be objected: Didn't Burr realize that even if he won the presidency in 1800--either through "faithless electors" or in the House--he would be regarded by a majority of Democratic-Republicans as a usurper, and that his presidency would become a shambles even before he took the oath of office? The problem with this line of reasoning is that it assumes that the future lay with the Jeffersonian Democratic-Republicans, and that the wise thing for an ambitious man like Burr to do was to ingratiate himself with them. This is obvious enough *to us* because we know that Jefferson's party was to dominate American politics for decades after 1800. But of course Burr could not know that in 1800. To quote Ferling again (p. 184):
"However, it must be remembered that the political parties in existence in 1800 were not entrenched institutions like those of today. They were less than a decade old and only recently had become reasonably well-disciplined entities. Both parties had members who shifted to the other side as new issues emerged or as the political wind changed direction. In fact, in the run-up to the canvass of 1800 many had been convinced that a party restructuring was under way. There had been much talk in 1799 and early 1800 that Adams and Jefferson would conclude a bargain that resurrected the so-called Adams-Lee Junto, the Virginia-New England alliance that had controlled the Continental Congress during the first several years of the American Revolution. Such a turn of affairs had probably never been in the works, but even some savvy politicians had believed it and suspected that a new party might supplant one of the two in existence or that a third party might come into being. In January and February some who pushed Burr's candidacy appeared to believe--and to welcome--his presidency as the means of restructuring the existing parties along sectional lines. If so, it would not have been inconceivable for Burr to have had the solid backing of a viable new party."
http://books.google.com/books?id=j0wB9SX1VrEC&pg=PA184
Given all that, Burr's decision to go after the big prize immediately rather than waiting four or eight years was actually a more reasonable decision than it may look like in retrospect. And anyway in this ATL he has not done anything actively to seek it: the office has been thrust on him, he explains...