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On Election Day you do not vote for a presidential candidate — you vote for a slate of electors pledged to that candidate. Each state controls its own electors, almost all of them by winner-take-all, and a candidate must assemble an absolute majority of the 538 electors nationwide. Two months of paperwork then run from state capitals to the floor of Congress before a president is legally elected.
538 electors, so a majority is 270. The decisive number is never the national total but the tipping-point state — the state that puts a candidate over 270 when states are ranked by margin. Because of winner-take-all, a candidate can run up huge margins in safe states and gain nothing extra; the whole contest is fought over the few states near the 50-yard line. Win the right combination of states by even a single vote each and you win the presidency.
If no candidate wins a majority of electors, the 12th Amendment (ratified 1804 after the deadlocked 1800 election) sends the presidential choice to the House of Representatives. There the math changes completely: each state delegation casts a single vote, so Wyoming and California count equally, and a candidate needs 26 of the 50 state votes to win.
This has happened twice. In 1800 the House broke a tie between Thomas Jefferson and Aaron Burr. In 1824, with four candidates splitting the vote and no one near a majority, the House chose John Quincy Adams over Andrew Jackson — even though Jackson had led in both the popular and electoral vote. The Senate, separately, chooses the vice president if no VP candidate gets a majority; it has done so once, in 1836.