This is something I noticed a while ago, but didn't post on because it isn't one of my usual topics. I was reminded of it because of discussion of the Electoral College and whether there might be another result that goes against the popular vote. That did not happen between 1888 (Benjamin Harrison vs. Grover Cleveland) and 2000. However, it came close to happening in 1916, when a shift of 2,000 votes in California would have given the election to Charles Evans Hughes, who got 46.1% against Woodrow Wilson's 49.2%. The electorate was much smaller then, so in proportional terms that would be equal to about 15,000 votes today, which is still not many. There was also the election of 1948, when Strom Thurmond ran. He had no chance of winning--his goal was to prevent either Truman or Dewey from winning a majority, so that the election would go to the House of Representatives and the south could make the candidates renounce any civil rights proposals as the condition of a deal. As it happened, Truman won both the popular and electoral vote by solid margins (49.6% to 46.1% and 303 to 189), but California and Ohio were very close. A shift of 9,000 votes in California and 4,000 in Ohio would have given Dewey both states, and would have left Truman with 253 electoral votes, short of the 266 then needed to win. That would be equal to about 36,000 votes in today's terms.
So part of the reason that the Electoral College matched the popular vote for over a century was just luck. And as these examples (and Trump vs. Clinton) show, there is a significant chance of discrepancy even when the popular vote is not all that close.
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