Inversions in US Presidential Elections: 1836-2016 – Michael Geruso, Dean Spears, Ishaana Talesara – NBER Working Paper No. 26247. Issued in September 2019.

“Inversions—in which the popular vote winner loses the election—have occurred in 4 US Presidential elections. We show that rather than being statistical flukes, inversions have been ex ante likely since the 1800s. In elections yielding a popular vote margin within one percentage point (which has happened in one-eighth of Presidential elections), 40% will be inversions in expectation. Inversion probabilities are asymmetric, in various periods favoring Whigs, Democrats, or Republicans. Feasible policy changes—including awarding each state’s Electoral College ballots proportionally between parties rather than awarding all to the state winner—could substantially reduce inversion probabilities, though not in close elections.”