Inversions—in which the popular vote winner loses the election— have occurred in four US presidential races. We show that rather than being statistical flukes, inversions have been ex ante likely since the early 1800s. In elections yielding a popular vote margin within 1 point (one-eighth of presidential elections), about 40 percent will be inversions in expectation. We show this conditional probability is remarkably stable across historical periods—despite differences in which groups voted, which states existed, and which parties participated. Our findings imply that the United States has experienced so few inversions merely because there have been so few elections (and fewer close elections). (JEL D72, N41, N42)

中文翻译：

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美国总统选举的逆转：1836 年至 2016 年


在四届美国总统竞选中，都出现过倒挂现象，即普选获胜者输掉选举。我们表明，自 1800 年代初期以来，倒置就可能是事前发生的，而不是统计上的侥幸。在普选票差距在 1 个百分点以内（总统选举的八分之一）的选举中，大约 40% 的结果与预期相反。我们证明，这种条件概率在各个历史时期都非常稳定——尽管投票群体、存在哪些国家以及参与哪些政党存在差异。我们的研究结果表明，美国经历的反转如此之少，仅仅是因为选举次数太少（而且势均力敌的选举也更少）。 (JEL D72、N41、N42)