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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美国总统选举中的倒置：1836-2016

在美国的四场总统竞选中都出现了普选获胜者输掉选举的倒置情况。我们表明，自 1800 年代初以来，倒置可能是事前发生的，而不是统计上的侥幸。在普选票差在 1 个百分点以内（总统选举的八分之一）的选举中，大约 40% 的人会出现预期反转。我们表明，这种条件概率在各个历史时期都非常稳定——尽管在哪些群体投票、哪些州存在以及哪些政党参与方面存在差异。我们的研究结果表明，美国之所以经历如此少的倒置，仅仅是因为选举如此之少（而且势均力敌的选举也更少）。(JEL D72, N41, N42)