Inversions in US Presidential Elections: 1836–2016
研究发现，自19世纪初以来，美国总统选举中普选票赢家输掉选举的逆转现象并非统计偶然，在普选票差距小于1个百分点的选举中，约40%预期会发生逆转，且这一概率在不同历史时期保持稳定。
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).