Replication data for: What the Numbers Say: A Digit-Based Test for Election Fraud

Is it possible to detect manipulation by looking only at electoral returns? Drawing on work in psychology, we exploit individuals' biases in generating numbers to highlight suspicious digit patterns in reported vote counts. First, we show that fair election procedures produce returns where last digits occur with equal frequency, but lab experiments indicate that individuals tend to favor some numerals over others, even when subjects have incentives to properly randomize. Second, individuals underestimate the likelihood of digit repetition in sequences of random integers, so we should observe relatively few instances of repeated numbers in manipulated vote tallies. Third, lab experiments demonstrate a preference for pairs of adjacent digits, which suggests that such pairs should be abundant on fraudulent return sheets. Fourth, subjects avoid pairs of distant numerals, so those should appear with lower frequency on tainted returns. We test for deviations in digit patterns using data from Sweden's 2002 parliamentary elections, Senegal's 2000 and 2007 presidential elections, vote returns from Chicago for the 1924 and 1928 presidential elections, and previously unavailable results from Nigeria's 2003 presidential election. We find weak evidence for fraud in Chicago and substantial evidence that manipulation occurred in Nigeria as well as in Senegal in 2007.仅通过选举计票结果能否侦测选举操纵行为？本文借鉴心理学领域的研究成果，利用人类在生成数字时的认知偏差，识别公开计票数据中的可疑数字模式。首先，我们证明合规选举流程产生的计票结果中，末位数字应呈现均匀分布的频率；但实验室实验表明，即便实验对象有动机进行真正的随机化操作，他们仍会倾向于偏爱部分数字。其次，人类会低估随机整数序列中数字重复出现的概率，因此在被操纵的计票数据中，重复数字的出现频次应相对偏低。第三，实验室实验证实人类偏好相邻数字组合，这意味着舞弊计票报告中这类相邻数字对的占比应偏高。第四，实验对象会刻意规避间距较大的数字组合，因此这类组合在被操纵的计票结果中出现的频率应更低。我们依托多组选举数据对数字模式的偏差进行检验，数据涵盖瑞典2002年议会选举、塞内加尔2000年与2007年总统选举、芝加哥1924年及1928年总统选举的计票结果，以及此前未公开的尼日利亚2003年总统选举计票数据。研究结果显示，芝加哥的选举舞弊证据较为薄弱，而尼日利亚及塞内加尔2007年总统选举存在选举操纵的显著证据。