Section for Science of Complex Systems, Medical University of Vienna, Vienna, Austria.
Proc Natl Acad Sci U S A. 2012 Oct 9;109(41):16469-73. doi: 10.1073/pnas.1210722109. Epub 2012 Sep 24.
Democratic societies are built around the principle of free and fair elections, and that each citizen's vote should count equally. National elections can be regarded as large-scale social experiments, where people are grouped into usually large numbers of electoral districts and vote according to their preferences. The large number of samples implies statistical consequences for the polling results, which can be used to identify election irregularities. Using a suitable data representation, we find that vote distributions of elections with alleged fraud show a kurtosis substantially exceeding the kurtosis of normal elections, depending on the level of data aggregation. As an example, we show that reported irregularities in recent Russian elections are, indeed, well-explained by systematic ballot stuffing. We develop a parametric model quantifying the extent to which fraudulent mechanisms are present. We formulate a parametric test detecting these statistical properties in election results. Remarkably, this technique produces robust outcomes with respect to the resolution of the data and therefore, allows for cross-country comparisons.
民主社会建立在自由和公正选举的原则之上，每个公民的选票应该平等地被计算。全国性选举可以被视为大规模的社会实验，人们通常被分为大量的选区，并根据自己的偏好进行投票。大量的样本对投票结果产生了统计后果，可以用来识别选举违规行为。通过适当的数据表示，我们发现，涉嫌欺诈的选举中的选票分布的峰度明显超过正常选举的峰度，具体取决于数据聚合的程度。例如，我们表明，最近俄罗斯选举中报告的违规行为确实可以通过系统的选票操纵得到很好的解释。我们开发了一个参数模型，量化了存在欺诈机制的程度。我们制定了一个参数检验，用于检测选举结果中的这些统计特性。值得注意的是，这种技术在数据分辨率方面产生了稳健的结果，因此可以进行跨国比较。
