Statistical detection of systematic election irregularities

TL;DR

This paper introduces a statistical method to detect election irregularities by analyzing vote distribution kurtosis, demonstrating its effectiveness in identifying systematic fraud across different countries and data resolutions.

Contribution

It develops a parametric model and a statistical test to identify election fraud, providing a cross-country applicable technique based on vote distribution analysis.

Findings

Elections with alleged fraud show significantly higher kurtosis in vote distributions.

The proposed method detects systematic ballot stuffing with high consistency.

Results are robust across different data granularities and countries.

Abstract

Democratic societies are built around the principle of free and fair elections, that each citizen's vote should count equal. 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 certain statistical consequences for the polling results which can be used to identify election irregularities. Using a suitable data collapse, we find that vote distributions of elections with alleged fraud show a kurtosis of hundred times more than normal elections on certain levels of data aggregation. As an example we show that reported irregularities in recent Russian elections are indeed well explained by systematic ballot stuffing and develop a parametric model quantifying to which extent fraudulent mechanisms are present. We show that if specific statistical properties are present in an election, the results do not represent the will of the people. We formulate a parametric test detecting these statistical properties in election results. Remarkably, this technique produces similar outcomes irrespective of the data resolution and thus allows for cross-country comparisons.