Statistical detection of systematic election irregularities (2012)

This is a landmark academic paper published in the *Proceedings of the National Academy of Sciences* (PNAS) in 2012, which introduced a statistical method for detecting election fraud. The authors — political scientists and statisticians (including Peter Klimek, Yuri Yegorov, and Stefan Thurner) — used a concept from physics called "Weibull distribution" to show that legitimate votes in an election follow a predictable statistical pattern. When vote-count distributions deviate significantly from that pattern (e.g., showing improbably high turnout or digit-pattern anomalies), it suggests systematic manipulation. The paper is best known for analyzing the 2009 Iranian presidential election and identifying anomalies consistent with fraud, which later became a touchstone in the debate over using quantitative methods to audit elections worldwide.