A first-digit anomaly in the 2009 Iranian presidential election

TL;DR

This paper introduces a local bootstrap method to analyze first-digit frequencies in election data, revealing significant anomalies in the 2009 Iranian presidential election that suggest possible irregularities.

Contribution

It presents a novel bootstrap-based approach for detecting digit anomalies in electoral data, complementing Benford's Law analysis and applied to Iranian election results.

Findings

Significant excess of vote counts starting with digit 7 for candidate K

Multiple anomalies with p-values around 0.1% to 1%

Pre-election polls significantly differ from official results unless certain data are isolated

Abstract

A local bootstrap method is proposed for the analysis of electoral vote-count first-digit frequencies, complementing the Benford's Law limit. The method is calibrated on five presidential-election first rounds (2002--2006) and applied to the 2009 Iranian presidential-election first round. Candidate K has a highly significant (p< 0.15%) excess of vote counts starting with the digit 7. This leads to other anomalies, two of which are individually significant at p\sim 0.1%, and one at p\sim 1%. Independently, Iranian pre-election opinion polls significantly reject the official results unless the five polls favouring candidate A are considered alone. If the latter represent normalised data and a linear, least-squares, equal-weighted fit is used, then either candidates R and K suffered a sudden, dramatic (70%\pm 15%) loss of electoral support just prior to the election, or the official results are rejected (p\sim 0.01%).