Does the Application of Benford's Law Reliably Identify Fraud on Election Day?

Abstract

In an attempt to bring mathematical certainty to uncertain situations, some have tried developing "election forensics" tools as a way of evaluating the quality of an election. Most election forensics tools involve applying statistical methods and underlying mathematical principles to official election results. One such tool is the application of Benford's Law to election results. In this paper, I use election data from the lowest level, that of polling station, to assess whether Benford's Law, as applied to the distribution of second-digits in vote count data, is an appropriate tool for detecting fraud. Unfortunately, my analysis shows that Benford's Law is an unreliable tool. And, as one applies more sophisticated methods of estimation, the results become increasingly inconsistent. Worse still, when compared with observational data, the application of Benford's Law frequently predicts fraud where none has occurred.