Abstract:

The Benford distribution, originally formulated by Simon Newcomb in 1881, is used in forensic accountancy to detect irregular charges and fraud. It is also used in electoral forensics to detect certain types of fraud in elections. Unfortunately, one assumption underlying the Benford distribution is not satisfied in elections. That assumption is that the upper bound in the underlying log-uniform distribution is an integer power of 10. This assumption is not met because the upper bound is the number of votes cast (turnout). If this assumption is not met in elections, then the Benford distribution should not be used to detect fraud in elections. This presentation examines the origin of the Benford distribution, as well as its assumptions. From there, it proposes a generalization designed to account for a finite upper bound on the underlying distribution. Unfortunately, this generalization offers its own challenges, namely that each electoral division has a different upper bound. Three solutions are explored and results are compared to elections.