Using the Logit-Normal Distribution in Electoral Forensics

• Activity Number: 423
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Social Statistics Section
• Author(s): Ole Forsberg*+
• Companies: Oklahoma State University
• Keywords: Benford test ; Hypothesis testing ; Simulation ; Electoral forensics ; Logit-normal distribution

Abstract

Electoral forensics is the study of statistical techniques designed to detect certain types of fraud in official election returns. It has been used to support charges of election fraud in Iran, Sri Lanka, and South Sudan. The Benford digit test is frequently also used in electoral forensics to detect the deliberate changing of vote counts. Unfortunately, the Benford digit test assumes that the distribution of the logarithm of the vote counts follows a uniform distribution. In general, vote counts do not follow such a distribution; vote counts depend on the precinct size and the multinomial nature of voters in the booth. This paper introduces the logit-normal distribution as an alternative to the uniform distribution to better describe candidate support in the precincts. The normal is a natural choice as a basis for candidate support due to the Central Limit Theorem. Transforming the normal into the (0,1) interval with the logistic function eliminates impossible predictions. The proposed testing procedure is illustrated on the 2008 US Presidential election in Colorado, using the logit-normal, the precinct sizes, and Monte Carlo to determine confidence regions and p-values.