MODELLING NIGERIA’S PRESIDENTIAL ELECTION DATA USING BENFORD’S LAW AND MONTE CARLO SIMULATION

Abstract

Allegations of fraudulent practices and bogus results led to application of election forensic tools in the analysis of election data. Previous studies examined the digital distributional patterns of electoral data using Zipfian and agent-based modelling, while neglecting sensitivity check that could reveal other anomalies. This study, therefore, was designed to analyse Nigeria’s presidential election data between 2007 and 2015 by applying Benford’s Law and Monte Carlo Simulation which can indicate voter distribution and reveal any anomalies in the election results, with a view to assessingthe integrity of the election process and results.

Benford’s Law and Monte Carlo Simulation models were used as framework, while Modelling and Simulation, which compares the observed patterns against the expected patterns, were adopted as design. Purposive sampling was used to select 2007, 2011 and 2015 presidential election results.Data wasobtained from the website of Independent National Electoral Commission. Political parties included in the analyses were those with at least four digits vote counts: 24 parties for 2007 election; PDP, CPC, ACN and ANPP for 2011 election; and APC and PDP for 2015 election. Also included were voters’ turnout for 2011 and 2015 elections (data was not available for 2007). Data were analysed using descriptive statistics and Spearman rank correlation test at 0.05 level of significance, while R programming was used for the Monte Carlo Simulation.

Whereas the 2007 election result contains only vote counts of the 24 political parties, collated at national level only, the 2011 and 2015 election results contain voters’ turnout and vote counts for each political party per state.The distribution of last digits of vote counts of 2007, 2011 and 2015 elections and voters’ turnouts of 2011 and 2015 elections did not follow the expected uniform distribution of last digits for fraud-free data. The distributional pattern of vote counts for 2011 and 2015 elections deviated from distributional pattern of Monte Carlo simulated vote counts. The first digits of vote counts in 2007 elections of the 24 political parties (r=0.68); in 2011 elections of ACN (r=0.96), PDP (r=0.93), CPC (r=0.75) and ANPP (r=0.73); and in 2015 elections of APC (r=0.96) and PDP (r=0.74) significantly correlate with Benford’s Law. The occurrence of first digits in voters turnouts of 2011 (r=0.07) and 2015 (r=0.37) elections did not follow Benford’s Law. The occurrence of second digits in vote counts of the 2007 elections (r=0.36), 2011 elections [PDP (r=0.51), ACN (r=0.51), CPC (r=0.20) and ANPP (r=0.17)] and 2015 elections [APC (r=-0.61) and PDP (r=0.02)] did not follow Benford’s Law. This was also the case in voters’ turnout of 2011 (r=-0.17) and 2015 (r=-0.09) elections.

The application of Benford’s Law and Monte Carlo Simulation on Nigerian presidential election data of selected years reveals that the election results are not error-free. Nigeria’s electoral process should apply these forensic analyses on electoral data and adjust the electoral process in line with findings.