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Anomalies in Nigeria Presidential Election Data and the Way Forward

Written By

Sunday Tunmibi and Wole Olatokun

Submitted: 28 April 2022 Reviewed: 02 May 2022 Published: 17 August 2022

DOI: 10.5772/intechopen.106657

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Nigeria presently runs a presidential system of government and the Independent National Electoral Commission (INEC) is saddled with the responsibility of conducting elections, every four years. A fraud-free and credible election is a necessary ingredient to the growth of democracy. However, election fraud has become a major challenge in the Nigerian political system. Till date, reports show that elections in Nigeria have been marred with vote buying, falsification of results, underage voting, and the use of security forces to intimidate voters, among others. Hence, the authors suggest the need for transparency in the voting process and in the collation of results. There is also a need for an electoral reform to address the issue of electronic voting and electronic transmission of results. Electronic voting should be supported and encouraged by all stakeholders. The INEC, executive and legislative arms of government are advised to work in tandem to provide credible electoral process and improve on the conducts of elections in Nigeria. The chapter concludes with suggestion on the possibility of adopting election forensic techniques to address anomalies in Nigeria electoral results. The authors believe that this chapter contribution will be of great benefit to Nigeria and Africa as a whole.


  • Nigeria
  • INEC
  • presidential elections
  • anomalies
  • election forensics

1. Introduction

Election is a process or a sequence of actions that results in a selection of a person for an office, dignity, or position of any kind; usually by the votes of a constituent body. This process may be as simple as counting raised hands in a room, or as complex as tallying votes across a multiplicity of jurisdictions [1]. The conduct of transparent and credible elections on a regular basis as established by the relevant constitutional and legal framework is a critical component of democracy. Generally, periodic and credible elections in a state or a nation are seen as a key component for enhancing the legitimacy of a government and strengthening the social contract between the government and the governed [2].

The mode and period of conducting elections vary in different parts of the world. Nigeria, like the United States of America, currently runs a presidential system of government. The Independent National Electoral Commission (INEC) is saddled with the responsibility of conducting elections every four years into offices of President and Vice President, Governors and deputy Governors, the Senate and House of Representatives and the 36 States Assemblies. Each of the 36 States and FCT (Federal Capital Territory) of Abuja has a REC (Resident Electoral Commissioners) who reports to the chairman of INEC. The processes involved in voting are voters’ accreditation, casting of ballots, votes counting, collation of results and announcement. It is expected that INEC should be impartial and transparent in conducting the elections [3].

Election fraud specifically refers to deceptive or negligent interference with the electoral process that intends to prevent the outcome from reflecting the will of the people. Electoral fraud are committed with the aim of influencing electoral results to favor a candidate through the adoption of bribery, cheating, illegal voting, intimidation, alteration of results and fraudulent pronouncement of the loser as winner with or without adjusting the electoral outcome [4]. The capacity of electoral officers to rig elections cast a shadow over the electoral process of many democratic countries, including those with advanced democracies [5].

While electoral fraud has a history in many of the world’s most advanced democracies such as the United States of America [6], today the most flagrant election fraud occurs in societies that are less democratic [7, 8]. For example, studies show that elections held in Gabon in 1998 were tainted by massive fraud [7]. Similarly, report revealed that though the elections held in Kenya in 1992 and 1997 were competitive, as the opposition received a clear majority of the votes, they were neither free nor fair [9]. The 2007 presidential election in Senegal also generated considerable controversy, which ultimately culminated in a boycott of the parliamentary elections by most of the opposition less than four months after the presidential ballot [10].

This chapter is a natural outgrowth of my PhD thesis, supervised by the co-author, which dealt with modeling Nigeria’s presidential election data using Benford’s Law (a variation of the Zipfian model) and Monte Carlo analysis (one of the approaches to agent-based modeling). According to Benford’s Law, the occurrence of different digits in a set of numbers differ. The Law proposes a skewed distributional pattern for first and second digits of numerals, while the distribution approaches uniform distribution for higher digits. Monte Carlo analysis, on the other hand, is a research strategy that incorporates randomness, usually in the form of computer simulation. Findings from the thesis revealed that the digit distribution of the vote counts for 2011 and 2015 presidential elections in Nigeria do not conform to the distributional pattern predicted by Benford’s Law for first and second digits, and the respective Monte Carlo simulated data.

A fraud-free and credible election is a necessary ingredient to the growth of democracy. However, election fraud, from 1959 till date, has become a challenge in the Nigerian political system. In this chapter, the authors discuss the way forward in addressing issues relating to election fraud in presidential elections in Nigeria. In the next section, we focus on election fraud in Nigeria; followed by a discussion on election forensics approach with specific focus on Bendford’s Law and Monte-Carlo, an agent based modeling. Suggestions on the way forward for improving the conduct of presidential election in Nigeria and conclusions finalized the chapter.


2. Election fraud in Nigeria

Records have shown that elections and electioneering in Nigeria have generated strong hostility, to the extent of threatening the unity of the country [11]. A lot of this hostility could be attributed to manipulated electoral results. The term “classic fraud” has been used to describe the correspondence between colonial officials over the 1959 elections and the request to produce evidence in order to investigate the matter [12]. The post-colonial elections of Nigeria’s First Republic (1960–1966) were greatly marred by electoral process that was characterized by manipulations [13]. The 1964 federal elections and 1965 western region elections, the first of such to be conducted after the colonial era, were also perceived to be characterized with massive irregularities [11]. This was evidenced in a statement by Nnamdi Azikwe that the rigging that characterized the 1964 election was obvious to most Nigerians [14].

During the Second Republic (1979–1983), the rigging that characterized the election was even worse than the First Republic. Of the five political parties that contested the August 11, 1979 presidential elections, three rejected the results on the ground that it was full of flaws. Similarly, the 1983 elections were believed to have been massively rigged in some states such as Oyo, Ondo, Anambra, Cross-River, and Imo among others [15]. Perhaps, the freest and fairest election in the history of Nigeria was the presidential election of the aborted Third Republic on June 12, 1993 [16].

The Fourth Republic 1999 election was also not credible because of so many irregularities, although it was generally believed to be violence-free. The results show wide variation between the total number of voters at polling units and the collated results from many states [4]. There was a peaceful civilian transition, which was the first in Nigeria political history, in 2003. But, the 2003 election was more openly rigged and flawed than the preceding election in 1999, and far bloodier [8]. More so, this apparently phantom election recorded extraordinary high turnout figures generally in excess of 90 percent [17].

According to reports, the worst election in the history of Nigeria, and perhaps in the world, was conducted in 2007 [8]. The election was full of many irregularities such as late arrival of voting materials in various polling units, insufficient polling materials, issues with ballot papers and voting, snatching and destruction of ballot boxes, no voting exercise in some polling units, intimation of voters by security agencies, perpetration of electoral fraud by government officials, and disenfranchising opponents supporters by omitting candidate names on ballot paper [18].

Observers commended the 2011 election as part of the most successful in the political history of Nigeria. However, reports also reveal snatching of ballot boxes, falsification of electoral results and under age voting in some states of the country [19]. Likewise, the 2015 general elections were marred by malpractices, despite being largely peaceful. The 2019 elections were also reported to be impaired by multiple voting, result manipulation and intimidation by security agencies [20, 21].

The commonest approaches often adopted in addressing election fraud and associated issues are for the aggrieved parties to go to court or election tribunals [6, 11]. Besides the judicial approaches, scholars have suggested the possibility of statistical approach which focus on deductions that could be made from digital patterns of electoral results [22, 23]. A typical statistical approach is election forensics.


3. The election forensics approach

Election forensics is a name coined to describe a nascent field of social science that intends to develop data analysis tools that can be used to detect discrepancy in election outcomes [24, 25]. Election fraud may take different forms, hence its measurement poses a fundamental difficulty. Generally, for quantitative cross-national studies, scholars measure election fraud based on the assessment by election observers. For single-country studies, scholars rely on petitions filed by the aggrieved and media reports in measuring election fraud. However, there are concerns about bias and consistency in adopting the aforementioned approaches because participants with different expectations, interests and standards across elections generate these measures. Hence, it is likely to underestimate the degree of election fraud in modern democracies, even in those elections that are perceived to be fairly free and fair. This implies the need to be cautious about empirical findings in the election forensics field [26, 27, 28, 29].

One of the major problems in uncovering fraud in electoral data is recognizing what makes the fraudulent data different from the valid data. Yet, to be absolutely sure of the validity of an election is often impossible. An appealing option in solving this major problem is to find out likely evidences of irregularities in the electoral data using deviation from known patterns or mathematical algorithms [30]. Hence, two of the most common electoral forensic techniques are based on Benford’s Law and agent based models.

3.1 Benford’s law

Benford’s Law originated with Frank Benford, who observed that the later pages of his common logarithm tables were not as worn out as the first few pages [31]. Hence, he hypothesized that viewers are more interested in common logarithms with lower first digits (1, 2, 3) than those with higher first digits (7, 8, 9). The digit at the leftmost end is the first digit and zero is not admissible as first digits. He also observed a marked skew favoring the lower digits in an empirical test of the first digits of 20 different lists of numbers having 20,229 records. Based on this observation, Benford made some assumptions which relate to geometric pattern of natural phenomenon. Although it can be argued that the data sets used by Benford have no relation to natural phenomenon. Nevertheless, Benford presented the expected pattern of distribution of first digits in a tabular form.

Since there is no mathematical derivation, scholars considered Benford’s Law as a law of nature. Therefore, the base-variance and scale-variance conditions have been used in explaining the law. Scholars have shown that both the base invariance and scale invariance conditions are satisfied by Benford’s Law [32, 33, 34]. The base-variance condition states that if the distribution of leading digits is governed by a universal law, the same distribution should occur if the numerical basis of the digits change arbitrarily. Similarly, the scale invariance conditions says that the distribution of leading digits should be independent of the units of measuring the numbers. This implies that the distribution of leading digits should be the same if the numbers are converted from one unit (such as km) to another (such as miles).

Benford’s Law characterizes the distribution of first significant digits (FSD) observed in large sets of data. Generally, the principle is that the most frequent leading digits in data sets is digit 1 while the least frequent digit is 9. This means that the occurrence of leading digits continuously decrease as you check from digit 1 to 9. However, apart from the leading digits, combination of digits (for example first two digits or last two digits, among others) can also be applied in advanced analysis. Also, additional test can be added to manipulate the law if it does not perfectly fit into some certain real life situation [35].

Benford’s Law has been demonstrated to hold with a large number of data sets and has been used to study election fraud [10, 36, 37]. Different studies have focused on the deviation of first, second and/or last digits of electoral data as indicators of possible fraud. However, studies have shown that Benford’s Law alone is not sufficient to provide useful insight into irregularities in electoral returns [25].

3.2 Agent based model

Agent based model is an approach that is well suited in determining the possible outcomes when many rational agents which are bounded, under certain rules and conditions, continuously relate with each other in a changing and evolving setting [38]. Agent based modeling has been deployed to analyze electoral outcomes [30, 39]. In applying the agent based model for simulation, scholars have adopted several approaches. One of these approaches is the adoption of game theory in a decision making scenario. The focus is to analyze the option of best strategy in diverse conflicting cases so as to achieve individual objectives out of common goals [40]. Other methods are the application of scripting techniques based on object-oriented methods [41] and the application of the Monte Carlo analysis [30]. Nevertheless, agent based models are often sufficiently complex that deriving explicit solutions for quantitative aspects of their macroscopic behavior is often impractical if not impossible, and hence they are often analyzed using Monte-Carlo methods [42].

Monte Carlo analysis is a general term that refers to research that employs random numbers, usually in the form of a computer simulation [43]. The Monte-Carlo approach has been specifically adopted in detecting suspicious electoral data [44, 45]. The focus is on deviation of distributional patterns of actual data from the simulated data.

3.3 Other election forensic approaches

A lot of scholars have developed election forensic indicators and procedures and also identified the techniques that can be applied to detect election fraud [10, 22, 25]. The identified election forensic techniques include the detection of anomalies in turnout distributions and in the relationship between turnout and share of votes; investigating irregularities in sequence of votes between elections; investigating irregularities in the distribution of digits; and investigating deviations between the actual votes and predicted votes [25]. Turnout represents the percentage of electorates or registered voters who actually vote in an election. Election might be considered fraudulent if there are anomalies in the turnout or in the relationship between turnout and vote counts. More so, vote shares of recent elections could be predicted using a model of past elections. Deviation of the results of the recent elections from the model raises suspicion for fraud. In addition, there is an expected pattern for the distribution of digits in a fraud-free election. Variation between the distribution of digits in the election results and the expected distribution also raises suspicion for fraud.


4. The way forward for improved elections in Nigeria

The conduct of elections in Nigeria follows the guidelines set by INEC. According to INEC guidelines [46], a person is eligible to vote at an election conducted by the commission if he/she is a Nigerian, registered as voter and with a valid Permanent Voter’s Card (PVC) at his/her polling unit. Voters are expected to be accredited at the polling units before casting their ballots. The accreditation process comprises reading of the PVC and the authentication of the voter’s fingerprint using the Smart Card Reader (SCR); checking the register of voters and inking of the cuticle of the specified finger of the voter to indicate he/she has been accredited to vote in that election. At the close of voting, the Presiding Officer counts, records and announces the votes scored by each political party.

The result sheets, together with all other used and unused materials from the polling units are moved to the Registration Area Collation Centres, and thereafter to the Local Government Area (LGA) collation centres. The results are batched and transferred from the LGA collation centres to the State Collation Centres not later than 48 hours after each poll. The results are forwarded from the State Collation Centres to the Presidential Returning Officer who, in return, forwards the results to the Chief Returning Officer. The Chief Returning Officer is the Chairman of INEC. He collates and announces the vote counts of candidates and declares the winner of the presidential election.

The major issue with the present approach adopted by INEC is in the manual collation and transmission of presidential electoral results. Quite a number of Nigerians are of the opinion that results are tampered with during collations, and not at the final stage of declaration by the Chief Returning Officer. Hence, the need for electronic transmission of results. The conduct of elections as described above is often fraught with anomalies. In the next sections, we suggest the possible ways of improving the conduct of elections in Nigeria.

4.1 Addressing the problem of multiple voting and collation

Although Smart Card Reader (SCR) has been adopted, since the 2015 general elections, as a means of verifying Permanent Voter’s Card (PVC), observations and reports have shown that the SCRs were abandoned in some situations where they failed or were inconsistent. More so, a major issue with the guidelines on use of smart card reader (SCR) is that if the SCR reads a PVC but does not accept the thumbprint of a voter whose name is on the voter’s register, the voter is allowed to do a thumbprint on the voter’s register, add his/her phone number and go ahead to collect ballot paper. How does INEC detect a voter with more than one PVC attempting to vote at different polling units since he/she can vote when SCR rejects his/her thumbprint? How does a thumbprint and phone number on voter’s register solve such problem? Considering the historical level of fraud in the system, how can the public be assured that due diligence would be followed afterwards to match the thumbprint and phone number in the case of multiple votes? Hence, there is need to ensure that all SCRs deployed for verification of PVCs are in good working state.

Apart from the issues with verification, so many Nigerians would argue that the problem with electoral process in the country is not in voting, but “counting”. A good way to achieve transparency and openness during collation of election results is to ensure that the results are pasted for public view at all collation centers, not just at the polling units. This could help to build public trust in the election process as fraudulent acts are believed to occur at collation centres.

4.2 Electoral reform

It is common knowledge that the validity of all presidential elections conducted by Independent National Electoral Commission (INEC) in Nigeria since 1999 has been contested up to the Supreme Court. There is also a Supreme Court ruling that the INEC manual that recognizes the use of the Smart Card Reader (SCR) in authenticating voters in any election is illegal. Hence, it is no surprise that the history of Nigeria’s democracy demonstrates so much electoral and political animosity which has, in part, threatened the corporate existence of the nation. The conduct of elections in any country is crucial to the survival of her democracy. Credible, free and fair elections with appropriate legal framework are prerequisites to sustainable democracy.

The challenges with electoral process in Nigeria include vote buying, monetization of politics, underage voting, election violence, manipulated votes, inappropriate legislative framework, long duration of election dispute resolution, and lack of independence of electoral commissions and so on. To resolve these challenges, it is important for the electoral commission (INEC) to be independent of the executive arm of government. The appointment of the head of the commission as well as the commission’s budget should be carried out independently. INEC should also have the freedom and support required to reform the electoral process in Nigeria.

Up till date, there are various enactments of the legislative and executive arms of government interfering with the constitutional powers of INEC to self-regulate the electoral process. For example, some electoral acts passed by the legislative arm contains provision prohibiting electronic transmission of election results and use of e-voting machine. INEC has the constitutional powers to order elections, conduct elections, decide on how to transmit the results (either electronically or not), count votes, collate results, declare and publish the results, among others. Therefore, there is need for the legislative arm to support and work with INEC in improving the electoral process in Nigeria.

4.3 Adopting election forensics

An error-free data generating process is expected to produce vote counts with a pattern which shows that the counts are close to a natural process. Election forensic techniques could be applied to find patterns in the distribution of election data that deviate from the expected distribution. The presence of such deviation in the distributional pattern of election data suggests that the data has been manipulated. The adoption of election forensic reports could help INEC to avoid the time and resources wasted in recounting votes and/or rerunning elections in order to address election petitions or related issues. More so, observations have shown that a rerun of election does not guarantee a fair and/or acceptable result. With more insight into suspicious electoral data patterns, INEC might uncover better perception of how to curb election fraud. This could also help to improve INEC’s capacity to take preventive measures in future election cycles.

Election forensic approaches (such as Monte Carlo simulation, Benford’s Law and other proven techniques) should be combined to test for anomalies in election data (vote counts and voters’ turnout). This is necessary because, in isolation, none of the methods is sufficient enough to give a clear view on the suspicion of election malpractice. If all the methods lead to similar indication of anomalies in the election data, there is a greater confidence in the suspicion that fraud has occurred. However, the result from the combined election forensic tools might not be sufficient proof to draw conclusion on election fraud.

Therefore, it is important to check for the influence of voters’ preferences and other factors on the results of the analysis. This will help to ascertain if the deviation in pattern detected during the analysis could be attributed to election fraud, rather than factors such as geographical or cultural influences. If the results of the analysis indicate that the election data might have been affected by other factors, the result of the tests should be compared with other election reports, such as election audit reports and election observer’s reports, before drawing conclusion on election malpractices. Information from on-the-ground monitors of elections could give more insight into malpractices. More so, the combined knowledge gained from the reports of the election forensic analysis and the other election reports from on-the-ground assessment would help INEC and other stakeholders to draw an objective and better conclusion. Hence, INEC should consider adjusting the electoral process in line with the findings.


5. Conclusion

Free and fair election is an essential ingredient to the growth of democracy. Although, Nigeria is known to be practicing democracy, the electoral process in Nigeria since the first republic till date reflects all manners of electoral fraud. Hence, this chapter focuses on the issues of irregularities in presidential electoral results in Nigeria and the way forward. The submissions of the authors could also be of great benefits to democracies in Africa as a whole.

This chapter suggests a review of the election collation process and the need to address issues with the use of Smart Card Reader (SCR) in verifying Permanent Voter’s Card (PVC). The electoral body (INEC) should improve on the accreditation process by ensuring that all voters PVCs are verified through the use of SCR, and not through any other dubious means. The chapter also argues that INEC has the constitutional power to self-regulate itself. Hence, the executive and legislative arms of government should work in synergy with INEC to support electronic voting and improve the electoral process in Nigeria.

The authors are of the opinion that the adoption of election forensics in Nigeria electoral process could also help to improve the process. Benford’s Law, Monte Carlo simulation approach and other proven techniques could help to give more insights into polling units and wards with history of anomalous electoral data. The results of the analyses with the election forensic techniques could be crosschecked with reports from on the ground assessment to verify necessary details. It is the submission of the authors that INEC could gain better insights from this approach and take necessary measures to prevent future reoccurrence.


Conflict of interest

No conflict of interest from the authors.


  1. 1. Simidchieva BI, Engle SJ, Clifford M, Jones AC, Peisert S, Bishop M, Clarke LA, Osterweil LJ. Modelling and analyzing faults to improve election process robustness. In: Proceedings of the 2010 Electronic Voting Technology Workshop/Workshop on Trustworthy Elections (EVT/WOTE ‘10). 2010
  2. 2. Maendeleo Policy Forum. Elections in the Sub-Saharan Africa: general trends, challenges and opportunites [Internet]. 2016. Available from: [Accessed: 2017-09-15]
  3. 3. Udu LE. INEC and the 2015 general elections in Nigeria: Matters arising. Research on Humanities and Social Sciences. 2015;5(12):96-108
  4. 4. Ogbeidi MM. A culture of failed elections: Revisiting democratic elections in Nigeria, 1959-2003. HAOL. 2010;21:43-56
  5. 5. Alvarez RM, Hall TE, Hyde SD. Election Fraud: Detecting and Deterring Electoral Manipulation. Washington, DC: Brookings Institution Press; 2008. p. 161
  6. 6. Mebane WR. The wrong man is president! Overvotes in the 2000 presidential election in Florida. Perspectives on Politics. 2004;2(3):525-535
  7. 7. Magaloni B. The game of electoral fraud and the ousting of authoritarian rule. American Journal of Political Science. 2010;54(3):751-765
  8. 8. Onebamhoi ON. Curbing electoral violence in Nigeria: The imperative of political education. International Multidisciplinary Journal, Ethiopia. 2011;5(5):99-110
  9. 9. Howard MM, Roessler PG. Liberalizing electoral outcomes in competitive authoritarian regimes. American Journal of Political Science. 2006;50(2):365-381
  10. 10. Beber B, Scacco A. What the number say: A digit-based test for election fraud. Political Analysis. 2012;20(2):211-234
  11. 11. Animashaun K. Regime character, electoral crisis and prospects of electoral reform in Nigeria. Journal of Nigeria Studies. 2010;1(1):1-33
  12. 12. Onoja A. Nature, character and outcomes of post election challenges in Nigeria. Journal of the Historical Society of Nigeria. 2009;18:79-104
  13. 13. Omodia SM. Election, governance and the challenge of national integration in the Nigerian fourth republic. British Journal of Arts and Social Sciences. 2012;5(2):307-314
  14. 14. Ojo EO. Leadership crisis and political instability in Nigeria, 1964-1966: The personalities, the parties and the policies. Global Advanced Research Journal of History, Political Science and International Relation. 2012;1(1):006-017
  15. 15. Awopeju A. Election rigging and the problems of electoral act in Nigeria. Afro Asian Journal of Social Sciences. 2011;2:1-17
  16. 16. Osimen GU, Ologunowa CS. 2011 post-electoral violence in Nigeria: Lesson for 2015 general election. American International Journal of Research in Humanities, Arts and Social Sciences. 2013;4(1):45-55
  17. 17. Osinakachukwu NP, Jawan JA. The electoral process and democratic consolidation in Nigeria. Journal of Politics and Law. 2011;4(2):128-138
  18. 18. Kia B. Electoral corruption and democratic sustainability in Nigeria. IOSR Journal of Humanities And Social Science. 2013;17(5):42-48
  19. 19. Yusuf I, Zaheruddin O. Challenges of electoral processes in Nigeria’s quest for democratic governance in the fourth republic. Research on Humanities and Social Sciences. 2015;5(22):1-10
  20. 20. European Union Election Observation Mission. Second Preliminary Statement on 2015 General Elections of the Federal Republic of Nigeria [Internet]. 2015. Available from: [Accessed: March 23, 2015]
  21. 21. European Union Election Observation Mission. Nigeria 2019 Final Report: General Elections 23 February, 9 and 23 March 2019 [Internet]. 2019. Available from: [Accessed: August 4, 2020]
  22. 22. Myagkov M, Ordeshook PC, Shaikin D. The Forensics of Election Fraud: With Applications to Russia and Ukraine. New York: Cambridge University Press; 2009
  23. 23. Leemann L, Bochsler D. A systematic approach to study electoral fraud. Electoral Studies. 2014;35:33-47
  24. 24. Mebane WR. A layman's Guide to Statistical Election Forensics. Election Guide Digest. Washington DC: IFES; 2010
  25. 25. Levin I, Alvarez RM. Introduction to the virtual issue: Election fraud and electoral integrity. Political Analysis. 2012;20(V4):1-7
  26. 26. Lehoucq F. Electoral fraud: Cause, types, and consequences. Annual Review of Political Science. 2003;6:233-256
  27. 27. Kelley J. Monitoring Democracy: When International Election Observation Works, and Why it Often Fails. Princeton, NJ: Princeton University Press; 2012
  28. 28. Birch S. Electoral systems and election misconduct. Comparative Political Studies. 2007;40(12):1533-1556
  29. 29. Ichino N, Schundeln M. Deterring or displacing electoral irregularities? Spillover effects of observers in a randomized field experiment in Ghana. The Journal of Politics. 2012;74(1):292-307
  30. 30. Cantu F, Saiegh SM. Fraudulent democracy? An analysis of Argentina’s infamous decade using supervised machine learning. Political Analysis. 2011;19(4):409-433
  31. 31. Benford F. The law of anomalous numbers. Proceedings of the American Philosophical Society. 1938;78(4):551-572
  32. 32. Raimi R. The first digit problem. American Mathematical Monthly. 1976;83(7):521-538
  33. 33. Fewster RM. Teachers corner: A simple explanation of Benford’s law. Amer. Statist. 2009;63(1):26-32
  34. 34. Judge G, Schechter L. Detecting problems in survey data using Benford’s law. Journal of Human Resources. 2009;44:1-24
  35. 35. Petucci SD. Benford’s law: Can it be used to detect irregularities in first party automobile insurance claims? Journal of Economic Crime Management. 2005;3(1):1-35
  36. 36. Mebane WR. Election forensics: Vote counts and Benford’s law. Davis, CA: Political Methodology Society: University of California at Davis. 2006
  37. 37. Tunmibi S, Olatokun W. Application of digits based test to analyse presidential election data in Nigeria. Commonwealth & Comparative Politics. 2021;59(1):1-24
  38. 38. MacGregor JN, Edward PC, Thomas CO. A comparison of heuristic and human performance on open versions of the traveling salesperson problem. Journal of Problem Solving. 2006;1(1):33-43
  39. 39. Quratul-Ann, M. Virtual Pakistan 2013: An agent-based modeling analysis. CUREJ: College Undergraduate Research Electronic Journal, University of Pennsylvania. 01 April 2013. Available from:
  40. 40. Nagaraju V, VIjender C, Bikshapathi V, Lingam PR. Application of game theory to assess conflicting election strategies – An empirical study. International eJournal of Mathematics and Engineering. 2012;196:1875-1880
  41. 41. Wilensky U, Rand W. An Introduction to Agent-Based Modelling: Modelling Natural, Social and Engineered Complex Systems with NetLogo. Cambridge, MA: MIT Press; 2011
  42. 42. Phelps S. Applying dependency injection to agent-based modelling: The JABM framework. Centre for Computational Finance and Economic Agents (CCFEA) Working Paper: WP056-12. 2012
  43. 43. Johnson PE. Monte Carlo Analysis in Academic Research [Thesis]. Department of Political Science and Center for Research Methods and Data Analysis. Kansas, United States: University of Kansas; 2011
  44. 44. Kobak D, Shpilkin S, Pshenichinkov M. Integer percentages as electoral falsification fingerprints. Preprint arXiv. 2014;1410:6059
  45. 45. Tunmibi S, Olatokun W. Monte Carlo simulation of vote counts from Nigeria presidential elections. Cogent Social Sciences. 2021;7(1):1914397
  46. 46. INEC. Regulations and Guidelines for the Conduct of Elections [Internet]. 2019. Available from: [Accessed: March 5, 2022]

Written By

Sunday Tunmibi and Wole Olatokun

Submitted: 28 April 2022 Reviewed: 02 May 2022 Published: 17 August 2022