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Election forensics

Election forensics research overview

During the last two decades, a special interest has been shown in the application of election forensics methods to election results in countries where there were grounds for suspicion that the results had been manipulated. At the same time, the election results in countries with stable democracies were analyzed, so the results of that analysis could be used as a benchmark against which the results of the analysis in countries where election frauds were found were compared. The election results of the parliamentary and presidential elections as well as the referendums, both at the national and regional levels, were analyzed. In several cases (e.g. Germany, Russia and Venezuela) the results from several election cycles were analyzed, which made it possible to conclude whether there was an increase or decrease in electoral fraud in the observed country over time.

There are many variations in how election fraud can be reported. Accordingly, there are also statistical tools that correspond to the specific manipulation that appeared in the election results. So the analysis can go in two directions. In the first case, it is assumed what should happen in elections where there is no manipulation. The other direction assumes what should happen if manipulation is attempted. When different methods of analysis lead to similar statistical indications – for example, an indication that there is a high probability that there are anomalies in the reported official data – this gives strength to our conclusions (i.e. that the election results were manipulated).

The first approach to detection of anomalies and fraud focuses on the figures of votes obtained as indicators of anomalies. This approach has been most often used in previous empirical research on election results, as can be seen in Table 1 (column: Tools based on numbers). The remaining tools and approaches for detecting electoral data manipulation (column: Other tools and approaches in Table 1) rely on the analysis of turnout data (e.g., deviations from the expected shape of the voter turnout distribution or the relationship between turnout and vote share for a leading candidate or electoral list ), invalid votes (e.g. the absence of invalid votes with a high percentage of votes for the leading candidate or electoral list) and finally the simulation method (data on the turnout, valid votes and the number of votes won by candidates or electoral lists at polling stations are used in the assessment of occurrence and size extreme fraud and fraud growth).

Table 1 provides an overview of possible election frauds research by country, type of election (parliamentary, presidential and referendum) and the type of methodological approach used in each research.

Table 1. Review of possible election frauds research

SourceCountryPresidentialParliamentaryReferendumTools and methodological approaches election results analysis
Digit-based toolsOther tools
Agyemany, Nortey, Minkah & Asah-Asante (2023)Ghana2012, 2020  Prva cifra, prve dve cifre, 2BL, Hi-kvadrat test, Srednja apsolutna odstupanja, Mantissa lučni test, Hartiganov test unimodalnosti, koeficijent bimodalnosti, asimetričnost, spljoštenost, srednja vrednost poslednje cifre 
Beber& Sacco (2012)Sweden Senegal Nigeria  2000, 2007 20032002 Poslednja cifra i par poslednje i pretposlednje cifre 
Breunig & Goerres (2011)Germany 1990, 1994, 1998, 2002, 2005 2BLKorelacija i metod najmanjih kvadrata
Cantu (2019)Mexico1988   Konvolucione neuronske mreže
Deckert, Myagkov & Ordeshook (2011)Ukraine Russia2004  2007 2004, 2008 2BLSimulacija
Eskov (2013)Canada    Izborni otisak prstiju, dijagram rasturanja, korelacija, prostorna autokorelacija
Filho, Silva & Carvahlo (2022)Brazil2018  2BL, srednja vrednost poslednje cifre, analiza frekvencije poslednje cifre 0 i 5Korelacija između procenta glasova pobednika i izlaznosti birača, empirijski raspored proporcije glasova pobednika
Fernández-Gracia & Lacasa (2017)Spain 2015, 2016 Prva cifra, 2BL, Hi-kvadrat, Mantissa lučni testIzborni otisak prstiju, funkcionalna analiza socijalnih mreža, dvostranački indeks
Forsberg (2020)Afghanistan2009  Prva cifra 
Forsberg (2020)Sri Lanka1994 – 2019   Beta-binomna regresija sa osvojenim glasovima i nevažećim listićima
Friedman, Kolakaluri & Rege (2020)USA 2018 Prva cifra, Kolmogorov-Smirnov test, kanonička korelaciona analiza, t-test 
Gorodnichenko, Mylovanov & Goriunov (2014)Ukraine 2014 Prva cifraKumulativni broj glasova pobednika, regresiona analiza
Gueron & Pellegrini (2022)Brazil, county Bahia 1994 Prva cifra 
Hausmann & Rigobon (2011)Venezuela  2004 Regresiona analiza
Hussein (2018)Sweden Uganda  20162018 Poslednja cifra, Hi-kvadrat test 
Jiménez & Hidalgo (2014)Venezuela1998, 2000, 2006, 20122005, 20101999, 2004, 2007, 20092BL, Hi-kvadrat test,Izborni otisak prstiju, Gaussov kvadratni klasifikator, kumulativni broj glasova pobednika, Z-raspored, bootstrap model
Jiménez, Hidalgo & Klimek (2017)Various    Izborni otisak prstiju, konturni dijagrami za mala i velika biračka mesta, test randomizacije, unakrsna validacija
Ketchley (2019)Egypt2018  Većina alata iz Electoral Forensics Toolkit autora MebaneIzborni otisak prstiju, konačni model mešavine
Klimek, Aykaç & Thurner (2023)Türkiye2023   Izborni otisak prstiju, kumulativni broj glasova pobednika
Klimek, Jiménez, Hidalgo, Hinteregger & Thurner (2018)Türkiye    Izborni otisak prstiju, kumulativni broj glasova pobednika, konturni dijagrami za mala i velika biračka mesta
Klimek, Yegorov, Hanel & Thurner (2012)Various    Izborni otisak prstiju, kumulativni broj glasova pobednika, grafikoni asimetrije i spljoštenosti
Kobak, Shpilkin & Pshenichnikov (2016b)Russia20122011  Izborni otisak prstiju, histogram osvojenih glasova i izlaznosti birača
Leemann & Bochsler (2013)Switzerland  2011Poslednja cifra, Hi-kvadrat testRegresiona analiza
Lioy (2021)Italy 2006 Prva i poslednja cifra, Hi-kvadrat testRegresiona analiza, testovi rasporeda
Lukinova, Myagkov & Ordeshook (2011)Russia 2000 – 2008  Histogram, funkcija gustine, Regresiona analiza
Mebane (2010b)USA 1980 – 2000 2BLSimulacija
Mebane (2010b)Mexico 2006 2BLSimulacija
Mebane (2010b)Iran2009  2BLSimulacija
Mitre (2021)USA2020   Izborni otisak prstiju
Myakgov, Ordeshook & Shaikin (2009)Russia20041995, 1999, 2000, 2003, 2004, 20071993 Histogram, regresiona analiza
Myakgov, Ordeshook & Shaikin (2009)Ukraine1999, 20042006, 2007  Histogram, regresiona analiza
Nogueira (2023)Brazil2022  Raspored poslednje cifre, poslednja cifra je 0 ili 5,Simulacija na osnovu uzorka biračkih mesta,
Shanaev, Shuraeva & Ghimire (2021)USA 2020 Prva cifra, prve dve cifre 
Shikano & Mack (2011)Germany 2009 2BL, Hi-kvadrat test 
Skovoroda & Lankina (2017)Russia2012  Raspored poslednje cifreMultinomijska logistička regresija
Шень (2020)Russia2008, 2012, 20182009, 20112020 Izborni otisak prstiju, histogram osvojenih glasova i izlaznosti birača
Zhang, Alvarez & Levin (2019)Argentina 2015  Mašinsko učenje

Literature

Agyemang, E. F., Nortey, E. N. N., Minkah, R., & Asah-Asante, K. (2023). Baseline comparative analysis and review of election forensics: Application to Ghana’s 2012 and 2020 presidential elections. Heliyon, 9, e18276.

Beber, B., & Sacco, A. (2012). What the numbers say: A digit-based test for election fraud. Political Analysis, 20, 211–234. https://doi.org/10.1093/pan/mps003

Bërdufi, D. (2014). Statistical detection of vote count fraud (2009 Albanian parliamentary election and Benford‘s law). Mediterrian Journal of Social Sciences, 5(2), 755

Cantu, F. (2019). The fingerprints of fraud: Evidence from Mexico‘s 1988 presidential election. American Political Science Review, 113(3), 710-726.

Deckert, J., Myagkov, M., & Ordeshook, P. C. (2011). Benford’s law and the detection of election fraud. Political Analysis, 19, 245-268, doi:10.1093/pan/mpr014

Eskov, A. (2013). Spatial patterns and irregularities of the electoral data: General elections in Canada. Master of Science Dissertation, Universitat Jaume, Departament de Matemàtique, https://core.ac.uk/download/157628338.pdf

Fernández-Gracia, J., & Lacasa, L. (2017). Bipartisanship breakdown, functional networks and forensic analysis in Spanish 2015 and 2016 national elections. ArXiv: 1607.02841v2.

Filho, D. F., Silva, L., & Carvalho, E. (2022). The forensics of fraud: Evidence from the 2018 Brazilian presidential election. Forensic Science International: Synergy, 5, 100286.

Forsberg, O. J. (2020). Understanding elections through statistics: Polling, prediction, and testing. Boca Raton, FL : CRC Press.

Friedman, E., Kolakaluri, R., & Rege, M. (2020). Benford‘s law applied to precinct level election data. Issues in Information Systems, 21(2), 238-247.

Gorodnichenko, Y., Mylovanov, T., & Goriunov, D. (2014). Election fraud in 2014 parliamentary elections. Vox Ukraine. https://voxukraine.org/en/election-fraud-in-2014-parliamentary-elections

Gueron, E., & Pellegrini, J. (2022). Application of Benford–Newcomb law with base change to electoral fraud detection. Physica A 607, 128208. https://doi.org/10.1016/j.physa.2022.128208

Hausmann, R., & Rigobon, R. (2011). In search of the black swan: Analysis of the statistical evidence of fraud in Venezuela. Statistical Science, 26(4), 543–563. https://doi.org/10.1214/11-STS373 

Hussein, A. (2018). An evaluation of last digit-based test as a tool for electoral fraud detection. Bachelor Thesis in Statistics, University of Gothenburg, School of Business, Economics and Law.

Jiménez, R., & Hidalgo, M.(2014). Forensic analysis of Venezuelan elections during the Chávez presidency. PLoS ONE 9(6): e100884. doi:10.1371/journal.pone.0100884

Jiménez, R., Hidalgo, M., & Klimek, P. (2017). Testing for voter rigging in small polling stations. Science Advances, 3, e1602363. https://doi.org/10.1126/sciadv.1602363 PMID: 28695193

Ketchley, N. (2019, September 26). Fraud in the 2018 Eqyptian presidential election? https://doi.org/10.31235/osf.io/4wf9s

Klimek, P., Aykaç, A., & Thurner, S. (2023). Forensic analysis of the Turkey 2023 presidential election reveals extreme vote swings in remote areas. PloS ONE, 18(11), e0293239, https://doi.org/10.1371/journal.pone.023239

Klimek, P., Jiménez, R., Hidalgo, M., Hinteregger, A., & Thurner, S. (2018). Forensic analysis of Turkish elections in 2017–2018. PLoS ONE, 13(10), e0204975. https://doi.org/10.1371/journal.pone.0204975, PMID: 30289899

Klimek, P., Yegorov, Y., Hanel, R., & Thurner, S. (2012). Statistical detection of systematic election irregularities. Proceedings of the National Academic of Science USA, 109: 16469–16473. https://doi.org/10.1073/pnas.1210722109 PMID: 23010929

Kobak, D., Shpilkin, S., & Pshenichnikov, M. (2012, May 18). Statistical anomalies in 2011-2012 Russian election revealed by 2D correlation analysis. arXiv:1205.0741v2.

Kobak, D., Shpilkin, S., & Pshenichnikov, M. (2016a). Integer percentages as electoral falsification fingerprints. The Annals of Applied Statistics, 10(1), 54-73.

Kobak, D., Shpilkin, S., & Pshenichnikov, M. (2016b, August). Statistical fingerprints of electoral fraud? Significance, 20-23.

Leemann, L., & Bochsler, D. (2014). A systematic approach to study electoral fraud. Electoral Studies, 35, 33-47.

Lioy, A. (2021). The blank ballot crisis: A multi-method study of fraud in the 2006 Italian election. Contemporary Italian Politics, 13(3), 352-381. https://doi.org/10.1080/23248823.2021.1955190

Lukinova, E., Myagkov, M., & Ordeshook, P. C. (2011). Metastasised fraud in Russia‘s 2008 presidential election. Europe-Asia Studies, 63(4), 603-621.

Mebane, Jr., W. R. (2010a). Fraud in the 2009 presidential election in Iran?. Chance, 23(1), 6–15. DOI: 10.1080/09332480.2010.10739785

Mebane, Jr., W. R. (2010b).  Election fraud or strategic voting. Prepared for presentation at the Annual Meeting of the Midwest Political Science Association, Chicago, IL, April 22–25, 2010.

Myakgov, M., Ordeshook, P. C., & Shaikin, D. (2009). The forensics of election fraud: Russia and Ukraine. Cambridge University Press.

Nogueira, A. J. A. (2023). Statistical methods and electoral integrity: The 2022 Brazilian elections. Beijing Law Review, 14, 727-738. https://doi.org/10.4236/blr.2023.142039

Shanaev, S., Shuraeva, A., & Ghimire, B. (2020). Detecting anomalies in the 2020 US presidential election votes with Benford’s law (November 11, 2020). Available at SSRN: https://ssrn.com/abstract=3728626 or http://dx.doi.org/10.2139/ssrn.3728626

Shikano, S., & Mack, V. (2011). When does the second-digit Benford‘s law-test signal an election fraud? Jahrbücher f. Nationalökonomie u. Statistik, 231(5+6), 719-732.

Skovoroda, R., & Lankina, T. (2017). Fabricating votes for Putin: New tests of fraud and electoral manipulations from Russia. Post-Soviet Affairs, 33(2), 100–123. DOI: https://doi.org/10.1080/1060586X.2016.1207988

Шень, A. (2020). Выборы и статистика: казус «Единой России» (2009–2020). arXiv: 1204.0307v4.

Zhang, M., Alvarez, R. M., & Levin, I. (2019). Election forensics: Using machine learning and synthetic data for possible election anomaly detection. PLoS ONE, 14(10): e0223950. https://doi.org/10.1371/journal.pone.0223950

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Director of Wellington based My Statistical Consultant Ltd company. Retired Associate Professor in Statistics. Has a PhD in Statistics and over 45 years experience as a university professor, international researcher and government consultant.