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
| Source | Country | Presidential | Parliamentary | Referendum | Tools and methodological approaches election results analysis | |
| Digit-based tools | Other tools | |||||
| Agyemany, Nortey, Minkah & Asah-Asante (2023) | Ghana | 2012, 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 2003 | 2002 | Poslednja cifra i par poslednje i pretposlednje cifre | ||
| Breunig & Goerres (2011) | Germany | 1990, 1994, 1998, 2002, 2005 | 2BL | Korelacija i metod najmanjih kvadrata | ||
| Cantu (2019) | Mexico | 1988 | Konvolucione neuronske mreže | |||
| Deckert, Myagkov & Ordeshook (2011) | Ukraine Russia | 2004 | 2007 2004, 2008 | 2BL | Simulacija | |
| Eskov (2013) | Canada | Izborni otisak prstiju, dijagram rasturanja, korelacija, prostorna autokorelacija | ||||
| Filho, Silva & Carvahlo (2022) | Brazil | 2018 | 2BL, srednja vrednost poslednje cifre, analiza frekvencije poslednje cifre 0 i 5 | Korelacija 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 test | Izborni otisak prstiju, funkcionalna analiza socijalnih mreža, dvostranački indeks | ||
| Forsberg (2020) | Afghanistan | 2009 | Prva cifra | |||
| Forsberg (2020) | Sri Lanka | 1994 – 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 cifra | Kumulativni 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 | 2016 | 2018 | Poslednja cifra, Hi-kvadrat test | ||
| Jiménez & Hidalgo (2014) | Venezuela | 1998, 2000, 2006, 2012 | 2005, 2010 | 1999, 2004, 2007, 2009 | 2BL, 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) | Egypt | 2018 | Većina alata iz Electoral Forensics Toolkit autora Mebane | Izborni otisak prstiju, konačni model mešavine | ||
| Klimek, Aykaç & Thurner (2023) | Türkiye | 2023 | 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) | Russia | 2012 | 2011 | Izborni otisak prstiju, histogram osvojenih glasova i izlaznosti birača | ||
| Leemann & Bochsler (2013) | Switzerland | 2011 | Poslednja cifra, Hi-kvadrat test | Regresiona analiza | ||
| Lioy (2021) | Italy | 2006 | Prva i poslednja cifra, Hi-kvadrat test | Regresiona analiza, testovi rasporeda | ||
| Lukinova, Myagkov & Ordeshook (2011) | Russia | 2000 – 2008 | Histogram, funkcija gustine, Regresiona analiza | |||
| Mebane (2010b) | USA | 1980 – 2000 | 2BL | Simulacija | ||
| Mebane (2010b) | Mexico | 2006 | 2BL | Simulacija | ||
| Mebane (2010b) | Iran | 2009 | 2BL | Simulacija | ||
| Mitre (2021) | USA | 2020 | Izborni otisak prstiju | |||
| Myakgov, Ordeshook & Shaikin (2009) | Russia | 2004 | 1995, 1999, 2000, 2003, 2004, 2007 | 1993 | Histogram, regresiona analiza | |
| Myakgov, Ordeshook & Shaikin (2009) | Ukraine | 1999, 2004 | 2006, 2007 | Histogram, regresiona analiza | ||
| Nogueira (2023) | Brazil | 2022 | 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) | Russia | 2012 | Raspored poslednje cifre | Multinomijska logistička regresija | ||
| Шень (2020) | Russia | 2008, 2012, 2018 | 2009, 2011 | 2020 | Izborni otisak prstiju, histogram osvojenih glasova i izlaznosti birača | |
| Zhang, Alvarez & Levin (2019) | Argentina | 2015 | Mašinsko učenje | |||
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