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What the Numbers Say: A Digit-Based Test for Election Fraud


  • Beber, Bernd
  • Scacco, Alexandra


Is it possible to detect manipulation by looking only at electoral returns? Drawing on work in psychology, we exploit individuals' biases in generating numbers to highlight suspicious digit patterns in reported vote counts. First, we show that fair election procedures produce returns where last digits occur with equal frequency, but laboratory experiments indicate that individuals tend to favor some numerals over others, even when subjects have incentives to properly randomize. Second, individuals underestimate the likelihood of digit repetition in sequences of random integers, so we should observe relatively few instances of repeated numbers in manipulated vote tallies. Third, laboratory experiments demonstrate a preference for pairs of adjacent digits, which suggests that such pairs should be abundant on fraudulent return sheets. Fourth, subjects avoid pairs of distant numerals, so those should appear with lower frequency on tainted returns. We test for deviations in digit patterns using data from Sweden's 2002 parliamentary elections, Senegal's 2000 and 2007 presidential elections, and previously unavailable results from Nigeria's 2003 presidential election. In line with observers' expectations, we find substantial evidence that manipulation occurred in Nigeria as well as in Senegal in 2007.

Suggested Citation

  • Beber, Bernd & Scacco, Alexandra, 2012. "What the Numbers Say: A Digit-Based Test for Election Fraud," Political Analysis, Cambridge University Press, vol. 20(2), pages 211-234, April.
  • Handle: RePEc:cup:polals:v:20:y:2012:i:02:p:211-234_01

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    Cited by:

    1. Koenig, Christoph, 2015. "Competence vs. Loyalty: Political survival and electoral fraud in Russia’s regions 2000–2012," Economic Research Papers 270014, University of Warwick - Department of Economics.
    2. Christopher Blattman & Horacio Larreguy & Benjamin Marx & Otis R Reid, 2019. "Eat Widely, Vote Wisely ? Lessons from a Campaign Against Vote Buying in Uganda," SciencePo Working papers Main hal-03873791, HAL.
    3. Eric Zitzewitz, 2012. "Forensic Economics," Journal of Economic Literature, American Economic Association, vol. 50(3), pages 731-769, September.
    4. repec:hal:wpspec:info:hdl:2441/7j1t12vvla8c887v4q18ihljej is not listed on IDEAS
    5. Casas, Agustín & Díaz, Guillermo & Trindade, André, 2017. "Who monitors the monitor? Effect of party observers on electoral outcomes," Journal of Public Economics, Elsevier, vol. 145(C), pages 136-149.
    6. Poulsen, Jonas, 2013. "After Apartheid: The Effects of ANC Power," Working Paper Series 2013:17, Uppsala University, Department of Economics.
    7. Poulsen, Jonas, 2013. "After Apartheid: The Effects of ANC Power," Working Paper Series, Center for Fiscal Studies 2013:10, Uppsala University, Department of Economics.
    8. Alexandre Donizeti Alves & Horacio Hideki Yanasse & Nei Yoshihiro Soma, 2014. "Benford’s Law and articles of scientific journals: comparison of JCR® and Scopus data," Scientometrics, Springer;Akadémiai Kiadó, vol. 98(1), pages 173-184, January.
    9. Dorina Bërdufi, 2017. "Possible Capture of Votes Fraud in 2015 Local Election in Albania," Academic Journal of Interdisciplinary Studies, Richtmann Publishing Ltd, vol. 6, March.
    10. Koenig, Christoph, 2019. "Patronage and Election Fraud: Insights from Russia’s Governors 2000–2012," CAGE Online Working Paper Series 433, Competitive Advantage in the Global Economy (CAGE).
    11. Petr Wawrosz, 2022. "How Corruption Is and Should Be Investigated by Economic Theory," Economies, MDPI, vol. 10(12), pages 1-23, December.
    12. Benjamin Crost & Joseph H. Felter & Hani Mansour & Daniel I. Rees, 2013. "Election Fraud and Post-Election Conflict: Evidence from the Philippines," HiCN Working Papers 158, Households in Conflict Network.
    13. Lasse Pröger & Paul Griesberger & Klaus Hackländer & Norbert Brunner & Manfred Kühleitner, 2021. "Benford’s Law for Telemetry Data of Wildlife," Stats, MDPI, vol. 4(4), pages 1-7, November.
    14. Montag, Josef, 2015. "Identifying Odometer Fraud: Evidence from the Used Car Market in the Czech Republic," MPRA Paper 65182, University Library of Munich, Germany.
    15. Christopher Blattman & Horacio Larreguy & Benjamin Marx & Otis Reid, 2019. "Eat Widely, Vote Wisely ? Lessons from a Campaign Against Vote Buying in Uganda," SciencePo Working papers hal-03608420, HAL.
    16. Escobari, Diego & Hoover, Gary A., 2024. "Late-Arriving Votes and Electoral Fraud: A Natural Experiment and Regression Discontinuity Evidence from Bolivia," World Development, Elsevier, vol. 173(C).
    17. Timothy Frye & John Reuter & David Szakonyi, 2012. "Political Machines at Work: Voter Mobilization and Electoral Subversion in the Workplace," HSE Working papers WP BRP 08/PS/2012, National Research University Higher School of Economics.
    18. Marius Jula, 2015. "Using R for Identification of Data Inconsistency in Electoral Models," Romanian Statistical Review, Romanian Statistical Review, vol. 63(3), pages 101-108, September.
    19. Nicolae-Marius Jula, 2014. "Software solutions for identifying outliers," Computational Methods in Social Sciences (CMSS), "Nicolae Titulescu" University of Bucharest, Faculty of Economic Sciences, vol. 2(2), pages 05-14, December.
    20. Oana Borcan, 2016. "The illicit beneficts of local party alignment in national elections," University of East Anglia School of Economics Working Paper Series 2016-10, School of Economics, University of East Anglia, Norwich, UK..
    21. Hygor P M Melo & Nuno A M Araújo & José S Andrade Jr., 2019. "Fundraising and vote distribution: A non-equilibrium statistical approach," PLOS ONE, Public Library of Science, vol. 14(10), pages 1-9, October.
    22. repec:hal:spmain:info:hdl:2441/7j1t12vvla8c887v4q18ihljej is not listed on IDEAS
    23. Callen, Michael & Long, James D., 2015. "Institutional corruption and election fraud: evidence from a field experiment in Afghanistan," LSE Research Online Documents on Economics 102931, London School of Economics and Political Science, LSE Library.
    24. Benjamin Crost & Joseph H Felter & Hani Mansour & Daniel I Rees, 0. "Narrow Incumbent Victories and Post-Election Conflict: Evidence from the Philippines," The World Bank Economic Review, World Bank, vol. 34(3), pages 767-789.
    25. Bernhard Rauch & Max G�ttsche & Stephan Langenegger, 2014. "Detecting Problems in Military Expenditure Data Using Digital Analysis," Defence and Peace Economics, Taylor & Francis Journals, vol. 25(2), pages 97-111, April.

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