Hostname: page-component-7c8c6479df-ph5wq Total loading time: 0 Render date: 2024-03-17T08:46:59.255Z Has data issue: false hasContentIssue false

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

Published online by Cambridge University Press:  12 March 2012

Bernd Beber*
Affiliation:
Department of Politics, New York University, 19 West 4th Street, New York, NY 10012. email: alex.scacco@nyu.edu
Alexandra Scacco
Affiliation:
Department of Politics, New York University, 19 West 4th Street, New York, NY 10012. email: alex.scacco@nyu.edu
*
e-mail: bernd.beber@nyu.edu (corresponding author)
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Type
Regular Articles
Copyright
Copyright © The Author 2012. Published by Oxford University Press on behalf of the Society for Political Methodology 

Footnotes

Edited by R. Michael Alvarez

Authors' note: Supplementary materials for this article are available on the Political Analysis Web site.

References

Agence France Presse. 2000. Mbeki congratulates Wade for winning Senegal election. Published March 22, 2000.Google Scholar
Agence France Presse. 2007. Catholic church joins critics of Nigeria poll amid fresh calls for re-run. Published April 25, 2007.Google Scholar
Al-Marzouki, Sanaa, Evans, Stephen, Marshall, Tom, and Roberts, Ian. 2005. Are these data real? Statistical methods for the detection of data fabrication in clinical trials. British Medical Journal 331: 267–70.Google Scholar
Alvarez, R. Michael, Hall, Thad E., and Hyde, Susan D., eds. 2008. Election fraud: Detecting and deterring electoral manipulation. Washington, DC: The Brookings Institution.Google Scholar
Beber, Bernd, and Scacco, Alexandra. 2011. Replication data for: What the numbers say: A digit-based test for election fraud. IQSS Dataverse Network [Distributor] V1 [Version]. http://hdl.handle.net/1902.1/17151 (accessed February 25, 2012).Google Scholar
Boland, Philip J., and Hutchinson, Kevin. 2000. Student selection of random digits. Statistician 49: 519–29.Google Scholar
Budescu, David V. 1987. A Markov model for generation of random binary sequences. Journal of Experimental Psychology 13: 2539.Google Scholar
Cantú, Francisco, and Saiegh, Sebastián M. 2011. Fraudulent democracy? An analysis of Argentina's Infamous Decade using supervised machine learning. Political Analysis 19: 409–33.Google Scholar
Chapanis, Alphonse. 1953. Random-number guessing behavior. American Psychologist 8: 332.Google Scholar
Corder, J. Kevin, and Wolbrecht, Christina. 2006. Political context and the turnout of new women voters after suffrage. Journal of Politics 68: 3449.CrossRefGoogle Scholar
Deckert, Joseph, Myagkov, Mikhail, and Ordeshook, Peter C. 2011. Benford's law and the detection of election fraud. Political Analysis 19: 245–68.Google Scholar
Diekmann, Andreas. 2007. Not the first digit! Using Benford's law to detect fraudulent scientific data. Journal of Applied Statistics 34: 321–9.Google Scholar
Dlugosz, Stephan, and Müller-Funk, Ulrich. 2009. The value of the last digit: Statistical fraud detection with digit analysis. Advances in Data Analysis and Classification 3: 281–90.Google Scholar
ECOWAS. 2007a. ECOWAS electoral observers in Senegal. Press release 11/2007, February 25, 2007.Google Scholar
ECOWAS. 2007b. ECOWAS observers endorse presidential election in Senegal. Press release 13/2007, February 27, 2007.Google Scholar
European Union Election Observation Mission. 2003. Nigeria 2003: Final report on the national assembly, presidential, gubernatorial, and state houses of assembly elections. http://ec.europa.eu/external_relations/human_rights/eu_election_ass_observ/nigeria/rep03.pdf (accessed March 20, 2008).Google Scholar
Ichino, Nahomi, and Schündeln, Matthias. 2011. Deterring or displacing electoral irregularities? Spillover effects of observers in a randomized field experiment in Ghana. Working paper.Google Scholar
Kevles, Daniel J. 1998. The Baltimore case: A trial of politics, science, and character. New York: W. W. Norton.Google Scholar
Kew, Darren. 1999. Democrazy: Dem go craze, O: Monitoring the 1999 elections. Issue: A Journal of Opinion 27: 2933.Google Scholar
Kew, Darren. 2004. The 2003 elections: Hardly credible, but acceptable. In Crafting the new Nigeria: Confronting the challenges, ed. Rotberg, Robert I., 139–73. Boulder, CO: Lynne Rienner.Google Scholar
Kuhl, J., and Schönpflug, W. 1974. Ordnungsverhalten, Lärmbelastung, und Persönlichkeit. Psychological Research 37: 143–76.Google Scholar
Levin, Ines, Cohn, Gabe, Michael Alvarez, R., and Ordeshook, Peter C. 2009. Detecting voter fraud in an electronic voting context: An analysis of the unlimited reelection vote in Venezuela. Online Proceedings of the Electronic Voting Technology Workshop.Google Scholar
Mebane, Walter R. Jr. 2006. Election forensics: Vote counts and Benford's law. Working paper.Google Scholar
Mebane, Walter R. Jr. 2008. Election forensics: The second-digit Benford law's test and recent American presidential elections. In Election fraud: Detecting and deterring electoral manipulation, eds. Michal Alvarez, R., Hall, Thad E., Hyde, Susan D., 162–81. Washington, DC: The Brookings Institution.Google Scholar
Mebane, Walter R. Jr. 2011. Comment on “Benford's law and the detection of election fraud.” Political Analysis 19: 269–72.Google Scholar
Mebane, Walter R. Jr., and Sekhon, Jasjeet S. 2004. Robust estimation and outlier detection for overdispersed multinomial models of count data. American Journal of Political Science 48: 392411.Google Scholar
Mosimann, James E., and Ratnaparkhi, Makarand V. 1996. Uniform occurrence of digits for folded and mixture distributions on finite intervals. Communications in Statistics—Simulation and Computation 25: 481506.Google Scholar
Mosimann, James E., Wiseman, Claire V., and Edelman, Ruth E. 1995. Data fabrication: Can people generate random digits? Accountability in Research 4: 3155.Google Scholar
Mosimann, James E., Dahlberg, John E., Davidian, Nancy M., and Krueger, John W. 2002. Terminal digits and the examination of questioned data. Accountability in Research 9: 7592.Google Scholar
Myagkov, Mikhail, Ordeshook, Peter C., and Shakin, Dimitry. 2005. Fraud or fairytales: Russia and Ukraine's electoral experience. Post-Soviet Affairs 21: 91131.Google Scholar
Myagkov, Misha, Ordeshook, Peter C., and Shakin, Dimitri. 2007. The disappearance of fraud: The forensics of Ukraine's 2006 parliamentary elections. Post-Soviet Affairs 23: 218–39.Google Scholar
Myagkov, Mikhail, Ordeshook, Peter C., and Shakin, Dimitri, eds. 2009. The forensics of election fraud: Russia and Ukraine. New York: Cambridge University Press.Google Scholar
Nickerson, Raymond S. 2002. Perception and production of randomness. Psychological Review 109: 330–57.CrossRefGoogle ScholarPubMed
Nigrini, Mark J. 1999. I've got your number: How a mathematical phenomenon can help CPAs uncover fraud and other irregularities. Journal of Accountancy 187: 7983.Google Scholar
Preece, D. A. 1981. Distributions of final digits in data. Statistician 30: 3160.Google Scholar
Rapoport, Amnon, and Budescu, David V. 1997. Randomization in individual choice behavior. Psychological Review 104: 603–17.Google Scholar
Rath, Gustave J. 1966. Randomization by humans. American Journal of Psychology 79: 97103.CrossRefGoogle Scholar
Reuters News. 2007a. Senegal court confirms Wade reelected president. Published March 11, 2007.Google Scholar
Reuters News. 2007b. Wade party wins Senegal poll: Foes threaten protest. Published June 7, 2007.Google Scholar
Schäfer, Christin, Schräpler, Jörg-Peter, Müller, Klaus-Robert, and Wagner, Gert. 2004. Automatic identification of faked and fraudulent interviews by two different methods. German Institute for Economic Research Discussion Paper.Google Scholar
Smith, Jane, and Godlee, Fiona. 2005. Investigating allegations of scientific misconduct: Journals can only do so much; institutions need to be willing to investigate. British Medical Journal 331: 245–6.CrossRefGoogle Scholar
The Economist. 2007. Nigeria: How to steal an election. Published April 18, 2007. http://www.economist.com/node/9032254 (accessed July 31, 2011).Google Scholar
Tversky, Amos, and Kahneman, Daniel. 1972. Subjective probability: A judgment of representativeness. Cognitive Psychology 3: 430–54.Google Scholar
United Nations Development Programme. 2007. Human Development Report 2007/2008. http://hdr.undp.org/en/media/HDR_20072008_EN_Complete.pdf (accessed July 31, 2011).Google Scholar
Wand, Jonathan N., Shotts, Kenneth W., Sekhon, Jasjeet S., Mebane, Walter R. Jr., Herron, Michael C., and Brady, Henry E. 2001. The butterfly did it: The aberrant vote for Buchanan in Palm Beach County, Florida. American Political Science Review 95: 793810.Google Scholar
Watrin, Christoph, Struffert, Ralf, and Ullmann, Robert. 2008. Benford's law: An instrument for selecting tax audit targets? Review of Managerial Science 2: 219–37.Google Scholar
White, Caroline. 2005. Suspected research fraud: Difficulties of getting at the truth. British Medical Journal 331: 245–6.Google Scholar
World Bank. 2011. World development indicators. http://databank.worldbank.org (accessed July 31, 2011).Google Scholar
Yule, G. Udny. 1927. On reading a scale. Journal of the Royal Statistical Society 90: 570–87.CrossRefGoogle Scholar
Supplementary material: PDF

Beber and Scacco supplementary material

Appendix A

Download Beber and Scacco supplementary material(PDF)
PDF 45.1 KB
Supplementary material: PDF

Beber and Scacco supplementary material

Appendix B

Download Beber and Scacco supplementary material(PDF)
PDF 36.9 KB
Supplementary material: PDF

Beber and Scacco supplementary material

Appendix C

Download Beber and Scacco supplementary material(PDF)
PDF 220.9 KB
Supplementary material: PDF

Beber and Scacco supplementary material

Appendix D

Download Beber and Scacco supplementary material(PDF)
PDF 38.6 KB
Supplementary material: File

Beber and Scacco supplementary material

Supplementary Material

Download Beber and Scacco supplementary material(File)
File 31.7 MB