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When Does the Second-Digit Benford’s Law-Test Signal an Election Fraud?: Facts or Misleading Test Results

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  • Shikano Susumu

    ()

  • Mack Verena

    () (Chair of Political Methodology, University of Konstanz, Universitätsstraße 10, 78457 Konstanz, Germany)

Abstract

Detecting election fraud with a simple statistical method and minimal information makes the application of Benford’s Law quite promising for a wide range of researchers. Whilst its specific form, the Second-Digit Benford’s Law (2BL)-test, is increasingly applied to fraud suspected elections, concerns about the validity of its test results have been raised. One important caveat of this kind of research is that the 2BL-test has been applied mostly to fraud suspected elections. Therefore, this article will apply the test to the 2009 German Federal Parliamentary Election against which no serious allegation of fraud has been raised. Surprisingly, the test results indicate that there should be electoral fraud in a number of constituencies. These counter intuitive results might be due to the naive application of the 2BL-test which is based on the conventional χ2 distribution. If we use an alternative distribution based on simulated election data, the 2BL-test indicates no significant deviation. Using the simulated election data, we also identified under which circumstances the naive application of the 2BL-test is inappropriate. Accordingly, constituencies with homogeneous precincts and a specific range of vote counts tend to have a higher value for the 2BL statistic.

Suggested Citation

  • Shikano Susumu & Mack Verena, 2011. "When Does the Second-Digit Benford’s Law-Test Signal an Election Fraud?: Facts or Misleading Test Results," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 231(5-6), pages 719-732, October.
  • Handle: RePEc:jns:jbstat:v:231:y:2011:i:5-6:p:719-732
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    References listed on IDEAS

    as
    1. Fewster, R. M., 2009. "A Simple Explanation of Benford's Law," The American Statistician, American Statistical Association, vol. 63(1), pages 26-32.
    2. Andreas Diekmann, 2007. "Not the First Digit! Using Benford's Law to Detect Fraudulent Scientif ic Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(3), pages 321-329.
    3. Andreas Diekmann & Ben Jann, 2010. "Benford's Law and Fraud Detection: Facts and Legends," German Economic Review, Verein für Socialpolitik, vol. 11, pages 397-401, August.
    4. repec:cup:apsrev:v:93:y:1999:i:01:p:15-32_21 is not listed on IDEAS
    5. Katz, Jonathan N. & King, Gary, 1999. "A Statistical Model for Multiparty Electoral Data," American Political Science Review, Cambridge University Press, vol. 93(01), pages 15-32, March.
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