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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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Author Info

  • Susumu Shikano

    ()
    (Uni Konstanz)

  • Verena Mack

    ()
    (Uni Konstanz)

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    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 appliedmostly 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 counterintuitive resultsmight be due to the naive application of the 2BL-test which is based on the conventional v2 distribution. If we use an alternative distribution based on simulated election data, the 2BLtest 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.

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    Bibliographic Info

    Article provided by Justus-Liebig University Giessen, Department of Statistics and Economics in its journal Journal of Economics and Statistics.

    Volume (Year): 231 (2011)
    Issue (Month): 5-6 (November)
    Pages: 719-732

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    Handle: RePEc:jns:jbstat:v:231:y:2011:i:5-6:p:719-732

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    Related research

    Keywords: Election fraud; Benford’s Law; German federal election; simulation;

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    References

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    1. Andreas Diekmann, 2005. "Not the First Digit! Using Benford’s Law to Detect Fraudulent Scientific Data," Others 0507001, EconWPA.
    2. Andreas Diekmann & Ben Jann, 2010. "Benford's Law and Fraud Detection. Facts and Legends," ETH Zurich Sociology Working Papers 8, ETH Zurich, Chair of Sociology.
    3. Fewster, R. M., 2009. "A Simple Explanation of Benford's Law," The American Statistician, American Statistical Association, vol. 63(1), pages 26-32.
    4. Katz, Jonathan N., 1997. "A Statistical Model for Multiparty Electoral Data," Working Papers 1005, California Institute of Technology, Division of the Humanities and Social Sciences.
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