A New Benford Test for Clustered Data with Applications to American Elections

Katherine M. Anderson, Kevin Dayaratna, Drew Gonshorowski and Steven J. Miller ()
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Katherine M. Anderson: Department of Economics, Brigham Young University-Idaho, 298 S 1st East SMI 214, Rexburg, ID 83460, USA
Kevin Dayaratna: Center for Data Analysis, The Heritage Foundation, 214 Massachusetts Ave. NE, Washington, DC 20002, USA
Drew Gonshorowski: Center for Data Analysis, The Heritage Foundation, 214 Massachusetts Ave. NE, Washington, DC 20002, USA
Steven J. Miller: Department of Mathematics and Statistics, Williams College, 880 Main St., Williamstown, MA 01267, USA

Stats, 2022, vol. 5, issue 3, 1-15

Abstract: A frequent problem with classic first digit applications of Benford’s law is the law’s inapplicability to clustered data, which becomes especially problematic for analyzing election data. This study offers a novel adaptation of Benford’s law by performing a first digit analysis after converting vote counts from election data to base 3 (referred to throughout the paper as 1-BL 3), spreading out the data and thus rendering the law significantly more useful. We test the efficacy of our approach on synthetic election data using discrete Weibull modeling, finding in many cases that election data often conforms to 1-BL 3. Lastly, we apply 1-BL 3 analysis to selected states from the 2004 US Presidential election to detect potential statistical anomalies.

Keywords: Benford’s law; election forensics; weibull modeling (search for similar items in EconPapers)
JEL-codes: C1 C10 C11 C14 C15 C16 (search for similar items in EconPapers)
Date: 2022
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