A New Benford Test for Clustered Data with Applications to American Elections
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Department of Economics, Brigham Young University-Idaho, 298 S 1st East SMI 214, Rexburg, ID 83460, USA
2
Center for Data Analysis, The Heritage Foundation, 214 Massachusetts Ave. NE, Washington, DC 20002, USA
3
Department of Mathematics and Statistics, Williams College, 880 Main St., Williamstown, MA 01267, USA
*
Author to whom correspondence should be addressed.
Academic Editors: Claudio Lupi, Roy Cerqueti and Marcel Ausloos
Stats 2022, 5(3), 841-855; https://doi.org/10.3390/stats5030049
Received: 30 June 2022
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Revised: 13 August 2022
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Accepted: 23 August 2022
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Published: 31 August 2022
(This article belongs to the Special Issue Benford's Law(s) and Applications)
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.
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Keywords:
Benford’s law; election forensics; weibull modeling
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MDPI and ACS Style
Anderson, K.M.; Dayaratna, K.; Gonshorowski, D.; Miller, S.J. A New Benford Test for Clustered Data with Applications to American Elections. Stats 2022, 5, 841-855. https://doi.org/10.3390/stats5030049
AMA Style
Anderson KM, Dayaratna K, Gonshorowski D, Miller SJ. A New Benford Test for Clustered Data with Applications to American Elections. Stats. 2022; 5(3):841-855. https://doi.org/10.3390/stats5030049
Chicago/Turabian StyleAnderson, Katherine M., Kevin Dayaratna, Drew Gonshorowski, and Steven J. Miller. 2022. "A New Benford Test for Clustered Data with Applications to American Elections" Stats 5, no. 3: 841-855. https://doi.org/10.3390/stats5030049
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