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> Furthermore, the law can be generalised to digits beyond the first Reminds me of a fun use for second digit analysis: "This study applies Benford’s law to d

> Furthermore, the law can be generalised to digits beyond the first Reminds me of a fun use for second digit analysis: "This study applies Benford’s law to detect anomalies in county-level vote data for the 2020 US presidential election. Most prominent distribution violations are observed with Republican vote counts in blue states, all vote counts in states won by the Democratic candidate, and Democratic vote counts in swing states. Distributions are anomalous in swing states won by the Democratic nominee and not anomalous in swing states won by the Republican nominee. The results are robust to two-digit analysis, Monte Carlo simulations of p-values, broad or narrow swing state definitions, and when compared to distributions observed in 2008, 2012, and 2016 elections." - ["Detecting Anomalies in the 2020 US Presidential Election Votes with Benford’s Law" (2020)](https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3728626 https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3728626)

anonymouskimmer 3y ago
It's too bad they don't disaggregate the data by state, instead assuming states which voted particular ways are equivalent. I guess that the Benford Law analysis wouldn't be as easy if they did due to the fewer number of counties to analyze per state? So I wish they had instead grouped counties by how they voted (since certifying votes is done on the county level, typically), and run the analysis that way. I'd also like to see an analysis based on county size (by population density, and by absolute population). As you get non-random effects based on density. It's also interesting that in certain cases they use a 10%-level for confidence. Edit to add a question: Does the registered voting population of these districts follow Benford's Law?
- gdavisson 3y ago
  I don't know about that particular analysis, but there've been a number of such claims that don't stand up (mostly because, as you ask, the districts themselves don't follow Benford's law). See, for example, "Inappropriate Applications of Benford’s Law Regularities to Some Data from the 2020 Presidential Election in the United States" by Walter R. Mebane, Jr. [0], and "Why do Biden's votes not follow Benford's Law?" by Matt Parker [1]. This fits the general pattern that there's been a lot of suspicion raised about fraud in the 2020 election, but none of it actually seems to pan out. [0] http://www-personal.umich.edu/~wmebane/inapB.pdf http://www-personal.umich.edu/~wmebane/inapB.pdf [1] https://www.youtube.com/watch?v=etx0k1nLn78 https://www.youtube.com/watch?v=etx0k1nLn78
  - anonymouskimmer 3y ago
    It seems like the Benford's Law distribution should be adjustable by the specifics of its input data.

anonymouskimmer 3y ago

It's too bad they don't disaggregate the data by state, instead assuming states which voted particular ways are equivalent. I guess that the Benford Law analysis wouldn't be as easy if they did due to the fewer number of counties to analyze per state? So I wish they had instead grouped counties by how they voted (since certifying votes is done on the county level, typically), and run the analysis that way. I'd also like to see an analysis based on county size (by population density, and by absolute population). As you get non-random effects based on density. It's also interesting that in certain cases they use a 10%-level for confidence. Edit to add a question: Does the registered voting population of these districts follow Benford's Law?

gdavisson 3y ago
I don't know about that particular analysis, but there've been a number of such claims that don't stand up (mostly because, as you ask, the districts themselves don't follow Benford's law). See, for example, "Inappropriate Applications of Benford’s Law Regularities to Some Data from the 2020 Presidential Election in the United States" by Walter R. Mebane, Jr. [0], and "Why do Biden's votes not follow Benford's Law?" by Matt Parker [1]. This fits the general pattern that there's been a lot of suspicion raised about fraud in the 2020 election, but none of it actually seems to pan out. [0] http://www-personal.umich.edu/~wmebane/inapB.pdf http://www-personal.umich.edu/~wmebane/inapB.pdf [1] https://www.youtube.com/watch?v=etx0k1nLn78 https://www.youtube.com/watch?v=etx0k1nLn78
- anonymouskimmer 3y ago
  It seems like the Benford's Law distribution should be adjustable by the specifics of its input data.