In the past month, Benford’s Law has risen from a niche, nerdy “fun fact” to become a key arguing point about the legitimacy of our national election. So what is this universal mathematical law?
Benford’s Law states that truly random data sets, whether it be Instagram followers or stars in a galaxy, all follow the same trend. The first digit of any given number in the entire universe is about 30% more likely to be a 1 than a 9. Crazy, right? It has been used to detect tax fraud, deep fakes, and Russian Twitter bots. In a messy world, the clean application of Benford’s Law acts like a magical lie detector.
Benford’s Law isn’t necessarily intuitive, but it’s simple enough that it can easily be applied incorrectly. Strangely, the first digit of certain precinct vote counts don’t match the elegant curve of Benford’s Law on a graph. Since the election, this disparity has been gaining popularity across social media and some news outlets as proof of voter fraud.
However, as University of Michigan professor Walter Mebane proves in recent research, this is an inaccurate interpretation of precinct voting data. After 20 years researching Benford’s Law, Mebane expresses alarm that people are oversimplifying it in such a high stakes situation.
Human minds are wired for stories, not statistics. Anyone who’s been frustrated by their math homework can relate. The proofs in Benford’s Law are especially complex, so it’s important to consult mathematical experts such as Mebane to ensure that our statistical assumptions are accurate.
In the words of Galileo, “Mathematics is the language with which God has written the universe.”
For an entertaining overview of Benford’s Law, watch the “Digits” episode of Netflix’s docuseries “Connected.” For an explanation of Benford’s Law in the election, listen to Radiolab’s recent podcast episode, “Breaking Benford.” Better yet, read Professor Walter Mebane’s study, which is titled “Inappropriate Applications of Benford’s Law Regularities to Some Data from the 2020 Presidential Election in the United States.”
— Ella Crowder is a senior at Davis High School.