With the 2020 elections marred by legal challenges and fraud allegations, some have used statistical analysis to try to determine if foul play was involved. In several states, analyses of election data indeed show statistically odd phenomena in the tallies of votes for the Democratic candidate, former Vice President Joe Biden.
One of the most common arguments is that in some localities, vote counts for Biden violate Benford’s Law.
In simple terms, the law states that in many real-world data sets, such as demographic data, geographical data, or even sports statistics, the first digit of the numbers will more likely be 1 than 2, and 2 more likely than 3, etc. following logarithmic scale. If the first-digit distribution significantly diverges from this rule, it could be evidence of artificial manipulation of the data.
The law has been used to identify fraudulent financial records and other illegal activities. Walter Mebane, a political science professor at the University of Michigan, used the law to back ballot-stuffing allegations in the 2009 Iran election (pdf). Some researchers also used the law to check for irregularities in the 2016 election in Wisconsin (pdf).
While the result in Georgia and Florida generally adhered to Benford’s Law, there were significant deviations in votes for Biden in Wisconsin, Illinois, and Pennsylvania.
Mebane acknowledged some anomalies in the data, but cautioned against using the first digit analysis on election results. [ … ]