There are many unsubstantiated claim about election fraud in the recent US presidential elections. Most of these claims provide no proofs or arguments, while there are few which are supposedly scientific. One of the example relies on the Benford's law, which specifies the expected frequency at which we should observe specific first digit of certain number. So if vote counts in polling stations do not follow Benford's law, it should be an indication of wide spread fraud!
Not so fast, as often in science, laws and models are applicable only when certain conditions (assumptions) are satisfied. In case of Benford's law, one main condition is that the original numbers (first digits of which we consider) should span multiple orders of magnitude. Also Benford's law is formulated as a rather general empirical observation. The law is supposedly observed in many naturally occurring data.
Vote counts is obviously an example of naturally occurring data. The issue is that vote counts do not span many order of magnitude. Also vote counts, especially in elections with two competitors, are not related to exponential growth (which is prevalent in many naturally occurring systems), which can actually be a driver for the Benford's law.
Watch the following video by Stand-up Maths for a video discussion on applicability of the Benford's law to the data from the recent presidential election in the US. The video below covers another simple method to check for the election fraud.