The most recent issue of Political Analysis, an academic journal that Jonathan Katz and I edit, has a paper by Joseph Deckert, Mikhail Myagkov and Peter Ordeshook on “Benford’s Law and the Detection of Election Fraud.” Non-academic readers might have trouble accessing the article, so there is the abstract:
The proliferation of elections in even those states that are arguably anything but democratic has given rise to a focused interest on developing methods for detecting fraud in the official statistics of a state’s election returns. Among these efforts are those that employ Benford’s Law, with the most common application being an attempt to proclaim some election or another fraud free or replete with fraud. This essay, however, argues that, despite its apparent utility in looking at other phenomena, Benford’s Law is problematical at best as a forensic tool when applied to elections. Looking at simulations designed to model both fair and fraudulent contests as well as data drawn from elections we know, on the basis of other investigations, were either permeated by fraud or unlikely to have experienced any measurable malfeasance, we find that conformity with and deviations from Benford’s Law follow no pattern. It is not simply that the Law occasionally judges a fraudulent election fair or a fair election fraudulent. Its “success rate” either way is essentially equivalent to a toss of a coin, thereby rendering it problematical at best as a forensic tool and wholly misleading at worst.
The same issue of the journal also has a comment from Walter Mebane, who has written extensively about the use of Benford’s Law for detecting election fraud, here is the abstract from Mebane’s commentary:
“Benford’s Law and the Detection of Election Fraud” raises doubts about whether a test based on the mean of the second significant digit of vote counts equals 4.187 is useful as a test for the occurrence of election fraud. The paper mistakenly associates such a test with Benford’s Law, considers a simulation exercise that has no apparent relevance for any actual election, applies the test to inappropriate levels of aggregation, and ignores existing analysis of recent elections in Russia. If tests based on the second significant digit of precinct-level vote counts are diagnostic of election fraud, the tests need to use expectations that take into account the features of ordinary elections, such as strategic actions. Whether the tests are useful for detecting fraud remains an open question, but approaching this question requires an approach more nuanced and tied to careful analysis of real election data than one sees in the discussed paper.
These two papers are must-reads for anyone interested in election fraud and the statistical detection of election fraud!