Benford's Law and the Detection of Election Fraud

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.

“Close but no Cigar”: the measurement of corruption

“…Specifically, within electoral fraud evaluations, the focus has been upon so-called "second-digit Benford's law" (2BL) tests, which apply essentially the same logic as the general Benford's law specifically to the second digit of electoral return numbers (see Mebane 2006aMebane , 2006bMebane , 2011Breunig and Goerres 2011; see also Beber and Scacco 2012; but cf. Deckert et al 2011). The argument here is that, if votes are rigged, the "natural" processes that would be expected to generate Benford distributions in the second digit of electoral return distributions will not operate.…”

Statistical detection of systematic election irregularities

“…Voting results from Russia (6), Germany (7), Argentina (8), and Nigeria (9) have been tested for the presence of election fraud using variations of this idea of digit-based analysis. However, the validity of Benford's law as a fraud detection method is subject to controversy (10,11). The problem is that one needs to firmly establish a baseline of the expected distribution of digit occurrences for fair elections.…”

“…Only then it can be asserted if actual numbers are over-or underrepresented and thus, suspicious. What is missing in this context is a theory that links specific fraud mechanisms to statistical anomalies (10).…”

A systematic approach to study electoral fraud

“…One method, which has gained increasing attention in the literature, relies on the statistical properties of the distribution of digits in aggregated election results, based on Benford's law (e.g., Mebane, 2008Mebane, , 2010bMebane, , 2011Deckert, Myagkov, and Ordeshook, 2011;Beber and Scacco, 2012). Benford's law is suited, however, only to detect one very particular, and not always very likely form of fraud.…”

“…21 The first digit of vote return data might not always stem from Benford's law (Mebane, 2008;Deckert, Myagkov, and Ordeshook, 2011). In a recent article Deckert, Myagkov, and Ordeshook (2011) argue against the use of Benford's law based on using the mean of the second digits and extensive simulations (see also Shikano and Mack, 2011). Whereas we do not doubt their results, we want to highlight that we are not performing any tests on the means of digits nor on the second digit (Mebane, 2011).…”