On (Newcomb-)Benford's law: a tale of two papers and of their disproportionate citations. How citation counts can become biased

Abstract

The first digit (FD) phenomenon i.e., the significant digits of numbers in large data are often distributed according to a logarithmically decreasing function was first reported by S. Newcomb and then many decades later independently by F. Benford. After its century long neglect the last three decades have seen huge growth in the number of relevant publications. However, notwithstanding the rising popularity the two independent proponents of the phenomenon are not equally acknowledged an indication of which is disproportionate number of citations accumulated by Newcomb (1881) and Benford (1938). In the present study we use citation analysis to show that the formalization of the eponym Benford's law, a name questionable itself for overlooking Newcomb's contribution, by Raimi (1976) had a strong adverse effect on the future citations of Newcomb (1881). Furthermore, we identify the papers published over various decades of the developmental history of the FD phenomenon, which latter turned out to be amongst the most cited ones in the field. We find that lack of its consideration, intentional or occasionally out of ignorance for referencing by the prominent papers, is responsible for a far lesser number of citations of Newcomb (1881) in comparison to Benford (1938).