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

Tariq Ahmad Mir, Marcel Ausloos

TL;DR

The paper investigates why Newcomb's 1881 observation of the first-digit phenomenon receives far fewer citations than Benford's 1938 work, despite both contributing to the same phenomenon. It uses citation data from the Benford Online Bibliography to quantify yearly and cocitation patterns, and shows that Raimi's 1976 formalization of the eponym 'Benford's law' coincided with a sharp rise in BF citations and a neglect of Newcomb in subsequent literature. The authors report that across 2028 qualifying items, BF accrued 1325 citations compared with 925 for NC, and that about 20% of papers do not cite NC at all, while cocitation is the dominant mode of reference. They conclude that publication timing, journal placement, and selective citing create a Matthew-effect-like bias that shapes the historical visibility of foundational contributions to the first-digit phenomenon.

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).

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

TL;DR

The paper investigates why Newcomb's 1881 observation of the first-digit phenomenon receives far fewer citations than Benford's 1938 work, despite both contributing to the same phenomenon. It uses citation data from the Benford Online Bibliography to quantify yearly and cocitation patterns, and shows that Raimi's 1976 formalization of the eponym 'Benford's law' coincided with a sharp rise in BF citations and a neglect of Newcomb in subsequent literature. The authors report that across 2028 qualifying items, BF accrued 1325 citations compared with 925 for NC, and that about 20% of papers do not cite NC at all, while cocitation is the dominant mode of reference. They conclude that publication timing, journal placement, and selective citing create a Matthew-effect-like bias that shapes the historical visibility of foundational contributions to the first-digit phenomenon.

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).
Paper Structure (7 sections, 1 equation, 4 figures, 2 tables)

This paper contains 7 sections, 1 equation, 4 figures, 2 tables.

Table of Contents

  1. Abstract
  2. Keywords
  3. Introduction
  4. Data
  5. Data analysis
  6. Discussion
  7. Conclusion

Figures (4)

  • Figure 1: Comparison of yearly publications on BL, those citing Benford (1938) (BF) and Newcomb (1881) (NC). Insert plot is for years 1938-1980.
  • Figure 2: Comparison of yearly citations received by Benford (1938) only (BF/NC), Newcomb (1881) only (NC/BF) and both (BF & NC). Insert plot is for years 1938-1978.
  • Figure 3: Comparison of yearly co-citations of Raimi (1976) with NC/BF, BF/NC and NC & BF.
  • Figure 4: Comparison of yearly cocitations of Nigrini (1996b) with NC/BF, BF/NC and NC & BF.