Everyone’s Name on Every Paper

Brian Ripley, my doctoral supervisor, published far fewer papers than his influence would suggest: he was among R core’s most active committers for two decades, and none of that work is a paper. He used to say code mattered more than citations — writing code debugs your thinking. Such counts are sums over a chosen author list.

Adding names multiplies papers by n, citations by more

Take \(n\) researchers with one solo paper each, drawing \(c_i\) citations, who put all \(n\) names on every paper. No new work exists, yet every paper count goes 1 → \(n\) and every citation count \(c_i\) → \(S = \sum_j c_j\):

\[\frac{S}{c_i} = n \cdot \frac{\bar{c}}{c_i}.\]

Papers multiply by exactly \(n\); citations by more, since heavy tails put the mean far above the median.

Simulated citations, because the tail decides

The counts are synthetic — \(c_i\) lognormal (\(\mu = 1.5\), \(\sigma = 1.2\) on the log scale), median near 4.5 with a long right tail, standing in for one field’s citations. The question is counterfactual, so only simulation has both branches; what rides on it is a hiring panel’s read of a CV.

Code

import numpy as np

RNG = np.random.default_rng(0)
MU, SIGMA = 1.5, 1.2          # lognormal, on the log scale
GROUPS = (5, 10, 20)
REPS = 20_000                 # many draws, so the medians are not a fluke of one

print(f"{'n':>3}  {'papers':>7}  {'median':>9}  {'share above':>12}  {'large-n':>8}")
print(f"{'':>3}  {'':>7}  {'citations':>9}  {'n times':>12}  {'limit':>8}")
for n in GROUPS:
    c = RNG.lognormal(MU, SIGMA, size=(REPS, n))
    # Everyone is credited with the group total, so the multiplier is S / c_i.
    mult = c.sum(axis=1, keepdims=True) / c
    limit = n * np.exp(SIGMA**2 / 2)   # what median(S / c_i) tends to as n grows
    print(f"{n:>3}  {n:>6}x  {np.median(mult):>8.1f}x  {np.mean(mult > n):>11.0%}"
          f"  {limit:>7.1f}x")

  n   papers     median   share above   large-n
              citations       n times     limit
  5       5x       7.3x          63%     10.3x
 10      10x      17.2x          67%     20.5x
 20      20x      37.3x          70%     41.1x

The median beats \(n\times\) at every size — 7.3× at \(n = 5\), 37× at \(n = 20\) — but hides who pays.

The gain is unequal, making it a transaction

Everyone ends on the same total \(S\), whatever they brought.

Code

import matplotlib.pyplot as plt

SOLO, COMBINED, REF = "#6b7280", "#4a3aa7", "#eb6834"
rng = np.random.default_rng(1)

fig, axes = plt.subplots(3, 1, figsize=(7.4, 8.2), sharex=True,
                         gridspec_kw={"height_ratios": GROUPS, "hspace": 0.16})

for ax, n in zip(axes, GROUPS):
    c = np.sort(rng.lognormal(MU, SIGMA, size=n))
    total, y = c.sum(), np.arange(n)
    ax.hlines(y, c, total, color=SOLO, lw=1.2, alpha=0.55, zorder=1)
    ax.scatter(c, y, s=34, color=SOLO, zorder=3, label="solo: own paper only")
    ax.scatter(np.full(n, total), y, s=34, color=COMBINED, zorder=3,
               label="combined: credited the group total")
    ax.scatter(n * c, y, s=52, marker="|", color=REF, lw=1.8, zorder=4,
               label=r"$n \times$ the solo count")
    ax.set_xscale("log")
    ax.set_ylim(-0.9, n - 0.1)
    ax.set_yticks([])
    ax.set_ylabel(f"$n = {n}$", fontsize=11)
    ax.grid(axis="x", color="0.9", lw=0.7)
    ax.set_axisbelow(True)
    for side in ("top", "right", "left"):
        ax.spines[side].set_visible(False)
for ax in axes[:-1]:
    ax.spines["bottom"].set_visible(False)
    ax.tick_params(axis="x", which="both", bottom=False)

axes[0].legend(frameon=False, fontsize=9, loc="upper left",
               bbox_to_anchor=(0.0, 1.6))
axes[-1].set_xlabel("credited citations (log scale)", fontsize=10)
plt.show()

Figure 1: One draw per group size. Left ends are what each researcher earned alone; right ends are what all of them are credited with after combining. The orange tick marks n times the solo count: left of the total, that researcher beat n times; right of it, they did worse.

Across the 20,000 draws above, two thirds clear \(n\times\) — and the most-cited member never can, since \(S \le n\,c_{\max}\). The swap costs whoever brought the tail, so the strong party must be paid.

Real publishing runs the same sum

Authors — seniority. A 2024 meta-analysis put honorary authorship in health sciences at 26% with no criteria supplied, 18% when shown ICMJE criteria, 51% when declared contributions were checked against them.

Journals — reciprocity. By 2019 the Journal Citation Reports had suspended 46 journal pairs — 55 journals — for excessive pairwise citation, which CIDRE detects from citation flow.

Institutions — cash. In 2011 Science reported 60-plus highly cited researchers adding King Abdulaziz University as a paid second affiliation; by 2014 it ranked second worldwide on the highly cited list.

Caveat: the temptation needs no conspiracy

No arrangement is needed to feel this. Teams already produce more-cited work than solo authors — Wuchty, Jones and Uzzi across 19.9 million papers — so the honest incentive and the dishonest one point the same way: add names. Most author lists are exactly what they look like; none of the cases above is the model at full strength. But the arithmetic cannot tell an earned name from a gifted one, and neither can the counts. Ripley’s could not see him.