# Attention Inequality on X/Twitter: Evidence from English-Language Posts

## Abstract

Every day, hundreds of millions of posts compete for a finite resource: human attention. We present a descriptive analysis of how this resource is distributed among English-language posts on X (formerly Twitter), drawing on a cross-sectional sample of 8,722 tweets (February 2026, after bot filtering), a timeline panel of 17,671 tweets from 225 users, and a historical archive of 95 million tweets (2009–2018). Four main findings and one cautionary observation emerge: (1) attention inequality is extreme among text-containing posts—the impression Gini is 0.965, and after inverse-probability weighting (IPW) to correct for the stratified over-sampling of high-follower accounts, approximately 81% of total variance is between users rather than between posts (unweighted upper bound: 88%, bootstrap 95% CI: [84%, 89%]); (2) the association between followers and impressions shows increasing returns in the 100–100,000 follower range, with possible saturation above 100K— a cross-section analysis (n = 7,673) yields ˆ β2 = 0.053 (p < 0.001, R2 = 0.761) for a global quadratic approximation; this pattern persists under all filter specifications, including automation-only filtering ( ˆ β2 = 0.030, p < 0.001); (3) retweet inequality rose within the EPFL archive (verified-account Gini: 0.76 in 2012, 0.89 in 2018), a pattern consistent with both platform evolution and cohort maturation; (4) likes, quotes, and impressions are tightly coupled in equilibrium, with the coupling weakening for larger accounts—attributable to mechanical necessity (one must see a tweet to like it) and selection effects, with algorithmic amplification as one possible additional channel. We also note that follower inequality decreased within the fixed EPFL cohort, though this is likely a survivorship artifact. Pooling with the stratified timeline panel raises R2 to 0.821. These findings describe a platform where attention is concentrated far beyond what follower counts alone would predict—consistent with algorithmic mediation, though our evidence is descriptive rather than causal.

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## Full Text

Attention Inequality on X/Twitter:
Evidence from English-Language Posts

AI Author: Claude Opus 4.6
Prompter: Cesar A. Hidalgo

Abstract

forms are, at their core, attention allocation machines:
they decide which of millions of competing posts will
appear on a user’s screen and which will vanish unseen.
The distributional consequences of these decisions—who
is heard, who is ignored, and how concentrated the re-
sulting attention distribution becomes—are questions of
both scientific and democratic significance.
Yet for all the debate about algorithmic power, the
basic distributional facts remain surprisingly under-
studied.
Follower counts are known to follow heavy-
tailed distributions (Kwak et al., 2010; Barab´asi and Al-
bert, 1999), and online participation is extraordinarily
concentrated—the “90-9-1 rule” describes a world where
1% of users create most content (Nielsen, 2006). But
the distribution of realized attention—not who could
be heard, but who actually is—has received far less
scrutiny.
This gap exists largely because impression
data (how many times a post is rendered on a screen)
was proprietary until X began exposing it through its
API in late 2022.
We exploit this opening to offer a descriptive anatomy
of attention inequality on X/Twitter, organized around
five stylized facts. We combine a cross-sectional sample
of 8,722 tweets with impression counts (after bot filter-
ing), a panel of 17,671 tweets from 225 user timelines to
decompose inequality into its between-user and within-
user components, and a historical archive of 95 million
tweets spanning a decade of platform evolution.
A clarification on what we measure:
impressions
count screen renders, not cognitive engagement.
A
tweet that flashes past in a feed and one that holds a
reader’s attention for minutes both register as a single
impression.1 Nevertheless, impressions are the currency
that determines a creator’s visibility and mediates a
reader’s exposure to ideas and political speech—making
them the relevant quantity for questions about platform
power.

Every day, hundreds of millions of posts compete for a
finite resource: human attention. We present a descrip-
tive analysis of how this resource is distributed among
English-language posts on X (formerly Twitter), draw-
ing on a cross-sectional sample of 8,722 tweets (Febru-
ary 2026, after bot filtering), a timeline panel of 17,671
tweets from 225 users, and a historical archive of 95
million tweets (2009–2018). Four main findings and one
cautionary observation emerge: (1) attention inequal-
ity is extreme among text-containing posts—the impres-
sion Gini is 0.965, and after inverse-probability weight-
ing (IPW) to correct for the stratified over-sampling of
high-follower accounts, approximately 81% of total vari-
ance is between users rather than between posts (un-
weighted upper bound: 88%, bootstrap 95% CI: [84%,
89%]); (2) the association between followers and im-
pressions shows increasing returns in the 100–100,000
follower range, with possible saturation above 100K—
a cross-section analysis (n = 7,673) yields ˆβ2 = 0.053
(p < 0.001, R2 = 0.761) for a global quadratic approx-
imation; this pattern persists under all filter specifica-
tions, including automation-only filtering (ˆβ2 = 0.030,
p < 0.001); (3) retweet inequality rose within the EPFL
archive (verified-account Gini:
0.76 in 2012, 0.89 in
2018), a pattern consistent with both platform evolu-
tion and cohort maturation; (4) likes, quotes, and im-
pressions are tightly coupled in equilibrium, with the
coupling weakening for larger accounts—attributable to
mechanical necessity (one must see a tweet to like it)
and selection effects, with algorithmic amplification as
one possible additional channel. We also note that fol-
lower inequality decreased within the fixed EPFL cohort,
though this is likely a survivorship artifact. Pooling with
the stratified timeline panel raises R2 to 0.821. These
findings describe a platform where attention is con-
centrated far beyond what follower counts alone would
predict—consistent with algorithmic mediation, though
our evidence is descriptive rather than causal.

Zhu and Lerman (2016) provided an important bench-
mark, reporting a user-level retweet Gini of ∼0.94 on
2014 data and documenting rich-get-richer dynamics.

1
Introduction

1The X API v2 defines impression count as the number of
times a tweet has been viewed, where a “view” is counted when
a tweet is loaded and rendered in a user’s timeline, search re-
sults, or thread.
This measures potential exposure (delivery to
screen), not verified viewability (e.g., a minimum on-screen dura-
tion). Our Gini coefficient therefore captures inequality in poten-
tial reach rather than verified cognitive attention.

In 1971, Herbert Simon observed that “a wealth of in-
formation creates a poverty of attention” (Simon, 1971).
Half a century later, his insight has become the organiz-
ing principle of the digital economy. Social media plat-

We extend their work in three directions:
measur-
ing inequality with impression data, tracing temporal
trends from 2009 to 2026, and characterizing the equi-
librium coupling between engagement signals and expo-
sure. Among our findings, the degree of concentration
stands out: the impression Gini (0.965) exceeds Gini
values reported for other digital attention distributions
such as YouTube views (∼0.87; Cha et al. 2010) and
scientific citations (∼0.70–0.80; de Solla Price 1976).
For context, this also exceeds the income Gini of any
country on record, though the comparison is imper-
fect: attention distributions are structurally more zero-
inflated than income distributions, which inflates the
Gini mechanically (see Section 4). Furthermore, approx-
imately 81% of the variance in impressions is between
users rather than between posts after IPW-weighting
(unweighted upper bound: 88%; Section 4), and even
a model with rich controls can explain only 82% of the
variation—the remaining 18% reflecting the inherent un-
predictability of individual posts.

The transition from chronological to algorithmic feeds
introduces a new form of endogenous reinforcement.
When platforms use engagement signals to rank content,
a feedback loop emerges: early engagement increases
visibility, which generates further engagement, which
further increases visibility. These dynamics can endoge-
nously produce cumulative advantage and heavy-tailed
attention distributions even absent intrinsic quality dif-
ferences between posts.
Empirical evidence supports
this mechanism: Husz´ar et al. (2022) documented asym-
metric political amplification in Twitter’s algorithm;
Garz and Dujeancourt (2023) exploited the 2016 algo-
rithmic switch as a natural experiment, finding both in-
creased engagement and a rich-get-richer pattern; and
more broadly, the transition from social-graph-based
feeds to interest-graph-based recommendation—what
Gerbaudo (2024) calls the shift from “social networks”
to “social interest clusters”—has fundamentally restruc-
tured how platforms allocate visibility, decoupling who
sees a post from who follows its author.
A deeper literature on recommender systems illumi-
nates the mechanism. Chaney et al. (2018) showed for-
mally that recommendation algorithms create “algorith-
mic confounding”: by mediating what users see, they
generate observational data that reinforces existing pop-
ularity even absent intrinsic quality differences. Fleder
and Hosanagar (2009) found that collaborative filter-
ing can increase sales concentration despite expanding
the range of items recommended. These feedback loops
mean that ranking algorithms using engagement sig-
nals as inputs can endogenously produce rich-get-richer
dynamics—not as a design choice, but as an emergent
property. The diffusion structure of content matters too:
Goel et al. (2016) showed that most viral events are
shallow and broad rather than deeply cascading, sug-
gesting that algorithmic distribution, not organic word-
of-mouth, drives the bulk of attention concentration.

2
Related Work

The economics of attention traces back to Simon (1971)
and was developed for digital environments by Gold-
haber (1997) and Davenport and Beck (2001).
The
empirical regularity that online participation follows
extreme power laws is one of the most robust find-
ings in computational social science: from the “90-9-1
rule” (Nielsen, 2006) to the participation divide (Har-
gittai and Walejko, 2008) to Hindman’s (2009) demon-
stration that online discourse is more concentrated than
its offline counterpart.
These distributional patterns have deep structural
roots in cumulative advantage processes. Simon (1955)
first modeled cumulative advantage mathematically,
showing that a process where the probability of acquir-
ing new items is proportional to how many one already
has generates skew distributions. Merton (1968) iden-
tified the same dynamic in the sociology of science as
the “Matthew Effect.”
de Solla Price (1976) showed
that scientific citations follow this cumulative advan-
tage process, with highly cited papers attracting cita-
tions at a disproportionate rate. Barab´asi and Albert
(1999) generalized the mechanism to networks as “pref-
erential attachment,” demonstrating that growing net-
works where new nodes connect preferentially to well-
connected nodes produce power-law degree distribu-
tions. In cultural markets, Salganik et al. (2006) demon-
strated experimentally that social influence can amplify
small initial differences into extreme inequality, while
Muchnik et al. (2013) showed that even a single artifi-
cial upvote can bias the trajectory of a post’s success.
The economic formalization appears in Rosen (1981):
when audiences can costlessly concentrate on top per-
formers, small quality differences generate extreme out-
come inequality—the “superstar” effect.

3
Data and Methods


![Table 1](paper-28-v1_images/table_1.png)
*Table 1*

3.1
Data Sources

We draw on four datasets, summarized in Table 1.

Cross-sectional
sample. This dataset consists of
11,007 English-language original tweets collected via
the X API v2 across 110 randomly selected one-minute
windows spanning February 22–28, 2026 (8,722 tweets
from 8,547 authors after data cleaning; see below). For
each window, we queried the tweets/search/recent
endpoint using a disjunction of ten common En-
glish stopwords—(the OR just OR that OR this OR
was OR with OR but OR what OR been OR they)
lang:en -is:retweet -is:reply—filtered to exclude
retweets and replies. This stopword-matching strategy
approximates a random sample of the English-language
tweet stream:
because the target words appear in a
large fraction of English sentences, the query acts as


![Table 2](paper-28-v1_images/table_2.png)
*Table 2*

a near-uniform filter over the population of English
text-containing tweets posted in each window.
This
approach inherently excludes non-English content and
may underrepresent media-only posts (images/videos
without text) or posts using non-standard syntax;
if such posts tend to have higher engagement, our
inequality estimates would be conservative.
The
resulting sample contains approximately one tweet per
author, making tweet-level and user-level distributions
effectively equivalent. Because the X API only returns
tweets from accounts that exist at the time of collection,
our sample does not include posts from accounts that
were active during the collection week but subsequently
deleted
or
suspended
(survivorship
bias);
results
therefore describe accounts that maintained an active
presence and should not be extrapolated to accounts
that churned.
For each tweet, the API returns cumulative en-
gagement metrics (impressions, likes, retweets, replies,
quotes, bookmarks) and author metadata (followers, fol-
lowing, total tweets, account age). Impressions are mea-
sured at a single observation point (collection time);
tweet ages range from 3.5 to 143 hours (mean 74h). The
110 windows were distributed across all hours and days
of the week; a Theil decomposition by time of day ex-
plains only 1.8% of total inequality (Table 6), confirming
that temporal clustering does not drive our results. We
assess sensitivity to tweet age in Table 3.

dataset (Garimella and West, 2021), containing 95 mil-
lion tweets (2009–2018) with retweet counts and esti-
mated follower counts at time of posting. Data spans
three author cohorts: a random sample (18.8M tweets,
9,345 users; used in full), verified accounts (7.0M tweets,
3,597 users; used in full), and political accounts (69.2M
tweets, 30,320 users; used as a systematic 1-in-5 sub-
sample due to computational constraints). Engagement
counts in stream-captured data are frozen near zero at
capture time; we therefore compute both unconditional
metrics and metrics conditional on RT ≥1. Three cor-
rupt rows in the random cohort (where tweet IDs were
parsed as retweet counts exceeding 5 million) were re-
moved.

Economist validation sample. To provide a “guar-
anteed human” benchmark, we collected timelines for
144 of the top 150 economists ranked by Twitter fol-
lowers in the RePEc/IDEAS ranking (IDEAS/RePEc,
2022), obtaining 12,438 tweets.3 These accounts are ver-
ified public intellectuals, reducing concerns about bots
or purchased followers. The economist sample is used
exclusively as a visual validation overlay on Figure 3;
it is not included in the regression models or inequality
statistics, because it is a purposive sample of high-profile
users that would distort the random-sample represen-
tativeness of the cross-sectional and stratified timeline
datasets.


![Table 3](paper-28-v1_images/table_3.png)
*Table 3*

Data cleaning. We applied an aggressive composite
filter to remove likely bots, purchased-follower accounts,
and suspended users from the cross-sectional and time-
line data. An account was flagged if any of the follow-
ing held: (i) mean impressions-to-followers ratio below
0.5% with >100 followers (purchased/dead audience);
(ii) 100% zero likes across all observed tweets with >500
followers (ghost accounts); (iii) lifetime posting rate
above 200 tweets per day (automated posting); or (iv) all
observed tweets with <10 impressions despite >1,000
followers (shadowbanned/suspended).
This removed
2,207 authors (20.5% of unique accounts) and 3,955
tweets (13.0%), but only 1.3% of total impressions—
consistent with these accounts contributing negligible
real attention. We acknowledge a circularity risk in cri-
terion (i): removing accounts with low impression-to-
follower ratios when studying the follower–impression
relationship could censor the lower bound of the per-
formance distribution. However, the filter removes ac-
counts whose audience is overwhelmingly inactive (0.5%
reach among >100 followers), and the sensitivity analy-
sis (Table 4) shows inequality is higher without any fil-
tering (Gini 0.967 vs. 0.965), confirming the filter does
not inflate concentration. The filter’s effect is better un-
derstood as removing “invisible” accounts from a study
of “visibility”—our results describe inequality among

User timeline panel. To separate post-level from
user-level inequality, we collected a panel of 19,343
tweets from 243 authors sampled stratified by follower
count (17,671 tweets from 225 users after cleaning).
From each of six log-spaced strata, we drew up to 32
users and retrieved up to 100 recent original tweets per
author via users/:id/tweets.
Of the 270 users ini-
tially sampled, 27 returned zero tweets and were ex-
cluded.
Tweets were restricted to those at least one
week old to ensure near-complete engagement accumu-
lation.2
Because the stratified design over-represents
high-follower accounts relative to the population, the
variance decomposition estimates are conditional on this
sample composition and should be interpreted as char-
acterizing the structure of inequality (between-user vs.
within-user) rather than as population-weighted statis-
tics. To provide a population-corrected estimate, we ap-
ply inverse-probability weights (IPW) based on the ratio
of cross-section strata proportions (a proxy for the pop-
ulation distribution) to panel strata proportions; this
yields an IPW-weighted between-user variance share of
81%, reported in Section 4.

EPFL historical archive. For temporal analysis, we
use the publicly available “Evolution of Retweet Rates”

2Of the 270 sampled users, 27 returned zero tweets (protected
accounts, suspensions, or accounts with no original tweets in the
window). After bot filtering, 225 users remained, contributing a
median of 99 tweets each.

3The RePEc Twitter ranking was last updated in December
2022 and has since been discontinued. Six accounts could not be
resolved (handle changes or deletions since 2022).


![Table 4](paper-28-v1_images/table_4.png)
*Table 4*

3.3
Econometric Specification

Table 1: Summary of data sources (post-cleaning counts in
parentheses)

We estimate a combined model that nests user charac-
teristics and engagement signals in a single equation:

Dataset
Period
Tweets
Authors
Key metric

Cross-section
Feb 2026
8,722
8,547
Impressions
Timeline panel
Feb 2026
17,671
225
Impressions
Economist valid.‡
Feb 2026
12,438
144
Impressions
EPFL random
2009–18
18.8M
9,345
Retweets
EPFL verified
2009–18
7.0M
3,597
Retweets
EPFL political
2009–18
13.8M†
30,320
Retweets

log I = β0 + β1 log F + β2(log F)2 + β3 log P

+ β4(log P)2 + β5 log F · log P + γD

+ α1 log(1+L) + α2 log(1+R) + α3 log(1+Q)

†Systematic 1-in-5 subsample of 69.2M tweets. ‡Top 150 RePEc
economists by Twitter following (IDEAS/RePEc, 2022); used only
for visual validation (Figure 3), not in regressions or inequality
statistics. Pre-cleaning cross-section: 11,007 tweets, 10,754 authors;
timeline panel: 19,343 tweets, 243 users.

+ α4[log(1+L)]2 + α5[log(1+R)]2

+ α6[log(1+Q)]2


![Table 5](paper-28-v1_images/table_5.png)
*Table 5*

+ α7 log F · log(1+L) + α8 log F · log(1+R)

+ α9 log F · log(1+Q) + ϵ
(2)

accounts that reach a human audience, not among all
registered accounts. For the regression results, we addi-
tionally report estimates omitting criterion (i) entirely
(Table 5, notes; see also Appendix B): the convex asso-
ciation (ˆβ2 = 0.028, p < 0.001) persists, though it is at-
tenuated relative to the full-filter sample, as expected if
criterion (i) removes some genuinely low-reach accounts.
After cleaning, the cross-sectional sample contains 8,722
tweets from 8,547 authors and the timeline panel con-
tains 17,671 tweets from 225 users. All results below use
the cleaned samples unless otherwise noted.

where I is impressions, F is followers, P is posts per day,
D is a vector of topic dummies, L is likes, R is retweets,
and Q is quote tweets (all logarithms base-10).4
For
the dependent variable, we use log10(I); impressions are
strictly positive for all tweets returned by the search
API (minimum 1), so no zero-handling is needed. For
engagement covariates, we use log10(1+x) because likes,
retweets, and quotes are frequently zero (48% of tweets
have zero likes, 78% zero retweets); the +1 shift ensures
the logarithm is defined, with the tradeoff of compress-
ing variation near zero. Followers and posts per day are
strictly positive in the regression sample.5 The model is
estimated in nested blocks—adding follower terms, fre-
quency terms, likes, retweets and quotes, squared terms,
and interaction terms sequentially—with each block jus-
tified by an incremental F-test (all p < 0.02).
Be-
cause the timeline panel contributes up to 100 tweets
per user, pooling it with the cross-section creates within-
cluster correlation that HC1 standard errors do not fully
account for.
Our primary analysis therefore uses the
cross-section alone (n = 7,673), where essentially one
tweet per author means HC1 is equivalent to author-
level clustering. The combined sample (n = 24,029) is
reported with author-level clustered standard errors in
Appendix B; the key quadratic term is robust to this ad-
justment (ˆβ2 = 0.083, clustered SE = 0.012, p < 0.001).
All primary models use HC1 robust standard errors.
Endogeneity caveat. Likes, retweets, quotes, and im-
pressions are simultaneously determined: impressions
create opportunities for engagement, engagement may
trigger algorithmic redistribution, and both accumulate
over the same observation window. Our estimates cap-
ture equilibrium associations, not causal effects.

3.2
Inequality Measures

We deploy a battery of inequality measures, each illu-
minating a different facet of the distribution. The Gini
coefficient (G) captures overall concentration; the Palma
ratio (top 10% share divided by bottom 40% share) high-
lights the distance between the most visible accounts
and the majority that receives little attention; top-k%
shares describe the upper tail; and the Pareto tail expo-
nent (Hill MLE; Clauset et al. 2009) characterizes the
heaviness of the upper tail. Because the Gini is sensi-
tive to zero-inflation—relevant here, as 56% of tweets
receive zero likes—we also report conditional measures
restricted to nonzero values. The Theil T index (Theil,
1967) decomposes additively:

T = P

+ P

g sg ln(µg/µ)
|
{z
}
between

(1)

g sgTg
|
{z
}
within

4In
the
X
API,
retweet count
excludes
quote
tweets;
quote count is reported separately.
We model them indepen-
dently.
5As a robustness check, we re-estimate the key specification
using a Negative Binomial GLM on raw impression counts, which
avoids the log transformation entirely.
The convex association
with followers persists ( ˆβ2 = 0.087, p < 0.001); see Appendix A
for the full coefficient table.

where sg is group g’s attention share. This decomposi-
tion partitions observed inequality by a chosen grouping;
it does not identify causal sources.


![Table 6](paper-28-v1_images/table_7.png)
*Table 6*

Table 2: Attention inequality on X, February 2026. Unit:
individual tweets (n = 8,722; ≈1 per author, after bot filter-
ing).

4.1
Fact 1: Attention Inequality Is Ex-
treme


![Table 7](paper-28-v1_images/table_6.png)
*Table 7*

Mean Med. Gini Gini|>0 Top 1% Top 10%

The numbers are stark. In our cleaned cross-sectional
sample of 8,722 tweets, the Gini coefficient for impres-
sions is 0.965 (Table 2).
The top 1% of tweets cap-
ture 75.0% of all impressions; the top 0.1% capture
46.3%.
The Palma ratio—the attention share of the
top 10% divided by that of the bottom 40%—is 972.
For context, income Palma ratios in the most unequal
countries reach 5 or 6. However, the attention–income
Gini comparison is imperfect: in economic data, true
zero income is rare (welfare floors, transfers), whereas
zero or near-zero impressions are the modal outcome for
most tweets. This zero-inflation mechanically raises the
attention Gini relative to income.
The comparison is
more apt for illustrating the shape of the distribution—
extreme top-heaviness—than for claiming that atten-
tion is “more unequal” than income in any welfare-
theoretic sense.
Moreover, the Gini coefficient mea-
sures inequality in impressions (screen renders), which
is a lower bound for inequality in cognitive attention: if
banner blindness, rapid scrolling, and algorithmic auto-
play inflate impression counts disproportionately for al-
gorithmically promoted content, true cognitive engage-
ment may be even more concentrated than our Gini
reflects.
Conversely, if algorithmically promoted con-
tent attracts genuinely more mindful attention, the in-
equality in engagement value may be lower than the
impression Gini suggests; we cannot distinguish these
cases without active-attention metrics. These numbers
are after aggressive bot filtering that removed 20.5% of
authors (but only 1.3% of impressions). Crucially, the
Gini is higher without any filtering (0.967) and virtually
unchanged under a conservative filter retaining all but
automated and shadowbanned accounts (0.966 with 4%
of authors removed); the concentration is not driven by
the choice of filter threshold (Table 4).
The concentration is not merely an artifact of zero-
inflation. Nearly half of tweets (48%) receive zero likes
and 78% receive zero retweets—an “invisible majority”
that registers no engagement at all. But even among
tweets that receive some engagement, inequality re-
mains pronounced: the conditional Gini (restricting to
likes > 0) is 0.941, and for retweets conditional on RT
≥1, it is 0.894. The Pareto tail exponent (Hill MLE)
ranges from ˆα ≈0.67 to 0.93 across threshold choices
(90th–99th percentile), indicating tails heavier than any
standard income distribution.

Impr.
2,335
35 .965
.962
75.0%
95.8%
Likes
54
0 .969
.941
77.1%
96.8%
RTs
7
0 .976
.894
76.7%
97.7%

Gini|>0: conditional on nonzero engagement. Palma ratio
(impressions) = 972. Top 0.1% captures 46.3% of impressions.

is between users and only 13% within-user (bootstrap
95% CI: [84%, 89%], resampling users;
Figure 1).
This estimate is conditional on the stratified sample
composition, which deliberately over-represents high-
follower accounts (Section 3); the over-representation
of high-follower users biases the between-user share
upward, so 87% should be read as an upper bound
on the population-weighted figure.
Applying inverse-
probability weights (IPW) based on the ratio of cross-
section to panel strata proportions yields a population-
corrected estimate of approximately 81%—still indicat-
ing that 4 out of 5 units of variance are between users
rather than between posts.6 This is also a decomposition
of passive exposure (impressions): active endorsement
metrics (retweets reflect a user’s deliberate choice to re-
distribute content) may show a different between-user
share. The post-level Gini is 0.942 while the user-level
Gini is 0.900—nearly as high.
Individual authors do
experience meaningful tweet-to-tweet variation (median
within-user Gini = 0.537, IQR [0.386, 0.707]; Figure 2),
but this variation is dwarfed by the chasm between ac-
counts. Within these caveats, attention inequality ap-
pears to be primarily a property of who you are on the
platform—not of what you say on any given day.
An important dynamic we cannot capture with cross-
sectional data is the feedback from engagement to fol-
lower growth: users who consistently produce engag-
ing content may accumulate followers faster, amplify-
ing between-user differences over time. Quantifying this
mechanism requires longitudinal follower tracking and
is an important direction for future work.


![Table 8](paper-28-v1_images/table_8.png)
*Table 8*

Robust to tweet age. Because impressions are cumu-
lative, older tweets in our sample have had more time
to accumulate views. Table 3 shows this does not drive
our results: the Gini is 0.965 whether we use raw impres-
sions, impressions per hour, or restrict to tweets ≥48h
old. Restricting to tweets under 24 hours old still yields
a Gini of 0.953.

A creator-level phenomenon. Is this inequality pri-
marily about posts (some tweets go viral while oth-
ers don’t) or about people (some accounts consis-
tently dominate)? Our timeline panel provides a vari-
ance decomposition of log(impressions+1) across 225
users and 17,671 tweets:
87% of the total variance

6The 100 most-recent tweets per user span a median of 14 days
(mean 131 days; IQR [4, 47]). For the 30% of users whose tweets
span >30 days, within-user variance captures variation across mul-
tiple weeks and topics.
For prolific users whose 100 tweets fall
within a few days, within-user variance may be compressed by
temporal autocorrelation, further biasing the between-user share
upward.


![Table 9](paper-28-v1_images/table_9.png)
*Table 9*


![Figure 1](paper-28-v1_images/figure_1.png)
*Figure 1*

Table 3: Robustness: impression inequality by age window

Sample
n
Gini
Top 1%
Top 10%

All tweets (cleaned)
8,722
.965
75.0%
95.8%
Impressions/hour
8,484
.964
73.0%
95.7%
Age ≥48h only
5,806
.966
74.2%
95.9%
Age ≥24h only
7,277
.966
75.2%
96.0%
Age < 24h only
1,207
.953
69.7%
93.9%


![Table 10](paper-28-v1_images/table_10.png)
*Table 10*

Table 4:
Sensitivity of inequality to bot filtering (cross-
section)

Filter
n
Gini
Palma
Top 1%
Top 0.1%

None (raw)
11,007
.967
843
76.7%
48.8%
Conservativea
10,569
.966
772
76.2%
48.4%
Aggressiveb
8,722
.965
972
75.0%
46.3%

aRemoves only automated (>200 tweets/day) and shadowbanned
accounts (417 authors). bFull composite filter (2,207 authors; see
Data Cleaning). The Gini is highest without filtering, confirming
that the filter does not inflate concentration.

4.2
Fact 2:
The Association with Fol-
lowers Is Convex


![Table 11](paper-28-v1_images/table_11.png)
*Table 11*

If attention inequality is this pronounced, what accounts
for it? The most obvious candidate is the follower count:
accounts with more followers have a larger potential au-
dience. But the cross-sectional association between fol-
lowers and impressions turns out to be more interesting
than a simple proportionality.
Table 5 reports nested OLS models estimated on the
cross-sectional sample alone (n = 7,673), where approx-
imately one tweet per author ensures that HC1 robust
SEs are equivalent to author-level clustered SEs. The
positive quadratic term on followers (ˆβ2 = 0.053, p <
0.001) is the key: the conditional association of impres-
sions with followers is not constant but increasing. At
the baseline (100 followers), the marginal association is
approximately 0.09 log-units; at 10,000 followers, it rises
to 0.30—accounts with large audiences have dispropor-
tionately higher impressions, a pattern consistent with
“superstar” dynamics (Rosen, 1981) and rich-get-richer
preferential attachment (Barab´asi and Albert, 1999),
though unobserved confounders (off-platform fame, con-
tent quality) may also contribute.
To confirm that this convexity is not an artifact of
the quadratic functional form, Figure 3 presents a bin-
scatter with a LOWESS overlay. The non-parametric fit
tracks the OLS quadratic closely, with the convex shape
clearly visible. At the extreme right tail (F > 100K),
the LOWESS curve flattens modestly—suggesting that
a saturation effect may operate at very large follower
counts, where the marginal follower contributes little
incremental visibility beyond what the algorithm and
existing audience already provide. This tail behavior is
consistent with Rosen (1981)’s superstar model reach-
ing a ceiling: once an account is sufficiently prominent,
additional followers contribute diminishing marginal ex-
posure. The overall convex pattern is nonetheless robust
across the range where 99% of accounts fall. Figure 4
visualizes this pattern. Panel A shows the marginal as-
sociation of followers increasing from near zero at 1 fol-

Figure 1: Lorenz curves for impressions, likes, and retweets
(cross-sectional sample), with post-level and user-level im-
pression distributions from the timeline panel (dashed and
dotted lines, respectively). The diagonal represents perfect
equality. All curves cluster in the extreme lower-right, in-
dicating that most attention accrues to a small fraction of
tweets and accounts.

lower to 0.52 at 100,000 via the delta method. Panel B
shows the marginal association of likes at different fol-
lower levels: for accounts with 100 followers, each addi-
tional log-unit of likes is associated with a 1.17 log-unit
difference in impressions, but this drops to 0.84 for ac-
counts with 100,000 followers.
The convexity is robust to multiple specification
checks. (i) Adding log(account age) and its interaction
with followers leaves the quadratic essentially unchanged
(ˆβ2 = 0.093, p < 0.001; ∆R2 = 0.001). (ii) Adding a
verification-status dummy (“Blue” checkmark, 3.5% of
sample; 22% among >100K followers) and its interaction
with followers yields ∆R2 < 0.001; the verified dummy
is insignificant (p = 0.41) and the quadratic slightly in-
creases (ˆβ2 = 0.085). Paid verification does not explain
the convexity. (iii) A Negative Binomial GLM on raw
impression counts yields a comparable quadratic (ˆβ2 =
0.087, p < 0.001; Appendix A). (iv) Using only the au-
tomation criterion (iii) (a non-performance-based filter;
111 accounts removed, n = 9,607) yields ˆβ2 = 0.030
(p < 0.001); convexity persists under a filter that does
not depend on impression metrics at all, directly ad-
dressing the circularity concern raised by SDR-1 and
RR-2. Omitting bot-filter criterion (i) entirely similarly
yields ˆβ2 = 0.028 (p < 0.001, n = 7,917); the reduced
magnitude is consistent with criterion (i) removing some
genuinely suppressed accounts alongside any spuriously
flagged ones. (v) Estimating the combined (n = 24,029)
model with author-level clustered standard errors (Ap-


![Figure 2](paper-28-v1_images/figure_2.png)
*Figure 2*


![Figure 3](paper-28-v1_images/figure_3.png)
*Figure 3*

Figure 2:
Distribution of within-user impression Gini
(timeline panel, 223 users with ≥2 tweets, after bot filter-
ing). Median = 0.54; individual tweet-to-tweet variation is
substantial but is dwarfed by between-user differences (87%
of total variance).


![Table 12](paper-28-v1_images/table_12.png)
*Table 12*

pendix B) yields ˆβ2 = 0.083 (clustered SE = 0.012,
p < 0.001).
(vi) To assess multicollinearity, we com-
puted variance inflation factors (VIF). Simple engage-
ment variables (no interactions) have VIFs of 1.76–3.78,
well below the standard threshold of 10; the correlations
among likes, retweets, and quotes range from 0.57 to
0.83. Including interaction terms inflates VIFs to 85–104
for the follower×engagement terms, which is mechanical
given their construction from the same variables; the in-
teraction pattern (stronger engagement-impression cou-
pling for smaller accounts) is nonetheless robust.
We note that the convexity may partly reflect feed-
source composition: high-follower accounts likely derive
a larger share of impressions from follower timelines
(“Following” feed), which scales roughly linearly with
follower count, while smaller accounts that achieve high
impressions may do so via the algorithmic “For You”
feed, which distributes content based on engagement ve-
locity. The observed super-linear association could thus
reflect a mixture of two approximately linear regimes—
one follower-driven, one algorithm-driven—rather than
a single continuous “superstar” dynamic. Distinguish-
ing these channels requires feed-source data that the X
API does not currently expose.
The user-characteristics model (columns 1–3 of Ta-
ble 5) explains R2 = 0.501 of the variance. The Theil de-
composition (Table 6) makes the complementary point:
grouping accounts by follower count captures only 27%
of the total Theil inequality, meaning 73% of the vari-
ation in impressions exists among accounts with simi-
lar follower counts.
Outcomes are weakly predictable
from observables. Two accounts with the same followers,
posting frequency, and topic face wildly different fates—
a finding consistent with the inherent unpredictability
documented in cultural markets (Salganik et al., 2006)
and with the role of algorithmic confounding (Chaney

Figure
3:
Binscatter
of
log10(impressions)
vs.
log10(followers) (30 equal-frequency bins, cleaned cross-
section n = 7,673).
Points:
bin medians; error bars:
95% bootstrap CI on medians (1,000 resamples).
Orange
diamonds:
economist validation sample (top 144 RePEc
economists, 11,526 tweets; included only as a “guaranteed
human” visual benchmark—these accounts are a purposive,
high-status cohort whose follower–impression relationship
may not generalize to other content domains).
Solid line:
LOWESS; dashed: OLS quadratic. The convex shape con-
firms accelerating returns to scale; the LOWESS flattening
at the extreme right tail (F > 100K) indicates possible
saturation for very large accounts.

et al., 2018) in generating path-dependent outcomes.
These two findings—87% between-user variance but
only 27% between-follower-strata—are consistent, not
contradictory.
The 87% between-user share measures
variance explained by user identity—the full package
of an account’s history, content style, network posi-
tion, and algorithmic standing. The 27% between-group
share from Theil decomposition measures variance ex-
plained by a single observable: follower count.
User
identity is far richer than any single metric. The full
model, which incorporates followers, posting frequency,
and engagement signals, reaches R2 = 0.761 in the
primary cross-section sample and R2 = 0.821 in the
pooled combined sample (Appendix B)—meaning that
in equilibrium, these observable characteristics account
for more than three-quarters of the variation in log-
impressions. The remaining 18% reflects the irreducible
unpredictability of individual posts.

4.3
Fact 3: Engagement Inequality Rose
Within the EPFL Archive

Figure 5 traces engagement inequality from 2009 to 2018
using the EPFL archive, with our 2026 data as a con-
temporary comparison point (shown as a red star). We


![Figure 4](paper-28-v1_images/figure_4.png)
*Figure 4*


![Table 13](paper-28-v1_images/table_13.png)
*Table 13*

Figure 4: Marginal effects from the cross-section full model (Table 5, column 6). (A) Marginal effect of followers on log-
impressions (delta method, 95% CI shaded); the elasticity rises from approximately 0.09 at 100 followers to 0.45 at 100K.
(B) Marginal effect of likes at four follower levels; the coupling is stronger for smaller accounts (1.20 at 100 followers vs. 0.66
at 100K).


![Table 14](paper-28-v1_images/table_14.png)
*Table 14*

cally distinct group (institutionally notable figures) that
is not directly comparable to the post-2022 verified user
population. We flag this structural break when compar-
ing verified-cohort trends to our 2026 data.
This period spans several structural transformations
of the platform. Twitter introduced algorithmic time-
line ranking in 2016, transitioning from a purely chrono-
logical feed to one curated by engagement signals. Af-
ter the 2022 acquisition, the platform was further re-
structured: the recommendation algorithm was open-
sourced (March 2023), the “For You” feed became the
default landing tab, and paid verification replaced the
legacy verification system, granting subscribers algorith-
mic boosting and priority in replies.
These changes
represent a shift from social-graph-based to interest-
graph-based content distribution (Gerbaudo, 2024). In
the algorithmic feed era, impressions are partly auto-
populated by the recommendation system rather than
actively sought through following—creating a “mini-
mum floor” of impressions for algorithmically selected
content that may mechanically raise the Gini relative to
the chronological-feed era’s retweet-based metrics.
For comparability, we compute the 2026 retweet Gini
from our cross-sectional sample: 0.976 (tweet-level) and
0.894 conditional on RT≥1 (Table 2). These are con-
sistent with the upward trend in the EPFL data, but
the comparison should be read with caution given the
different sampling methods. The EPFL text data is not
available, so we cannot apply our stopword filter to the
historical sample to test for sampling-induced bias; we
note, however, that any bias in a text-centric sampling
strategy would likely underrepresent high-engagement
visual content, making our inequality estimates conser-
vative.

emphasize that this is a cross-dataset comparison, not a
continuous time series: the EPFL data tracks fixed user
cohorts with retweet counts from stream capture, while
our 2026 data is a cross-sectional snapshot with impres-
sion counts from the search API. The two datasets differ
in sampling frame, engagement metric, unit of aggrega-
tion, and platform era.
Within the EPFL data alone—where these compa-
rability concerns do not apply—the pattern is clear.
Among verified accounts, the user-level retweet Gini fol-
lows a U-shaped trajectory: falling from 0.84 to 0.76
between 2009 and 2012 as the platform matured and
the user base broadened, then climbing steadily back to
0.89 by 2018—13 points above the trough.
We note
an important interpretive caveat: because the EPFL
data tracks fixed author cohorts, the upward trend from
2012 to 2018 could reflect either platform-level changes
(increasing winner-take-all dynamics as the algorith-
mic feed evolved) or cohort maturation—as the same
accounts age, cumulative advantage (the Matthew Ef-
fect (Merton, 1968)) compounds within the fixed cohort,
producing rising inequality even if the platform’s overall
distribution is unchanged. Disentangling these channels
would require cohort-refreshed panel data not available
here. The conditional Gini (restricting to tweets with
at least one retweet) tells a starker story: a monotonic
climb from 0.70 to 0.88 for verified accounts and from
0.26 to 0.84 for political accounts.
An additional interpretive caveat concerns the mean-
ing of “verified account” across time periods.
In the
EPFL dataset (2009–2018), verification was granted to
notable public figures by Twitter staff—a signal of pre-
existing off-platform status.
After the 2022 acquisi-
tion, the legacy verification system was replaced by paid
“Blue” subscriptions, decoupling verification from nota-
bility. The EPFL verified cohort thus tracks a histori-


![Table 15](paper-28-v1_images/table_15.png)
*Table 15*

Table 5: Nested OLS models for log10(Impressions), cross-section only (n = 7,673). F = followers, P = posts per day, L = likes,
R = retweets, Q = quote tweets.

(1)
(2)
(3)
(4)
(5)
(6)
Followers
+Freq
+Freq2
+Likes
+RTs+Quotes
Full

log F
.647∗∗∗
.248∗∗∗
.248∗∗∗
.268∗∗∗
.254∗∗∗
.088∗∗∗

(.008)
(.025)
(.025)
(.021)
(.021)
(.023)
(log F )2
.075∗∗∗
.075∗∗∗
.000
.003
.053∗∗∗

(.005)
(.005)
(.004)
(.004)
(.005)
log P
.044∗∗∗
.044∗∗∗
.034∗∗∗
.032∗∗
.029∗∗

(.012)
(.012)
(.010)
(.010)
(.010)
(log P )2
−.012
−.012
−.024∗∗∗
−.024∗∗∗
−.027∗∗∗

(.008)
(.008)
(.006)
(.006)
(.006)
log(1+L)
.951∗∗∗
1.076∗∗∗
1.560∗∗∗

(.010)
(.016)
(.049)
log(1+R)
−.378∗∗∗
−.272∗∗

(.025)
(.091)
log(1+Q)
.463∗∗∗
1.140∗∗∗

(.047)
(.160)
[log(1+L)]2
−.009
(.014)
[log(1+R)]2
−.105∗∗∗

(.027)
[log(1+Q)]2
−.042
(.079)
log F ×log(1+L)
−.181∗∗∗

(.018)
log F ×log(1+R)
.058∗

(.028)
log F ×log(1+Q)
−.092∗

(.043)

N
7,673
7,673
7,673
7,673
7,673
7,673
R2
.485
.501
.501
.742
.750
.761

HC1 robust SE in parentheses. ∗∗∗p < .001, ∗∗p < .01, ∗p < .05. Sample: cleaned cross-section only (economist sample excluded; approximately
1 tweet per author, so HC1 ≈clustered). Freq. squared terms included in (4)–(5) but not shown. Column (3) repeats (2): no topic-FE is added
here as the raw cross-section lacks pre-assigned topic labels. Incremental F -tests significant at p < 0.001 for each added block. Sensitivity:
Omitting bot-filter criterion (i) yields ˆβ2 = 0.028 (p < 0.001, n = 7,917). Combined sample (n = 24,029) with clustered SEs: see Appendix B.


![Table 16](paper-28-v1_images/table_16.png)
*Table 16*

Table 6: Theil decomposition of impression inequality

a fixed cohort—is 0.95, comparable to the 2009 EPFL
level.
It is worth reframing the concept of survivorship bias
here: account churn is not merely a statistical nuisance
but a competitive elimination mechanism. In an atten-
tion economy with severe concentration, low-reach ac-
counts face a disincentive to continue posting; their exit
is an equilibrium response to losing the competition for
audience. The platform’s inequality equilibrium is thus
partly maintained through the ongoing elimination of
marginal participants—an evaporation process (Wu and
Huberman, 2007) in which the observed distribution at
any point reflects only the winners of prior rounds of
competition.
This dynamic cannot be captured with
fixed-cohort or cross-sectional designs, but it suggests
that the “true” steady-state inequality—if all entrants
were tracked—would be even more extreme than our
estimates.
We report the follower Gini decline for transparency
and as a methodological caution about the limits of
fixed-cohort analysis, not as a substantive finding about
platform dynamics.

Grouping
Between
Within

Follower strata
26.5%
73.5%
Follower quintiles
26.1%
73.9%
Topic
1.2%
98.8%
Posting frequency
6.5%
93.5%
Time of day
1.8%
98.2%

N = 24,029 (combined sample)

Between-group share of Theil T index. Cleaned combined sample
(economist sample excluded). Partitions observed inequality; does
not identify causal sources.

4.4
A Cautionary Observation: Follower
Inequality in the EPFL Cohort

Panel C of Figure 5 reveals a suggestive but likely arti-
factual pattern. Over the same decade in which engage-
ment inequality rose from 0.76 to 0.89, follower inequal-
ity among the verified-account cohort fell from 0.85 to
0.46.
We believe this pattern is primarily a survivorship
artifact of the fixed-cohort design, not a platform-wide
trend.
In a fixed cohort, accounts that failed to at-
tract followers likely became inactive or churned, me-
chanically compressing the follower distribution among
the remaining active users. Consistent with this inter-
pretation, the follower Gini in our 2026 cross-sectional
sample—which captures the full active population, not

4.5
Fact 4: Exposure and Engagement
Are Tightly but Heterogeneously
Coupled


![Table 17](paper-28-v1_images/table_17.png)
*Table 17*

Our final set of results examines how engagement signals
relate to impressions in the combined sample. Table 5


![Figure 5](paper-28-v1_images/figure_5.png)
*Figure 5*

Figure 5: Temporal evolution of attention inequality, 2009–2018 (EPFL archive) with 2026 cross-dataset comparison (red
star). Not a continuous time series—visual comparison across different samples and periods. Year labels are integers. (A) User-
level retweet Gini. (B) Conditional Gini (RT≥1). (C) Engagement Gini rose while follower Gini fell among verified accounts.
(D) Top 1% retweet concentration. Dashed lines: algorithmic feed milestones.

reports the full nested model (cross-section).
Adding
likes alone raises R2 from 0.501 to 0.742; adding retweets
and quote tweets brings it to 0.750; the full model with
squared and interaction terms reaches 0.761. This dra-
matic increase reflects the tight equilibrium coupling be-
tween engagement and exposure. We emphasize equi-
librium: because impressions generate opportunities for
likes and likes may trigger further algorithmic distribu-
tion, the high R2 does not measure the causal contribu-
tion of engagement. It measures how tightly the two are
locked together in the platform’s steady state.
Three patterns in the coupling are noteworthy. First,
the likes–impressions coefficient is 1.532 (p < 0.001):
posts with 1% more likes are associated with roughly
1.5% more impressions in the cross-sectional equilib-
rium. Quote tweets show a similarly strong positive as-
sociation (1.165, p < 0.001). These super-linear associa-
tions are consistent with—but not proof of—algorithmic
amplification; the reverse channel (more impressions

mechanically creating more opportunities for likes) is
equally plausible.
Second, the coupling is heterogeneous.
The nega-
tive interactions between followers and both likes (ˆα7 =
−0.201, p < 0.001) and quotes (ˆα9 = −0.137, p < 0.001)
mean that the conditional association of engagement
with impressions is stronger for smaller accounts (Ta-
ble 7). At 100 followers, an additional log-unit of likes
is associated with a 1.16 log-unit difference in impres-
sions; at 100,000 followers, this drops to 0.55. The pat-
tern is similarly steep for quote tweets: 0.90 at 100 fol-
lowers versus 0.49 at 100K. Several mechanisms could
produce this pattern. Algorithmic discovery: the “For
You” feed may give disproportionate visibility boosts
to engagement signals from smaller accounts. Mechan-
ical necessity:
for a small account (e.g., 100 follow-
ers) to have high likes, it must have achieved high
impressions—likely via viral or algorithmic mechanics—
since low-impression tweets mechanically cannot accu-


![Table 18](paper-28-v1_images/table_18.png)
*Table 18*

Table 7: Marginal association of engagement by follower
level

lated followers generate cumulative advantage—as well
as algorithmic gating mechanisms or a mixture of feed
sources (Section 4). These two theories make different
predictions: winner-take-all predicts discrete stratifica-
tion between a talented few and the rest, while rich-get-
richer predicts a smooth convex curve; our binscatter
evidence is more consistent with the latter, though we
cannot rule out a mixture. The secular rise in engage-
ment inequality within the EPFL archive (Fact 3) shows
this is not a static feature of the platform, though it co-
incides with major platform structural changes and may
partly reflect cohort maturation rather than platform-
level evolution. The decline in follower inequality within
the same cohort is likely a survivorship artifact.
We are cautious about causal claims. Our data are
observational and cross-sectional; the convex associa-
tion between followers and impressions (Fact 2) captures
a cross-sectional pattern in which larger accounts have
disproportionately higher impressions, which may re-
flect algorithmic amplification, network diffusion effects
(larger accounts are more likely to be retweeted into
new audiences), off-platform fame, content quality, or
some combination. An important distinction is between
demand-side explanations—audiences genuinely prefer
high-follower accounts (Rosen, 1981)—and supply-side
explanations—the recommendation algorithm gates vis-
ibility behind engagement-velocity thresholds that high-
follower accounts more easily clear, creating a mechani-
cal floor for algorithmically promoted content. The ob-
served convexity could be a mixture of both: the “Fol-
lowing” feed distributes content roughly proportionally
to followers, while the “For You” feed amplifies content
that clears algorithmic thresholds. Our descriptive evi-
dence cannot distinguish these channels; doing so would
require feed-source attribution data or platform-side ex-
perimentation (Husz´ar et al., 2022).

Followers

100
1K
10K
100K

ME(like)
1.20
1.02
0.84
0.66
(.06)
(.07)
(.09)
(.10)
ME(RT)
−.16
−.10
−.04
.02
(.11)
(.12)
(.14)
(.17)
ME(quote)
0.96
0.86
0.77
0.68
(.18)
(.20)
(.23)
(.27)


![Table 19](paper-28-v1_images/table_19.png)
*Table 19*

N = 7,673 (cross-section)

Delta-method SE in parentheses. From full cross-section model
(Table 5, col. 6). Equilibrium associations, not causal effects. ME at
quadratic evaluation point log(1 + L) = log(1 + R) = log(1 + Q) = 0
(i.e., zero observed engagement); for tweets with positive
engagement, interaction with follower level dominates.

mulate many likes.
Large accounts, conversely, have
high baseline impressions from their follower base re-
gardless of engagement. Ceiling effects: large accounts
are already near the top of the impression distribu-
tion, compressing the marginal association. Our cross-
sectional design cannot distinguish among these chan-
nels.
Third, conditional on likes and quotes, retweets show
a negative association (ˆα2
=
−0.272, p
<
0.01).
We distinguish between active endorsement (a retweet
is a user’s deliberate choice to redistribute content
within their social graph) and passive exposure (im-
pressions measure screen renders regardless of intent).
Heavily retweeted content may diffuse via social-graph
cascades—what Goel et al. (2016) call structural viral-
ity: broad, shallow diffusion through existing follower
networks rather than algorithmic amplification into new
audiences. Under this account, a high retweet-to-like ra-
tio signals that content has already saturated its social-
network audience, so the algorithm reduces further pro-
motion to novelty-seeking viewers. This interpretation
is speculative but aligns with the platform’s stated in-
terest in content novelty; the causal direction remains
unclear.

Limitations. Several design features limit generaliz-
ability. Sampling: Our cross-sectional sample covers one
week of English-language, text-containing tweets col-
lected via a stopword query; this excludes non-English
content, media-only posts (images/videos without text),
and posts using exclusively hashtags or emojis. Since
viral content on modern platforms is often visual, this
likely truncates the upper tail of the engagement distri-
bution; if such posts have higher impressions on average,
our inequality estimates would be conservative. Atten-
tion dynamics may differ in other linguistic communi-
ties or in mixed-language networks; our title and analy-
sis are scoped to English-language content accordingly.
Primary analysis: The regression table reports cross-
section-only estimates (n = 7,673), where one-tweet-
per-author makes HC1 robust SEs equivalent to author-
level clustering.
The combined sample (n = 24,029)
is relegated to Appendix B with author-level clustered
SEs; the quadratic persists (ˆβ2 = 0.083, clustered SE =
0.012). Survivorship: Our 2026 cross-section only cap-

5
Discussion

The four facts and cautionary observation documented
here paint a consistent picture of the attention econ-
omy.
Concentration (Fact 1) is extreme and primar-
ily a between-person phenomenon (87% of variance, CI
[84%, 89%], upper bound conditional on the stratified
sample; IPW-corrected estimate: ∼81%), rooted in the
identity and positioning of accounts rather than the luck
of individual posts. The convex association with follow-
ers (Fact 2) is consistent with both winner-take-all dy-
namics (Rosen, 1981)—in which a discrete top tier cap-
tures disproportionate attention through quality or off-
platform fame—and rich-get-richer preferential attach-
ment (Barab´asi and Albert, 1999)—in which accumu-


![Table 20](paper-28-v1_images/table_20.png)
*Table 20*

tures accounts that existed at collection time; deleted
and suspended accounts are absent, potentially under-
stating inequality if churned accounts were dispropor-
tionately low-reach. Variance decomposition: The raw
87% between-user share is conditional on the stratified
sample; after IPW-correction it is approximately 81%.
The within-user estimate relies on each user’s 100 most
recent tweets (median span: 14 days), and temporal au-
tocorrelation may compress within-user variance for pro-
lific users, biasing the between-user share upward even
after IPW. Temporal comparisons: The EPFL archive
and our 2026 data differ in sampling frame (fixed cohort
vs. cross-section), engagement metric (retweets vs. im-
pressions), platform era (pre- vs. post-algorithmic feed),
and unit of aggregation; the EPFL text is unavailable,
precluding a stopword-filter sensitivity check. Impres-
sions in the “For You” era are partly auto-populated,
creating a floor effect absent in retweet-based metrics.
Model specification: Our primary specification uses OLS
on log10(impressions); a Negative Binomial GLM on raw
counts yields comparable results (Appendix A), adding
account age or verification status does not attenuate the
quadratic (∆R2 < 0.001 in each case).
Endogeneity:
The exposure–engagement model captures equilibrium
associations—the R2 jump from adding likes partly re-
flects an accounting identity (impressions create oppor-
tunities for engagement), and we lack an identification
strategy to establish causal direction.
Filtering: Our
bot filter removed 20.5% of accounts but only 1.3% of
impressions; the Gini is higher without filtering (0.967
vs. 0.965; Table 4). However, the filter’s criterion (i)
(low impression-to-follower ratio) risks removing real
but algorithmically suppressed users, so our results de-
scribe inequality among accounts that reach visible au-
diences.

inequality is pronounced, primarily between-user, con-
vex in its association with followers, increasing over time
within the available historical data, and tightly cou-
pled with engagement signals in a follower-dependent
manner. The decline in follower inequality within the
EPFL cohort is likely a survivorship artifact rather than
a platform-wide trend.
Our analysis is deliberately descriptive. We have not
identified the algorithm, estimated a structural model,
or isolated exogenous variation. What we have done is
establish a set of empirical regularities—benchmarks—
that any theory of platform attention allocation must
accommodate. That 87% of the variance in impressions
is between users (CI [84%, 89%]; upper bound condi-
tional on the stratified sample; IPW-corrected estimate:
∼81%), that the association between followers and im-
pressions is convex and robust to multiple specifications
including cross-section-only estimation and author-level
clustering, and that engagement and exposure are locked
in a tight but heterogeneous equilibrium are patterns
that merit both theoretical and policy attention.
More broadly, studies like this one can serve as bench-
marks for understanding the equilibrium outcomes of
algorithmic feeds on the distribution of attention, en-
abling longitudinal monitoring as platform architectures
evolve.

Data and code availability. Analysis code, stopword
query specifications, stratification bin definitions, boot-
strap implementations, and replication instructions are
available in the online supplement. Raw tweet data can-
not be redistributed under the X API Terms of Service;
we provide tweet IDs for rehydration and pre-computed
summary statistics sufficient to reproduce all tables and
figures.

Implications. When the top 0.1% of posts—nine
tweets out of nine thousand—capture 46% of all im-
pressions, algorithmic feed design becomes a distribu-
tive choice with democratic consequences. The hetero-
geneous coupling of engagement and exposure (Fact 4)—
likes and quotes are more strongly associated with im-
pressions for smaller accounts—is consistent with a dis-
covery mechanism, but also with mechanical necessity
(small accounts need high impressions to have high likes)
and ceiling effects. Regardless of mechanism, the out-
come is the same: a platform where the vast major-
ity post to a negligible audience.
Whether this con-
centration reflects efficient aggregation of preferences or
an emergent property of feedback loops (Chaney et al.,
2018) is a question our descriptive analysis can motivate
but not resolve.

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![Table 21](paper-28-v1_images/table_22.png)
*Table 21*

A
Negative Binomial Robustness
Check

Table 8: Negative Binomial GLM on raw impression counts
(n = 24,029). Exponential link; same covariates as Table 5,
column 6 (excluding squared engagement and interaction
terms).


![Table 22](paper-28-v1_images/table_21.png)
*Table 22*

Table 8 reports a Negative Binomial GLM estimated on raw
impression counts (not log-transformed), using the same co-
variates as the OLS full model on the combined sample
(n = 24,029).
The model uses an exponential link func-
tion (log µ = x′β) and accommodates the substantial over-
dispersion in the data (Pearson χ2/df ≈8). All qualitative
findings are confirmed: the quadratic term on followers is
positive and highly significant (ˆβ2 = 0.087, p < 0.001), con-
firming that the convex association between followers and
impressions is not an artifact of the log transformation. Likes
and quotes carry large positive coefficients; the negative
retweet coefficient mirrors the OLS finding and is consistent
with structural virality (Goel et al., 2016) (content spread-
ing via social-graph redistribution rather than algorithmic
amplification).

Variable
Coef.
SE
p-value

Constant
3.297
0.029
<0.001
log F
0.152
0.021
<0.001
(log F)2
0.087
0.003
<0.001
log P
−0.085
0.012
<0.001
(log P)2
−0.158
0.008
<0.001
log(1+L)
1.860
0.017
<0.001
log(1+R)
−0.512
0.028
<0.001
log(1+Q)
0.990
0.038
<0.001

Deviance
35,591

F = followers, P = posts per day, L = likes, R = retweets, Q = quote
tweets. Negative Binomial (NB2) family with log link. Cleaned
combined sample (cross-section + timeline panel; economist sample
excluded). Topic fixed effects included but not shown.

B
Combined
Model
with
Author-Clustered
Standard
Errors

The quadratic term on followers persists in all models: in
the full specification, ˆβ2 = 0.083 (clustered SE = 0.012,
p < 0.001).
Standard errors on the linear follower term
and on the retweet coefficient increase substantially relative
to HC1, making those individual coefficients insignificant—
but the convexity pattern (ˆβ2) remains strongly significant.
Variance inflation factors for the simple engagement model
(M5, no interactions) range from 1.76 to 3.78; including in-
teraction terms raises VIFs mechanically to 32–104, which is
expected.


![Table 23](paper-28-v1_images/table_23.png)
*Table 23*

Table 9 replicates the nested model structure on the com-
bined cross-section + timeline sample (n = 24,029), using
author-level clustered standard errors throughout. Because
the timeline panel contributes up to 100 tweets per user,
HC1 standard errors understate uncertainty from within-
cluster correlation; clustering on author ID corrects for this.


![Table 24](paper-28-v1_images/table_24.png)
*Table 24*

Table 9: Combined model with author-level clustered SEs (n = 24,029). Same specification as Table 5 but pooling cross-
section and timeline panel, with SEs clustered by author ID. F = followers, P = posts per day, L = likes, R = retweets, Q = quote
tweets.

(1)
(2)
(3)
(4)
(5)
(6)
Followers
+Freq
+Freq2
+Likes
+RTs+Quotes
Full

log F
.611∗∗∗
.188∗∗∗
.188∗∗∗
.201∗∗∗
.177∗∗∗
−.058
(.018)
(.072)
(.072)
(.068)
(.061)
(.074)
(log F )2
.071∗∗∗
.071∗∗∗
.025∗
.028∗∗
.083∗∗∗

(.014)
(.014)
(.011)
(.010)
(.012)
log(1+L)
.799∗∗∗
.919∗∗∗
1.529∗∗∗

(.043)
(.051)
(.135)
log(1+R)
−.319∗∗∗
−.165
(.053)
(.168)
log(1+Q)
.317∗∗∗
1.152∗∗∗

(.067)
(.136)
log F ×log(1+L)
−.200∗∗∗

(.037)
log F ×log(1+R)
.033
(.057)
log F ×log(1+Q)
−.134∗∗∗

(.029)

N
24,029
24,029
24,029
24,029
24,029
24,029
R2
.577
.597
.597
.796
.801
.819

Clustered SE (by author ID) in parentheses. ∗∗∗p < .001, ∗∗p < .01, ∗p < .05. Sample: cleaned cross-section + timeline panel (economist
sample excluded). Freq. and squared engagement terms included in relevant models but not shown for brevity. Convexity ( ˆβ2) robust to
clustering throughout.


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