# The Effects of Group Sanctions on Participation and Toxicity:
Quasi-experimental Evidence from the Fediverse

Carl Colglazier1, Nathan TeBlunthuis2, Aaron Shaw1  1Northwestern University
2University of Michigan

###### Abstract

Online communities often overlap and coexist, despite incongruent norms and
approaches to content moderation. When communities diverge, decentralized and
federated communities may pursue group-level sanctions, including defederation
(disconnection) to block communication between members of specific
communities. We investigate the effects of defederation in the context of the
Fediverse, a set of decentralized, interconnected social networks with
independent governance. Mastodon and Pleroma, the most popular software
powering the Fediverse, allow administrators on one server to defederate from
another. We use a difference-in-differences approach and matched controls to
estimate the effects of defederation events on participation and message
toxicity among affected members of the blocked and blocking servers. We find
that defederation causes a drop in activity for accounts on the blocked
servers, but not on the blocking servers. Also, we find no evidence of an
effect of defederation on message toxicity.

## Introduction

Content moderation in response to toxic and anti-social behavior is pervasive
in social media. In general, moderation interventions strive to balance the
value of wide and active user bases with the threats posed by conflicts and
hate speech (Gillespie, 2018). Websites that host user-generated content and
sub-communities apply many kinds of policies and interventions. However, when
norms diverge across interconnected, independent communities in the absence of
a single (corporate or not) parent or owner, governance and moderation pose
acute challenges.

A growing empirical literature has investigated social media content
moderation and governance. Moderation actions most frequently target
individual posts and accounts, but other group-level sanctions affect entire
communities or websites. For example, Reddit has banned subreddits and Discord
has blocked servers, reducing the prevalence of unwanted behavior within and
sometimes beyond the targeted groups (Chandrasekharan et al., 2017, 2022;
Ribeiro et al., 2021, 2023; Russo et al., 2023; Zhang and Zhu, 2011). Most
prior work on group-level sanctions focuses on sanctions applied by central
actors such as commercial social media platform staff. However, autonomous
community administrators can also enact group-level sanctions such as when a
sub-community restricts contributions from members of another sub-community.
These decentralized group-level sanctions are distinct in that the targeted
sub-community remains part of the larger network. To our knowledge, the
effects of such sanctions remain unexplored empirically.

Servers pre-defederationServers post-defederationAccounts pre-
defederationAccounts pre-defederation Figure 1: Illustration of how
defederation disconnects two servers and thereby disconnects the subnetworks
of people using each server. The top row shows the network of servers before
(left) and after (right) defederation. The bottom row shows the corresponding
networks of users. On the left, an edge connects a user on one server with a
user on a different server. Defederation (right) disconnects them so they can
no longer exchange messages.

To investigate the effects of decentralized group-level sanctions, we analyze
_defederation events_ in the Fediverse, a decentralized social media system
which consists of independently managed servers that host individual accounts
and pass messages using shared protocols. Communication between servers can
happen only when the administrators of both servers permit it. Server
administrators can revoke such permission by “defederating” from (blocking all
interactions with) specific servers. Defederation is one of the few tools
administrators in a decentralized system have to protect against bad actors or
enforce norms from beyond their own servers. While many defederation events on
the Fediverse occur between servers with no known interaction history, many
also come in response to norm violations and toxic interactions across server
boundaries with a history of previous interactions. Defederations that cutoff
cross-server interactions provide an opportunity to identify the effects of
these group sanctions on accounts most likely to be directly affected.

We collect data from 214 defederation events between January 1, 2021 to August
31, 2022 that involved 275 servers and 661 accounts which had previously
communicated across subsequently defederated inter-server connections. Using a
combination of non-parametric and parametric methods, we estimate the effects
of defederation on two outcomes: posting activity and toxic posting behavior
among affected accounts. We find an asymmetric impact on posting activity:
Accounts on blocked servers reduce their activity, but not accounts on
blocking servers. By contrast, we find that defederation has no effects on
post toxicity on either the blocked or blocking servers.

These findings suggest that defederation, although a common group-level
sanction on the Fediverse, has mixed effectiveness: Despite the risks of
severing communication channels, communities implementing group-level
sanctions do not lose activity. This implies that defederation may avoid some
of the costs associated with other moderation techniques such as account
requirements or group sanctions like geographic blocks (Hill and Shaw, 2021;
Zhang and Zhu, 2011). Although defederation reduces activity by blocked
accounts, we did not find evidence that it made their posts less toxic. This
suggests that defederation may not improve adherence to broadly held norms.
Our study contributes to knowledge of content moderation on social media in
that it (1) describes defederation, a novel form of group-level sanction as
instantiated on the Fediverse, (2) derives hypotheses regarding the effects of
defederation from prior literature, (3) creates a novel dataset of
defederation events, (4) conducts a quasi-experimental analyses to quantify
effects of defederation on parties affected on the blocked and blocking
servers and (5) finds that defederation has asymmetric effects on activity and
no measurable effect on toxicity.

## Background

### Social media content moderation and governance

Challenges of decentralized governance and content moderation in networked
communication systems are ubiquitous. Threats to public safety, trust, and
health resulting from toxicity, misinformation, and incivility online are now
widely perceived and addressed by various content moderation and governance
tools (Gruzd, Soares, and Mai, 2023). National and supra-national governments
impose disparate legal regimes such as the GDPR in Europe or the DCMA in the
United States. Simultaneously, corporate platforms employ many strategies,
from algorithmic filters to user and content monitoring systems, to monitor
and shape content visibility. Leaders of communities such as subreddits and
Facebook groups institute their own rules and norms and seek to hold community
participants to them (Gillespie, 2018). Interdependence among these components
makes effective policymaking, design, and analysis of social media governance
especially difficult.

Large corporate platforms and autonomous communities alike must grapple with
incongruent norms about online behavior and the appropriate role of the above
governance components. For instance, today’s regulatory assemblage governing
social media departs from earlier eras characterized by utopian notions of
freedom of expression on the “electronic frontier” (Kaye, 2019). Whether
governance interventions are understood as “censorship” or “content
moderation” depends not only on one’s perspective, but also the on their
origin within the institutional hierarchy (Myers West, 2018). At the highest
level, state-led interventions prevent access to sites, domains, services, IP
blocks, or protocols (King, Pan, and Roberts, 2013). Similarly, network
service providers and other intermediaries also engage in blocks or website
takedowns justified by terms of service violations or legal risks (Vu,
Hutchings, and Anderson, 2023; Ribeiro et al., 2023; Han, Kumar, and
Durumeric, 2022). Lower in the hierarchy, owners and administrators of
specific sites or platforms set their own policies and can enforce them
through sanctions applied to individuals as well as whole (sub-)communities
(Jhaver et al., 2021; Chandrasekharan et al., 2022; Ribeiro et al., 2021).
Devolving policy setting and enforcement to increasingly low-level actors
poses a trade-off. Low-level governance can institute local norms and advance
a community’s specific goals, but may lack the necessary means to prevent
important categories of harm.

A growing literature in the social and computational sciences evaluates the
empirical effects of specific content moderation and governance techniques at
various institutional levels. Previously studied techniques include
deplatforming, quarantines, censorship and geographic blocks, banning, account
requirements, and pre-publication filtering (Ribeiro et al., 2023;
Chandrasekharan et al., 2022; King, Pan, and Roberts, 2013; Ribeiro et al.,
2021; Zhang and Zhu, 2011; Hill and Shaw, 2021; Tran et al., 2022). In
general, this prior work finds that barriers to specific kinds of
contributions from specific kinds of actors cause immediate decreases in the
targeted activity among the targeted accounts. As examples, requiring accounts
on wikis decreased the quantity of low-quality contributions (Hill and Shaw,
2021); mainland China’s block of Chinese language Wikipedia decreased
contributions from editors inside and outside of China (Zhang and Zhu, 2011),
and pre-publication moderation increased quality contributions (Tran et al.,
2022).

Some governance interventions spill-over or have indirect effects (intended or
not) beyond their immediate targets. Banning hateful communities on Reddit,
for example, reduced speech characteristic of the banned communities by both
the active participants in those communities and within the other communities
they participated in following the ban (Chandrasekharan et al., 2022).
However, when Reddit banned two toxic communities, they subsequently
reorganized on other platforms where they experienced declining activity and
one had increasing radicalization and toxicity (Ribeiro et al., 2021). Banning
whole sub-communities may also create spillovers of antisocial and toxic
behavior when the former members of banned communities migrate their
activities elsewhere (Ribeiro et al., 2021, 2023).

The majority of prior work in this area has identified effects of governance
and moderation interventions on the largest “mainstream” social media
platforms such as Facebook, Twitter, or Twitch (Jhaver et al., 2021; Mitts,
Pisharody, and Shapiro, 2022; Seering, Kraut, and Dabbish, 2017). A few have
focused on more decentralized or autonomous community environments like
subreddits or independently managed wikis (Chandrasekharan et al., 2022; Hill
and Shaw, 2021). Many of the interventions studied include group-level
sanctions such as political blocks and censorship events affecting whole
geographic regions (Zhang and Zhu, 2011), as well as decisions and enforcement
actions by “local” administrators or moderators (Srinivasan et al., 2019).
Several more recent studies have considered alternative social media sites,
such as alt-right communities Voat, Parler, or Gab, often with an eye towards
understanding how interventions on mainstream platforms may have impacted
participation in less regulated environments (Ribeiro et al., 2023; Stocking
et al., 2022). The current project expands this literature by analyzing the
effects of a previously unstudied group-level sanction in a decentralized and
federated social media network.

### Governance and moderation in federated communication networks

The architectures of federated communication systems create distinct
opportunities and obstacles to governance and moderation. Federated
communication networks, such as email, are defined by independently operated
servers which let users pass messages both within and across servers.
Protocol-based interoperability underpins this design and affords cross-server
communication. The resulting server-level autonomy may also offer benefits in
terms of scalability and resilience. For instance, new servers may join or
leave the network without coordinating with other servers. Such decentralized
and complex systems of communication tend to possess a scale-free structure
with superior robustness to the failure of single nodes over other classes of
large, complex graphs (Albert, Jeong, and Barabási, 2000).

Scalability and resilience are particularly important qualities for
communication networks, where the value of the network is often a superlinear
function of its size (Van Hove, 2016). Expanding a communication network can
produce collective benefits to members driven by both the increased space of
potential connections (_connectivity_) as well as the increased opportunities
for pooled information (_communality_) (Fulk et al., 1996). Federated networks
also offer profuse opportunities for decentralized action, including modular
extensions and localized content and norms (Datta et al., 2010).

At the same time, the decentralized structure of federated networks also makes
it difficult to centrally control or apply uniformity. Technical features
typically require a sufficient level of adoption across servers to be useful.
The overall result is that the user experience in a federated communication
network can vary enormously depending on how one connects to it.

This variability extends to governance. No server can directly dictate the
rules or decisions of another. The administrators of each server hold complete
autonomous control over their internal affairs. In choosing which server to
connect to the network through, individuals also choose a governance regime
(intentionally or not). If unsatisfied with one regime, they can (at least in
theory) move to another and take their data and social ties with them. Among
dissatisfied members of a community, the opportunity for “exit” may be
especially easy when it costs little time or effort to join another subnetwork
(Frey and Sumner, 2019; Frey and Schneider, 2021). Individuals wishing to
behave anti-socially—to harass, troll, or make offensive posts—may select a
server that allows them to do so. Other servers within a federated social
media network must address this to protect their own users.

Governance in federated communication networks is not limited to servers’
authority over individuals: servers also implement sanctions against each
other. If one server hosts anti-social behavior, other servers can implement a
server-level intervention. Such interventions, for instance group-level bans
or blocks, also happen among semi-autonomous communities within platforms or
more centralized environments like Reddit, Wikipedia, and multiplayer video
game servers. Yet, to our knowledge, prior work on governance in social media
has not analyzed the effects of these sorts of group-level interventions.
Doing so offers a valuable opportunity to expand the empirical knowledge in
this domain.

### The effects of community-level defederation as a group sanction

Servers in a federated network can enact sanctions against other servers in
several ways, all of which regulate interactions among their users. For
example, servers may filter, limit or slow the propagation of messages from
another server through their subnetwork. Of the possible approaches,
defederation—which completely blocks all communication across server
boundaries—is the most extreme. Defederation is widely used when server
administrators determine that another server is causing problems to such a
degree that managing continued interactions is not worth the trouble. For
example, email spam filters often include rules blocking all messages
originating from a given email domain or server.

Based on prior content moderation research and the characteristics of
defederation as a specific type of governance intervention in decentralized
social media, we pursue the following research questions:

  1. 1.

How does defederation impact the activity levels for affected accounts on (a)
the _defederated_ instance (blocked server); and (b) the _defederating_
instance (blocking server)?

  2. 2.

How does defederation impact toxic posting behavior among the affected
accounts on either (a) the blocked or (b) blocking servers?

When one Fediverse server blocks another, the blocked server no long
propagates messages to the blocking server. This reduces the size of the
audience that can be reached from the blocked server and thereby may decrease
the utility of posting on that server. As with interventions studied in prior
research such as bans, quarantines, and deplatforming, we expect that
defederation reduces activity among affected accounts on the blocked servers.

The likely consequences of defederation for the blocking server are less
clear. Disconnecting from the blocked server decreases the potential audience
of the blocking server’s users. As a result, individuals who lose valuable
connections might have fewer reasons to use the network. On the other hand,
server administrators who initiate defederation likely have an informed
rationale. They may anticipate the costs and benefits of defederation by
observing messages between their server and the servers they consider
blocking. Perhaps more importantly, some volunteer administrators struggle to
effectively protect their users from anti-social behavior. By enacting
defederation, administrators demonstrate competence in server governance,
eliciting increased trust and commitment from members of their communities. If
users tend to value such competence more than their connections to the blocked
server then defederation is unlikely to decrease their activity and could even
increase it.

Similarly, it is unclear how defederation will affect toxic posting behavior.
Some past studies of deplatforming have found that toxicity increases after
some deplatforming events (Ali et al., 2021; Buntain et al., 2023;
Chandrasekharan et al., 2017). Such increases may happen when group-level
sanctions provoke blowback or revolts against the imposition of sanctions in
the form of non-compliance with sanctions or increasing anti-social behavior
(Heckathorn, 1988). However, other studies have found that group-level
sanctions decrease or do not change toxicity (Jhaver et al., 2021;
Chandrasekharan et al., 2022).

Therefore, we anticipate that defederation will have limited or negligible
effects on toxic posting behavior. Accounts on blocked servers may not receive
any indication of the reasons for the intervention. While server
administrators may choose to publicize their defederation decisions, no
mechanism propagates the decisions to the users of targeted servers (much less
the users whose behavior may have triggered the block in the first place).
Users on the blocking serer who had interacted across the severed connection
likewise experience no other direct effects and retain access to the rest of
their communication networks. In the absence of more targeted or focused
information about the reasons behind the block, we do not expect it to impact
toxic behavior substantially.

Figure 2: The y-axis shows the cumulative number of blocked and blocking
accounts included in our analysis over our study period.

## Data, Measures, and Methods

We pursue an observational, quasi-experimental research design to identify
effects of defederation on the activity and toxic posting behavior in the
Fediverse. We collected longitudinal trace data from 7,445 publicly listed
defederation events and about 104 million public posts that occurred in the
Fediverse on either the Mastodon or Pleroma networks between April 2, 2021 and
May 31, 2022. Using this data, we analyze activity of user accounts (for RQ1)
and the toxicity of their messages (for RQ2) on the blocking and blocked
servers impacted by these events in comparison to matched control accounts. We
apply a difference-in-differences approach and present both non-parametric and
parametric estimates of the effects of defederation.

### Empirical Setting

Term |  Description
---|---
Fediverse |  A group of independently operated social media servers which interoperate with shared protocols.
Defederation |  A server-to-server block between servers in a federated system.
Mastodon |  The most popular and widely used software on the Fediverse.
Pleroma |  A lightweight Fediverse software with an API similar to Mastodon and an alternative feature set.
Server administrator |  A person or group who controls the technical infrastructure and configuration of a Fediverse server.
Group sanction |  A moderation action against a group, not an individual.
TABLE I: Glossary of key terms.

The Fediverse is a decentralized social network comprised of many servers
which each institute their own rules, policies, and moderation practices. Each
account connects to the network through a home server and can send and receive
posts from accounts both within and outside the home server via the
ActivityPub protocol. Mastodon and Pleroma are two popular, interoperable
ActivityPub-based microblogging systems with overlapping but distinct
features.

Fediverse administrators have nearly complete control over their servers, from
choosing and configuring software to setting rules. However, administrators
only have direct control over their own server. Although users of one server
can report rule-breaking posts by another server’s accounts, only the
administrator of an account’s home server can sanction the user, such as by
removing the post or sending a warning. Consequently, when two servers come
into conflict, administrators must either use persuasion, ignore the problem,
or block or filter the other server.

Defederation is the process of severing ties between servers to restrict
interactions, typically due to differences in policies, norms, or content.
Administrators are responsible for defederation decisions, and they can choose
to defederate from specific servers. Defederation helps maintain the autonomy
of servers and allows them to adhere to their own values and rules.
Individuals with accounts on Fediverse servers do not tend to receive direct
notifications about defederation events, though they may either see an
announcement by their server administrator. On Mastodon, defederations delete
records of the defederated server, meaning that affected accounts lose
followers from the defederated server and no longer follow accounts on the
defederated server.

Figure 3: A screenshot shows a cross-server interaction on Mastodon. Note that
the account name of the replying user indicates their home server (@_user_
@_server_).

### Data Collection

We first identify a list of Fediverse servers involved in defederation by
compiling a set of known servers which federate with other servers on the
list, starting with the set of servers on
mastodon.social111https://mastodon.social/. We then iteratively add servers
with peer connections to members of this set using an API feature which
discloses server-to-server connections. This approach identified 11,025
servers and 7,445 defederation records. We collected data from these servers
by running a script daily. The script uses publicly available and documented
REST APIs provided by Mastodon and Pleroma to collect timelines of posts. We
collected approximately 104 million posts in total. The post data allows us to
identify accounts that engaged in cross-server interaction because usernames
indicate the home server.

We identify defederation from the public records servers publish of which
other servers they block. We check these records each day and infer the date
that defederation occurred by the day a server first appears in the list. We
exclude 472 defederation events where we do not know the exact date of
defederation because we are missing a daily snapshot of the record. We only
analyzed defederation events where the public record persisted at least 92
days after the initial event, excluding 1,347 that did not. Accounts are
affected by a defederation event if they had previously sent a reply to an
account on the blocked or blocking server. We excluded accounts that may have
been affected by defederation events we dropped due to missing data issues.

Our analysis is designed to identify the effects of defederation accounting
for trends in activity and toxicity before and after defederation events
(defined below). We therefore analyze data from the 91 days prior to and
following each defederation event (dropping the day of the defederation
itself). The outcomes of interest are quantities and qualities of posting
activity, so we exclude inactive accounts by dropping those that posted fewer
than 10 times in the 91 days before a defederation event involving their home
server. We also include only accounts that posted at least once prior to the
91 day period and at least once in the final 45 days of this period.

Some servers experience multiple defederation events. In order to avoid
potential confounding of our estimates from multiple exposures to
defederation, we exclude accounts that experienced defederation events on
multiple days. After dropping some additional accounts in the matching process
(described below), the resulting dataset includes 258 accounts whose 71 home
servers were defederated and 150 accounts whose 52 home servers defederated
another server. This included a total of 214 defederation events.

### Measures

We construct measures within the analytic window for all accounts and servers
involved in defederations. We also aggregate our measures over 7 day periods
(weeks).

Defederation events: We observe defederation events via the records of
federation policies published by Mastodon and Pleroma servers within the
Fediverse systems we study. We collected data on 440 blocking servers and
1,136 blocked servers. We record the timestamp of each defederation event,
which we use to construct a timeline of defederation events.

Activity: The response variable of our analysis for RQ1 is the posting
$activity$ of user accounts affected by defederation events. We measure
activity as the number of posts an account makes each week.

Toxic behavior: RQ2 investigates the impact of defederation on toxic posting
behavior. We measure post toxicity using the Perspective API model for
toxicity, which uses machine learning to predict if a post is a ”rude,
disrespectful, or unreasonable comment that is likely to make someone leave a
discussion” (Jigsaw, 2021). For each post, the model outputs a score ranging
from 0–1 corresponding to the estimated probability that the post contains
toxic speech. For each account, we aggregated their toxicity during each week
by taking the mean toxicity score for their posts during that window.

Blocked user accounts: Defederation is a directional action from one server to
another and may not be reciprocated. In our research questions, we estimate
the effects of user accounts being blocked from cross-server interactions in a
defederation event. We assign accounts to the _blocked treatment group_ if
(1) their home server was defederated (blocked) by another server (the
blocking server),  (2) they replied to an account on the blocking server in
the 91 days before defederation, and to ensure the account is active at the
time of treatment,  (3) they post at least once in the last 45 days prior to
defederation  . For clarity we refer to the blocked treatment group as $U_{0}$
below.

Blocking user accounts: In our research questions, we are also interested in
effects of defederation on the blocking servers’ accounts. We assign accounts
on the blocking server to the blocking treatment group ($U_{1}$) if they meet
the parallel conditions to those described above for the blocked treatment
group.

Time: As noted above, we aggregate our measures over 7 day periods. We
therefore measure ($time$) as the number of such weekly periods before/after
the defederation event affecting the account in question excluding the day
defederation occurred.

## Analytic Plan

We pursue an identification strategy to estimate the effects of defederation
events. For both sets of outcomes—activity levels and toxic posts—we visualize
time series, conduct non-parametric statistical tests, and perform regression
analysis using difference-in-differences (DiD) estimators that infer the
effects of the treatment on treated accounts from both blocked and blocking
servers against a set of matched controls. We use coarsened exact matching to
construct this synthetic control group of accounts that are similar to the
accounts impacted by defederation (treated accounts).

### Constructing Matched Control Groups

All of our analyses depend on comparing user accounts that experienced
defederation events with similar accounts that did not. The goal of
statistical matching is to reduce bias and account for potential confounders.
In this case, we use observable, pre-treatment attributes of accounts that
capture how they engage with the wider Fediverse through posting replies to
external servers. We match on the following variables: total number of account
posts, the number of posts in the 45 days prior to treatment (“post count
(45)”), the number of replies sent, the number of other servers engaged with
replies, and the number of active accounts on their home server. We applied a
log transformation to each of these (highly skewed count) variables. We
construct all matching measures over weeks during the 91 days prior to the
defederation event experienced by the treated user in question.

We use coarsened exact matching (Iacus, King, and Porro, 2012) with Sturges’
rule to determine the number of bins for all variables except the number of
active accounts on the server, for which we used four bins to be less strict.
We used one-to-one matching, selecting the closest match according to
Mahalanobis distance and discarded accounts for which there was not a
sufficiently good match (139 for the blocked accounts; 63 for the blocking
accounts). Accounts that were treated were not eligible to be matched
controls.

We denote the resulting matched control groups as $C_{0}$, the control group
for blocked server users $U_{0}$, and $C_{1}$, the control group for blocking
server users $U_{1}$. The blocked accounts had 258 matched units from 397
potential units; the blocking accounts had 150 from 213 potential units.
Figure 4 shows the covariate balance using standardized mean differences
before and after matching across these groups.

Figure 4: A covariate balance plot shows the standardized mean difference
between treatment and control groups for each measure used in our matching
procedure before (unadjusted) and after (adjusted) matching. Our procedure
effectively found a group of matched controls similar to the treated accounts
along these measures.

### Analysis

Our analysis proceeds in three parts: descriptive comparison and
visualization; non-parametric tests; and difference-in-differences estimation.

##### Descriptive comparison and visualization:

We calculate descriptive and summary statistics for all measures across the
treated and control groups. We also visualize posting activity before and
after defederation, plotting the number of weekly posts made by the median
user account in each of our four study groups ($U_{0}$, $U_{1}$, $C_{0}$,
$C_{1}$) in the 12 weeks prior to and following defederation with 95%
confidence intervals based on order statistics. Both the descriptive analysis
and the visualization justify and complement our non-parametric and
difference-in-differences analyses.

##### Non-parametric tests:

We first compare changes in activity level and median post toxicity before and
after defederation using a non-parametric Wilcoxon signed-rank test, which
returns a $W$ test statistic representing the sum of the ranks of the positive
differences between paired observation and a p-value which compares to the
null hypothesis that the changes between the two groups are zero. This test is
robust to outliers, independent of distributional assumptions, and assigns
equal weight to each user account irrespective of their activity levels. For
toxicity in particular, this non-parametric approach reduces threats of bias
due to the opaque machine learning systems that create the values reported
from the Perspective API. We conduct this test over all user accounts in both
the blocked and blocking groups.

##### Difference-in-differences (DiD) estimation:

Our primary analysis estimates the causal effect of defederation on the
_blocked accounts_ ($U_{0}$) and the _blocking accounts_ ($U_{1}$) using a
difference-in-differences (DiD) framework. DiD systematically quantifies the
changes in a treatment group (i.e., blocked accounts; $U_{0}$) following an
intervention (i.e., a defederation event) relative to changes in a control
group (i.e., accounts matched to blocked accounts; $C_{0}$). It does this by
modeling temporal trends for each group (treatment; $U_{i}$ and control;
$U_{i}$) before and after the defederation as well as group-dependent
discontinuous “jumps” at the moment of intervention.

Our DiD estimates support causal inferences under several assumptions: The
matching procedure should result in control groups of accounts that were not
affected by defederation, but were just as likely to have been affected as the
accounts that were, the two groups’ trends in the outcome variables should be
parallel prior to treatment, and the trends should be linear. If so, then the
difference between the jumps of the two groups quantifies a “local average
treatment effect” (LATE).222We say local average treatment effect because the
estimate applies in specific times and places that may not generalize to other
contexts. We include random intercepts in our model to account for variability
between subjects. We fit versions of this model for both outcomes and types of
server (blocked and blocking) using the brms R package.

##### Model for activity:

$Activity$, the number of posts an account makes per week, is an over-
dispersed count variable. We therefore use a negative binomial model formally
represented as:

$\displaystyle y_{i,t}$ $\displaystyle\sim NegBinomial(\mu_{i,t},\phi)$
$\displaystyle\mu_{i,t}$ $\displaystyle=\beta_{0}+\zeta_{i}+\beta_{1}I(i\in
U_{k})$ $\displaystyle+\beta_{2}I(t>T)+\beta_{3}t+\beta_{4}I(t>T)\cdot t$
$\displaystyle+\beta_{5}I(i\in U_{k})\cdot I(t>T)+\beta_{6}I(i\in U_{k})\cdot
t$ $\displaystyle+\beta_{7}I(t>T)\cdot I(i\in U_{k})\cdot t$

Where $y_{i,t}$ is the activity of user account $i$ in week $t$. $T$ indicates
the time of defederation, $U_{k}$ is the treatment group ($U_{0}$ is the set
of blocked accounts and $U_{1}$ is the set of blocking accounts), $I$ is the
indicator function equal to 1 when its parameter is true and 0 if not, and
$\zeta_{i}$ is the random intercept for user account $i$. Our parameter of
interest is $\beta_{5}$, the coefficient for post-treatment membership in the
treatment group, for testing whether activity increases ($\beta_{5}>0$) or
decreases ($\beta_{5}<0$) upon defederation. The model’s other terms are
intercepts and trends pre-treatment ($\beta_{0}$,$\beta_{3}$) and post-
treatment ($\beta_{2}$,$\beta_{4}$,$\beta_{6}$) and membership in the
treatment group ($\beta_{1}$).333We note that the $\beta_{6}$ and $\beta_{7}$
coefficients model the group-specific trends before and after treatment. If
these are both 0, this would provide evidence supporting the parallel trends
assumption of our DiD models. As shown in Table III, the 95% credible
intervals for both coefficients contain 0, suggesting the assumption is
reasonable.

##### Model for toxicity:

Our measure for toxicity is calculated at the post level, leading to several
key differences in how we model this outcome. Instead of aggregating this at
the account level, which would obscure variation, we use a multi-level model
with random slopes for group to estimate the effects of defederation as an
account-level treatment on post-level toxicity. We use beta regression for our
analysis of toxicity because the Perspective API scores are on a range between
0 and 1 and are designed to quantify the probability that a comment is toxic.
Our model of toxicity is thus:

$\displaystyle y_{k,i,t}$ $\displaystyle\sim Beta(\mu_{i,t},\phi)$
$\displaystyle\mu_{i,t}$ $\displaystyle=K_{0}+\zeta_{i}+\eta_{0}(i\in
U_{k})+\eta_{1}(i\notin U_{k})$ $\displaystyle\eta_{0}$
$\displaystyle=\beta_{0}+\beta_{1}I(t>T)+\beta_{2}t+\beta_{3}I(t>T)\cdot t$
$\displaystyle\eta_{1}$
$\displaystyle=\beta_{4}+\beta_{5}I(t>T)+\beta_{6}t+\beta_{7}I(t>T)\cdot t$

where $y_{k,i,t}$ is the toxicity of a given post $k$ by account $i$ in week
$t$, $K_{0}$ is the overall intercept, $\zeta_{i}$ are the random intercepts
for each account, $\eta_{0}$ are random effects for the treatment group and
$\eta_{1}$ are random effects for the matched control group.

## Results

Figure 5 summarizes our dependent variables across the treatment and matched
control groups during the pre- and post-treatment periods. Below, we present
results for the two outcomes—activity and toxicity—separately.

Figure 5: Box and whisker plots visualize the distributions of our dependent
variables within the blocked and blocking groups of user accounts and their
matched controls before and after defederation. The lines correspond to the
median, the boxes to the inter-quartile range (IQR), the whiskers to the range
of the data within 1.5 * IQR, and the dots to data points outside the range of
the whiskers.

### Effects on Activity

Research question 1 asks how defederation affected activity among user
accounts whose home server either blocked (blocking group) or was blocked by
(blocked group) another server. Our visualization of the time series of
affected accounts compared to matched controls, non-parametric tests, and
difference-in-differences analysis all indicate that blocked group users
decreased their activity following defederation while changes among blocking
group users were minor or noisy.

Figure 6:  Visualization of activity among blocked and blocking user accounts
shows an asymmetric change in activity following defederation. An account with
a median post count on the blocked server declines in activity much more
rapidly following defederation compared to matched controls while an account
with a median post count on the blocking server declines similarly to matched
controls.

Before defederation, the trends and weekly median activity levels remained
comparable for accounts on both the blocked and blocking servers. Although all
groups reduced activity somewhat after defederation, Figure 6 shows the
activity levels on the blocked servers quickly diverged from their matched
controls after defederation. For instance, while the median post count for
treated accounts on blocked servers ($U_{0}$) was 18.5 posts one week before
defederation, this dropped to 13 posts one week after defederation. Compare
this to the analogous median post count among matched controls which was 20.5
posts per week both before and after defederation. In contrast, the median
post count among treated accounts on blocking servers ($U_{1}$) was 17 in the
week before and 13 in the week after defederation compared to 15 and 13 for
the matched controls ($C_{1}$).

#### Non-parametric tests:

Group | median | W | p
---|---|---|---
$U_{0}$ | -135.5 | 41197.5 | 0.000
$C_{0}$ | -18.0 | 35762.0 | 0.143
$U_{1}$ | -54.5 | 12413.0 | 0.122
$C_{1}$ | -53.5 | 12520.0 | 0.091
$\Delta_{0}$ | -39.0 | 39927.0 | 0.000
$\Delta_{1}$ | 3.0 | 10645.5 | 0.421
TABLE II: Non-parametric tests for differences in activity before and after
defederation events (summed across all weeks) find a measurable decrease in
posting activity for the accounts on blocked servers compared to matched
controls but no such change for accounts on blocking servers.

This strong response among the treated accounts on the blocked servers
($U_{0}$) also appears in the non-parametric test based on post counts summed
for all weeks and shown in Table II. Prior to defederation, median activity
among blocked accounts and matched controls was similar, yet following
treatment, activity for the treated blocked accounts decreased by a median of
135.5 posts (21.9%) compared to 18 posts (9.5%) for the matched controls. By
contrast, among the user accounts on the blocking servers, we observe very
similar post-defederation activity decreases for the treatment and matched
control accounts on the blocking server with a decrease in the median of 54.5
posts (10.7%) by treated accounts compared to 53.5 post (11.1%) by the the
matched controls. In sum, we observe asymmetric effects of defederation:
activity decreases for affected accounts on blocked servers, but not on
blocking servers.

#### DiD Analysis:

Our DiD results corroborate the same pattern: decreased activity among users
on the blocked servers, and no change among users on the blocking servers.
Table III shows the regression results for both models. Figure 7 plots the
modeled activity levels of a median account in each group along with the
corresponding 95% credible intervals quantifying uncertainty in the model’s
parameter estimates. User accounts on the the blocked servers ($U_{0}$)
decrease their activity compared to matched controls
($\beta_{5}=-0.24;SE=0.07$). For a user account with median pre-treatment
activity levels on the blocked server, this corresponds to a reduction from
$24.9$ posts per week immediately before treatment to $19.6$ posts per week
immediately after treatment (a $21.4$% reduction), compared to $22.8$ posts
per week after treatment for its matched control.

Consistent with our other results for user accounts on the blocking server,
the 95% credible interval for the effect of defederation on activity by
accounts on the blocking server ($U_{1}$) contains 0
($\beta_{5}=-0.08;SE=0.08$).

| Blocked | Blocking
---|---|---
Term | Estimate | Std error | 2.5% | 97.5% | Estimate | Std error | 2.5% | 97.5%
$\beta_{0}$ (Intercept) | 3.216 | 0.086 | 3.049 | 3.380 | 2.901 | 0.118 | 2.684 | 3.121
$\beta_{1}$ Group | -0.024 | 0.116 | -0.255 | 0.198 | 0.023 | 0.177 | -0.290 | 0.367
$\beta_{2}$ Treatment | -0.089 | 0.045 | -0.178 | 0.002 | -0.080 | 0.060 | -0.201 | 0.034
$\beta_{3}$ Time | 0.006 | 0.004 | -0.002 | 0.015 | -0.002 | 0.006 | -0.014 | 0.009
$\beta_{4}$ Treatment : Time | -0.026 | 0.006 | -0.038 | -0.014 | -0.027 | 0.008 | -0.042 | -0.010
$\beta_{5}$ Group : Treatment | -0.241 | 0.065 | -0.367 | -0.116 | -0.084 | 0.082 | -0.247 | 0.072
$\beta_{6}$ Group : Time | -0.007 | 0.006 | -0.020 | 0.004 | 0.006 | 0.008 | -0.010 | 0.021
$\beta_{7}$ Group : Treatment : Time | -0.015 | 0.009 | -0.031 | 0.002 | 0.009 | 0.011 | -0.013 | 0.032
TABLE III: Difference-in-differences analysis of activity level for user
accounts whose server was defederated (blocked group) or whose server
defederated another (blocking group). The 95% credible interval negative
coefficient for membership in the blocked group post-defederation
($\beta_{5}$) is less than 0, indicating that activity by accounts in this
group decreased more than accounts in the matched control group. We do not
draw such a conclusion about members of the blocking server because the
corresponding credible interval contains 0. Figure 7: A marginal effects plot
visualizes results from our difference-in-differences analysis of account
activity by week. We observe a discontinuous activity decrease among accounts
on the blocked server that exceeds any decrease in the matched controls, but
no corresponding change among accounts on the blocking server. The bands are
95% credible intervals that account for uncertainty in parameter estimates.

### Effects on Anti-Social Behavior

We now present results for our second research question on the effects of
defederation on the toxicity of posts by user accounts on the blocked and
blocking servers. Our three analyses: visualization of the time-series of
affected accounts compared to matched controls, non-parametric tests, and
difference-in-differences analysis are in agreement that defederation did not
result in a statistically detectable change in toxicity for affected accounts
on either server.

Figure 8:  Median toxicity among accounts which posted each week for blocked
and blocking user accounts. The median toxicity remained flat for all groups.

The median toxicity plotted in Figure 8 remained at consistent levels for
accounts which posted on a given week for both treatment and matched control
groups on both the blocked and blocking servers. The trends remained similar
before defederation between the treatment and control groups for accounts on
both the blocked and blocking servers.

#### Non-parametric tests

Table IV summarizes aggregate changes in anti-social behavior (toxicity) after
defederation for all groups. Anti-social behavior by user accounts on blocked
servers decreases slightly. For example, the median toxicity score for posts
from these accounts declined by 0.005, but we lack sufficient statistical
power to distinguish this from the null hypothesis that there was no
difference in changes between treatment and control groups on the blocked
server $(p=0.072)$. We do not observe even such a small change in toxicity
among posts from accounts on the blocking server.

Group | median | W | p
---|---|---|---
$U_{0}$ | -0.006 | 17746 | 0.538
$C_{0}$ | 0.004 | 14000 | 0.950
$U_{1}$ | -0.008 | 6514 | 0.619
$C_{1}$ | 0.001 | 5546 | 0.873
$\Delta_{0}$ | -0.005 | 17161 | 0.072
$\Delta_{1}$ | 0.000 | 6414 | 0.305
TABLE IV: Non-parametric difference-in-differences for median post toxicity before and after de-federation events. The $W$ test statistic represents the sum of the ranks of the positive differences between paired observations while the p-value compares to the alternative hypothesis that the changes are zero. | Blocked | Blocking
---|---|---
Group | Term | Estimate | Std error | 2.5% | 97.5% | Estimate | Std error | 2.5% | 97.5%
Treatment |  $\beta_{0}$ (Intercept) | -0.143 | 0.438 | -1.197 | 0.763 | -0.042 | 0.284 | -0.754 | 0.518
|  $\beta_{1}$ Treatment | 0.002 | 0.006 | -0.009 | 0.018 | -0.001 | 0.010 | -0.020 | 0.017
|  $\beta_{2}$ Time | 0.001 | 0.001 | 0.000 | 0.002 | 0.001 | 0.001 | -0.001 | 0.003
|  $\beta_{3}$ Treatment : Time | -0.002 | 0.001 | -0.004 | 0.000 | -0.001 | 0.002 | -0.004 | 0.003
Control |  $\beta_{4}$ (Intercept) | 0.136 | 0.436 | -0.907 | 1.044 | 0.048 | 0.283 | -0.613 | 0.649
|  $\beta_{5}$ Treatment | 0.000 | 0.006 | -0.016 | 0.011 | 0.004 | 0.009 | -0.014 | 0.024
|  $\beta_{6}$ Time | 0.001 | 0.001 | 0.000 | 0.002 | 0.003 | 0.001 | 0.001 | 0.005
|  $\beta_{7}$ Treatment : Time | -0.005 | 0.001 | -0.007 | -0.003 | -0.006 | 0.002 | -0.009 | -0.002
TABLE V: Beta regression coefficients drawn from the posterior of the
parametric toxicity DiD model for user accounts whose server was defederated
(blocked group) or whose server defederated another (blocking group). For all
groups, the 95% credible intervals for a change in toxicity levels after
treatment ($\beta_{1}$, $\beta_{5}$) contain 0.

#### DiD Analysis

Again, the results of the DiD analysis for toxicity tell a similar story to
the data visualization and non-parametric tests. Our models estimate that
toxicity levels of posts from affected accounts on both blocked and blocking
servers do not change following defederation events. Full regression results
are in Table V. We find no evidence for any significant changes in post
toxicity among accounts on either blocked or blocking servers.

## Discussion

We investigated defederation, a group-level sanction where administrators of
the blocking server disconnect communication channels between users of their
server and the blocked server. Although one of few actions by which leaders in
such networks can protect their community’s servers from trolls, harassers,
and objectionable content from other servers, defederation’s consequences are
poorly understood. Therefore, in a quasi-experimental study, we estimate the
effects of defederation on the activity and toxicity of users on both the
blocking and blocked servers who had sent or received messages across server
boundaries. Our results provide the first evidence concerning the impacts of
defederation in Fediverse communication networks. This evidence can inform
governance decisions among Fediverse server administrators and moderators and
the design of future decentralized social media networks.

Research question 1a asked how defederation changed posting activity by
affected users on the blocked server. We find that losing communication
channels to users on the blocking server causes users on the blocked server
who had used such channels to decrease their activity. This helps us
understand defederation’s potential as an intervention against undesirable
behavior. Not only does it protect the blocking server’s users from the
blocked server, it may decrease the blocked server’s value. Defederation may
cause a user on the blocked server to lose valued audiences, sources of
content, or interpersonal connections and therefore to become less active.

If this positive effect of defederation results from lost connections,
defederation might also have a negative consequence: Users of the blocking
server may decrease their activity for the same reason. However, our results
for research question 1b, which inquired into defederation’s consequences on
posting activity by affected users on the blocking server, show no measurable
effect. These asymmetric effects of defederation on posting activity suggest
that administrators may find defederation an effective response to undesirable
behavior on other servers without negative impacts on activity by affected
user accounts on their own server.

Although sanctions are typically intended to promote normative compliance,
group-level sanctions in some prior empirical studies have been met with
increases in anti-social behavior or rebellious non-compliance (Mitts,
Pisharody, and Shapiro, 2022; Ribeiro et al., 2021; Russo et al., 2023).
Therefore, we investigated defederation’s effects on toxicity in research
question 2. If defederation causes an increase in anti-social behavior, we
would expect an increase in toxicity on the blocked server. If defederation
causes non-compliance, we would expect toxicity on the blocking server to
increase. However, we do not find evidence of either of these adverse indirect
outcomes. In this sense, defederation appears similar to individual and
collective sanctions analyzed in prior studies such as account banning,
quarantine, and sub-community removal (Chandrasekharan et al., 2022, 2017;
Jhaver et al., 2021). Some of these group-level sanctions have even improved
compliance with widely-held norms (Chandrasekharan et al., 2017). If
defederation also does so then we would expect affected users on the blocked
server to become less toxic. Yet we observe no such effect.

Among the various kinds of content moderation and governance interventions
available to social media systems administrators, server defederation may be
among the more extreme group sanctions. However, our analysis suggests that it
may also provide administrators with an effective response to undesirable
behavior that does not undermine the activity of affected user accounts on the
server implementing the block. User accounts affected by defederation events
can continue to communicate with others on their respective servers as well as
other servers where federated interactions remain permitted. The disconnection
from the network is not total and can respect the local norms that operate
among distinct sub-components of the larger network. We believe this is a
design feature of federated systems that distinguishes them from other kinds
of content moderation and governance systems in social media environments.
Other, more centralized, platforms may wish to experiment with similar
features as doing so may advance user trust and safety without undermining
activity.

That said, further research is needed to support recommendations about
defederation’s overall benefits and limitations in decentralized social media
systems. Such research should uncover the mechanisms that drive the observed
changes in activity levels and toxic behaviors, such as changes in user
motivations or migration to alternative servers or communication channels.
Future work should also investigate how defederation events are perceived and
experienced by the people operating affected accounts on both blocked and
blocking servers. In addition, insights into the reasons behind administrator
decisions to implement defederation blocks as well as the timing of such
changes would enrich the findings reported here. As noted above, the
defederation events in our study did not occur at random and were likely
undertaken with some awareness of the various actors involved. For these
reasons, we encourage caution around the generalizability of our findings
beyond the specific context of our study.

Additional limitations of the study relate to the constraints around our data
collection, measurement, and analysis strategies. First, our data collection
was limited to public status posts, which do not fully capture user
interactions within the Fediverse. Private posts and direct messages, which
are not accessible through the APIs we used, might exhibit different patterns
in response to defederation events. In addition, some servers choose not to
publish defederation information. If the effects of defederation emerge
anywhere other than public posts, our analysis could not capture them.

Our analysis also relied on the Perspective API to analyze the content of
posts by quantifying their toxicity. While this tool provides a useful proxy,
its accuracy may vary across languages and contexts and its errors may affect
our statistical results (TeBlunthuis, Hase, and Chan, 2023). Moreover, it is
conceivable that the contexts for which Perspective designed depart from the
Fediverse so substantially that Perspective fails to detect forms of
misbehavior affected by defederation. Future research could explore
alternative methods for assessing content quality and toxicity. Although
language models like those utilized in the Perspective API have significant
limitations, we believe that these are likely to be time invariant, at least
in the short-run. That is, they would happen on both sides of a defederation
event. In addition, defederation might affect forms of behavior beyond
toxicity that future research may investigate such as topics of post or the
extent to which they elicit replies or boosts (analogous to retweets).

In terms of the analysis, our study incorporated several critical assumptions
and focused on the effects of defederation events within a relatively narrow
timeframe. Matching entails an assumption that selection into treatment or
control occurred due to observable variables incorporated into the matching
process. A quasi-experimental difference-in-differences analysis similarly
assumes parallel trends and comparability across units conditional only on
“as-if” random exposure to the treatment in question. For example, possible
advanced announcements of defederation events may drive changes in user
behavior prior to defederation itself. While we tried to support such
assumptions empirically, they may not hold uniformly, and in addition, the
effects of defederation on user behavior might change over time as users adapt
to new norms and technologies. Additional and longer duration analyses could
address these concerns and shed light on the long-term consequences of
defederation events.

## Conclusion

In this study, we investigated the effects of defederation events on the
activity levels and toxic posting behavior of accounts in the Fediverse. The
results indicate that such events produce asymmetric effects on activity for
affected accounts on blocked servers versus those on blocking servers with no
increase in toxicity for any groups. The results also highlight the potential
of decentralized social networks and their unique mechanisms, such as
defederation, in providing communities with tools to manage content moderation
and other aspects of online interactions. Future research could explore the
causes or reasons behind defederation events, the long-term consequences of
defederation, as well as the mechanisms by which defederation produces
(asymmetric) effects. By continuing to study the Fediverse and its
affordances, we can better understand how to foster healthy online communities
and effective content moderation strategies in a decentralized environment.

## Acknowledgements

The authors would like to thank Ceren Budak and the Community Data Science
Collective. Support for this work was provided by the U.S. National Science
Foundation (IIS-191020, IIS-1908850). Additionally, Dr. TeBlunthuis was
partially supported by NSF grant IIS-1815875.

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