Overview

This paper studies how censorship on social media affects polarization, disagreement, and internal conflict using a formal opinion dynamics model. The central result is a trade-off: stronger censorship tends to increase polarization but reduce internal conflict, while the effect on disagreement depends on how connected the network is and how much cross-group communication exists.

Introduction

Social media platforms increasingly shape real-world opinion formation, but governance and regulation remain limited. This creates an important policy question: what are the welfare effects of censorship on social media? In particular:

  • Does censorship reduce harmful conflict, or does it deepen polarization?
  • Is there an optimal level of censorship?
  • Does the answer depend on homophily (whether people mostly talk to like-minded users versus across groups)?

The paper approaches these questions through a stylized opinion dynamics framework with two opposing groups, where a platform/network administrator chooses a censorship threshold before opinions evolve.

The paper connects three strands of literature:

  1. Opinion dynamics, especially models like DeGroot, bounded confidence, and Friedkin–Johnsen.
  2. Freedom of speech and moderation in social media, including concerns about arbitrary censorship and platform control over information flow.
  3. Social media and welfare, where much of the empirical literature focuses on well-being and life satisfaction rather than formal network-level opinion dynamics.

A key contribution here is to provide a quantitative framework for studying censorship as a policy variable in a social network.

Methodology

1) Network structure

The model assumes a network of n agents split into two equally sized groups with opposing viewpoints (think of them as two ideological camps).

  • Opinions lie on a continuous interval [-1, 1]
  • Left-group innate opinions are distributed on [-1, 0]
  • Right-group innate opinions are distributed on [0, 1]
  • The two distributions are symmetric around zero

Communication intensity is parameterized by:

  • p: within-group communication intensity
  • q: across-group communication intensity

This allows the paper to study both high-homophily and low-homophily environments.

2) Opinion dynamics (Friedkin–Johnsen)

Each agent starts with an innate opinion and updates over time by combining:

  • their own innate view (stubbornness),
  • and the opinions of their neighbors (weighted by communication intensity).

Opinions evolve until they reach an equilibrium.

3) Censorship as a threshold rule

Censorship is modeled as a threshold policy chosen by a network administrator.

  • Let c ∈ [0,1] be the censor point.
  • Agents with opinions outside [-c, c] are banned.
  • Banned agents keep their current opinion and stop participating in further opinion formation.

Important convention in the paper:

  • Smaller c = stronger censorship (because fewer opinions are allowed)

4) Welfare measures

The paper evaluates censorship using three equilibrium outcomes:

Polarization

Measures dispersion of opinions (variance-like concept).

Disagreement

Measures how far apart connected agents are in equilibrium (weighted by network ties).

Internal Conflict

Measures how far each agent’s equilibrium opinion moves from their innate opinion.

Finally, welfare is defined as a weighted negative sum of these three costs:

  • higher polarization = worse
  • higher disagreement = worse
  • higher internal conflict = worse

So welfare depends on policy weights over the three indices.

Main Results

General case

The paper derives analytical and numerical results for the expected effects of censorship.

1) More censorship increases polarization

As censorship becomes stronger, extreme users are removed from interaction, so they stop updating and remain at more extreme opinions. This raises equilibrium polarization.

2) More censorship reduces internal conflict

When fewer people interact, opinions move less from their original values, so internal conflict declines.

3) Disagreement is non-monotonic

The effect on disagreement depends on network size and connectivity:

  • In smaller / weakly connected networks, disagreement tends to decrease with censorship
  • In larger / highly connected networks, disagreement may initially increase and only later decline

This is one of the paper’s most interesting findings: censorship can simultaneously reduce communication while increasing distance between surviving opinions in some parameter regions.

Welfare and Optimal Censorship

Because censorship affects polarization, disagreement, and internal conflict differently, the welfare effect is not one-directional.

The paper shows that depending on:

  • network connectivity (p, q, n)
  • and welfare weights (how much the administrator cares about polarization vs disagreement vs internal conflict)

the optimal policy may be:

  • no censorship
  • partial censorship
  • near-total / total censorship

In other words, there is no single universal moderation rule — the “best” censorship level is parameter-dependent.

Role of Homophily

A major contribution of the paper is showing how censorship effects change with network homophily.

Extremely high homophily (q = 0)

Agents only communicate within their own group.

  • Censorship has a smaller effect overall
  • Opinions are already evolving mostly inside echo chambers
  • Removing cross-group interaction does not change much (because it was already absent)

Extremely low homophily (q = p)

Agents communicate across groups as much as within groups.

  • Censorship has a stronger effect
  • Cross-group communication normally helps pull opinions closer together
  • Censorship shuts down that mixing, so the welfare and disagreement effects become more pronounced

A key takeaway is that censorship matters more in networks where cross-group exchange is active.

Interpretation

This framework highlights why moderation policy is hard:

  • Censorship can reduce conflict-like outcomes (especially internal conflict, sometimes disagreement)
  • But it can also entrench ideological distance and increase polarization

So moderation is not just a “more vs less” question — it is a design problem shaped by:

  • network structure,
  • communication patterns,
  • and the platform’s objective function.

Limitations and Future Work

The paper explicitly notes that the model takes the perspective of a welfare-oriented network administrator. A natural extension is to model a profit-maximizing platform instead, where moderation policy also depends on:

  • enforcement costs,
  • engagement,
  • user retention,
  • and platform incentives.

Another important next step is empirical calibration using real-world social media data (e.g., Twitter/X or Reddit) to estimate network and opinion parameters.

Citation

Krasowski, Kacper. Impact of Censorship in Social Media.