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Harmonizing vs Polarizing Platform Influence Functions

Hind AlMahmoud, Frederik Mallmann-trenn

Abstract

We investigate the dynamics of opinion formation on social networking platforms, focusing on how individual opinions, influenced by both social connections and platform algorithms, evolve. We model this process using a differential equation, accounting for both peer influence and the platform's content curation based on user preferences. Our primary aim is to analyze how these factors contribute to opinion polarization and identify potential strategies for its mitigation. We explore the conditions under which opinions converge to a consensus or remain polarized, emphasizing the role of the platform's influence function. Our findings in two-agent, complete graphs, and stochastic block model provide insights into the impact of social media algorithms on public discourse and offer a framework for understanding how polarization can be avoided.

Harmonizing vs Polarizing Platform Influence Functions

Abstract

We investigate the dynamics of opinion formation on social networking platforms, focusing on how individual opinions, influenced by both social connections and platform algorithms, evolve. We model this process using a differential equation, accounting for both peer influence and the platform's content curation based on user preferences. Our primary aim is to analyze how these factors contribute to opinion polarization and identify potential strategies for its mitigation. We explore the conditions under which opinions converge to a consensus or remain polarized, emphasizing the role of the platform's influence function. Our findings in two-agent, complete graphs, and stochastic block model provide insights into the impact of social media algorithms on public discourse and offer a framework for understanding how polarization can be avoided.

Paper Structure

This paper contains 22 sections, 13 theorems, 59 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Contributions
  3. Related Literature
  4. Outline
  5. Model and Notation
  6. Platform Influence Functions Properties
  7. Polarization Planes in Two Agent System
  8. Persistent Disagreement Results
  9. Polarization Conditions in Complete Graphs
  10. Results for General Platform Functions for Two-Agent System
  11. Results for General Platform Functions for Complete Graph of n Agents
  12. Results for the Stochastic Block Model with Two Blocks
  13. Results for Specific Platform Functions
  14. Examples of Polarizing Platform Influence Functions (PPIF)
  15. Sign Function
  16. ...and 7 more sections

Key Result

lemma thmcounterlemma

Consider the system at time $t$. Let $z=x_1(t)$ and $y=x_2(t)$. If $(z,y)$ is an equilibrium, it must be that $F_1$ intersects with $G$ at $(z,y)$ and, simultaneously, $F_2$ intersects with $H$ at $(z,y)$. Moreover, we have that if $f(z) > G(z,y,b)$, then $\dot x_1(t) > 0$. Conversely, if $f(z) < G(

Figures (9)

  • Figure 1: A depiction of the sign function along with the intersection points and polarization planes: $G$ (purple), $F_1$ (red), $F_2$ (yellow) and $H$ (green).
  • Figure 2: A second viewing angle of Figure \ref{['fig:SignFunctionWithIntersectionPoints']} highlighting the intersection point of $F_1$ (red) and the polarization plane: $G$ (purple).
  • Figure 3: A third viewing angle of Figure \ref{['fig:SignFunctionWithIntersectionPoints']} highlighting the intersection point of $F_2$ (yellow) and the polarization plane: $H$ (green).
  • Figure 4: A depiction of the sign function and polarization planes: $G$ (purple), $F_1$ (red), $F_2$ (yellow) and $H$ (green).
  • Figure 5: A depiction of the sign function and polarization planes: $G$ (purple), $F_1$ (red), $F_2$ (yellow) and $H$ (green) from a different viewing angle
  • ...and 4 more figures

Theorems & Definitions (30)

  • definition thmcounterdefinition: Equilibrium State or Steady State
  • definition thmcounterdefinition: (Strong) Consensus
  • definition thmcounterdefinition: Persistent Disagreement
  • definition thmcounterdefinition: Harmonizing Platform Influence Functions-HPIF
  • definition thmcounterdefinition: Polarizing Platform Influence Functions-PPIF
  • lemma thmcounterlemma
  • proof
  • theorem thmcountertheorem: Sufficient and Necessary Conditions for Strong Consensus
  • proof
  • theorem thmcountertheorem: Sufficient Condition for PD
  • ...and 20 more