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Large Language Models can Achieve Social Balance

Pedro Cisneros-Velarde

TL;DR

The paper investigates how Large Language Models (LLMs) update positive and negative interactions under the sociological framework of social balance, examining both single-triad and multi-triad populations. It analyzes multiple open-source LLMs across interaction types (relationships, appraisals, opinions) and update rules (homophily, influence), revealing that social balance emerges across models but with type, frequency, and diversity depending on model size, alignment, and population scale. Key findings include that larger models tend to stronger structural balance in single-triad settings, while smaller models may balance more readily in larger populations and clustering balance becomes more common; dissonance-based justifications are model-dependent and diminish in bigger groups. The results inform deployment considerations for agentic LLMs in social networks, highlighting potential implications for user experience, information diffusion, and echo chambers, and suggest future directions including incorporating memory of past interactions to study persistence of balance over time.

Abstract

Large Language Models (LLMs) can be deployed in situations where they process positive/negative interactions with other agents. We study how this is done under the sociological framework of social balance, which explains the emergence of one faction or multiple antagonistic ones among agents. Across different LLM models, we find that balance depends on the (i) type of interaction, (ii) update mechanism, and (iii) population size. Across (i)-(iii), we characterize the frequency at which social balance is achieved, the justifications for the social dynamics, and the diversity and stability of interactions. Finally, we explain how our findings inform the deployment of agentic systems.

Large Language Models can Achieve Social Balance

TL;DR

The paper investigates how Large Language Models (LLMs) update positive and negative interactions under the sociological framework of social balance, examining both single-triad and multi-triad populations. It analyzes multiple open-source LLMs across interaction types (relationships, appraisals, opinions) and update rules (homophily, influence), revealing that social balance emerges across models but with type, frequency, and diversity depending on model size, alignment, and population scale. Key findings include that larger models tend to stronger structural balance in single-triad settings, while smaller models may balance more readily in larger populations and clustering balance becomes more common; dissonance-based justifications are model-dependent and diminish in bigger groups. The results inform deployment considerations for agentic LLMs in social networks, highlighting potential implications for user experience, information diffusion, and echo chambers, and suggest future directions including incorporating memory of past interactions to study persistence of balance over time.

Abstract

Large Language Models (LLMs) can be deployed in situations where they process positive/negative interactions with other agents. We study how this is done under the sociological framework of social balance, which explains the emergence of one faction or multiple antagonistic ones among agents. Across different LLM models, we find that balance depends on the (i) type of interaction, (ii) update mechanism, and (iii) population size. Across (i)-(iii), we characterize the frequency at which social balance is achieved, the justifications for the social dynamics, and the diversity and stability of interactions. Finally, we explain how our findings inform the deployment of agentic systems.
Paper Structure (42 sections, 4 figures, 8 tables)

This paper contains 42 sections, 4 figures, 8 tables.

Table of Contents

  1. Introduction
  2. Problem Setting
  3. Analysis: Single Triad Population
  4. Achieving social balance
  5. Stability of interactions
  6. The justification of interaction updates
  7. Analysis: Multiple Triads Population
  8. Further Discussion
  9. Conclusion
  10. Further Motivation for Our Work
  11. The focus on social balance.
  12. A connection with size complexity.
  13. A connection with alignment.
  14. Our focus on LLM-to-LLM interactions.
  15. Related Literature
  16. ...and 27 more sections

Figures (4)

  • Figure 1: Sign configurations of a balanced triad. Consider a triad as a graph with three nodes corresponding to the agents $0$, $1$, and $2$. The first four triads define structural balance (e.g., in the first triad: agent $2$ is an enemy of $1$, who in turn is an enemy of $0$; therefore, $2$ is a friend of $0$). All five triads define clustering balance.
  • Figure 2: Agent $i$ updates its interaction toward Agent $j$. The update depends on how both relate to every other Agent $k$ in the population.
  • Figure 3: Frequency (%) of balanced triads. For each model, we present the histogram of types of balanced triads that emerge at the end of all simulations.
  • Figure 4: Examples: stability of interactions for gpt-oss-120b (left) and Llama 3 70B (right) according to the second criterion of Section \ref{['sec:stabl-interact']}. Changes on the number of positive cycles (blue curve), and positive (orange) and negative (green) interactions across ten iterations (x-axis, starting at $t=0$) and taking values from $0$ to $6$ (y-axis). Social balance is achieved at the tenth iteration in all cases.