When LLMs Play the Telephone Game: Cultural Attractors as Conceptual Tools to Evaluate LLMs in Multi-turn Settings

TL;DR

This work investigates how content evolves when LLMs interact across multiple turns by framing the process through cultural attractor theory and transmission chains. It introduces a rigorous experimental design across multiple models, tasks, and initial texts to quantify how four text properties—toxicity, positivity, difficulty, and length—change over 50 generations and identifies attractor dynamics. The findings show that multi-turn interactions produce distributions that diverge from single-turn outcomes, with strong, task- and model-dependent attractors—most notably for toxicity—and that factors like temperature and fine-tuning modulate these dynamics. The study highlights the need to evaluate LLMs in multi-turn settings and offers attractor-based metrics as tools for understanding and guiding multi-agent, iterative AI systems.

Abstract

As large language models (LLMs) start interacting with each other and generating an increasing amount of text online, it becomes crucial to better understand how information is transformed as it passes from one LLM to the next. While significant research has examined individual LLM behaviors, existing studies have largely overlooked the collective behaviors and information distortions arising from iterated LLM interactions. Small biases, negligible at the single output level, risk being amplified in iterated interactions, potentially leading the content to evolve towards attractor states. In a series of telephone game experiments, we apply a transmission chain design borrowed from the human cultural evolution literature: LLM agents iteratively receive, produce, and transmit texts from the previous to the next agent in the chain. By tracking the evolution of text toxicity, positivity, difficulty, and length across transmission chains, we uncover the existence of biases and attractors, and study their dependence on the initial text, the instructions, language model, and model size. For instance, we find that more open-ended instructions lead to stronger attraction effects compared to more constrained tasks. We also find that different text properties display different sensitivity to attraction effects, with toxicity leading to stronger attractors than length. These findings highlight the importance of accounting for multi-step transmission dynamics and represent a first step towards a more comprehensive understanding of LLM cultural dynamics.

Figures (33)

• Figure 1: The transmission chain experimental design. (a) Single-turn transmission: an LLM agent receives a human-generated input text (e.g. a story) and a task (e.g. "rephrase the text") and generates an output text. (b) Multi-turn transmission: a chain of LLM agents is given the same task, with the first agent receiving an initial text and subsequent agents receiving the output of the preceding agent. Measures of toxicity, positivity, difficulty, and length are recorded at each step of the chain.
• Figure 2: Evolution of the distribution of text properties across generations. We here represent the distribution of each of the four properties at each generation, for each model and task. These distributions thus represent the properties observed in the set of 100 transmission chains (20 initial texts * 5 seeds) for each model and task. For each property, task and model, the 50 generations are arranged vertically, with first generations at the top and last generations at the bottom.
• Figure 3: Text properties are affected by transmissions beyond the first one. p-values of the KS-test for the null hypothesis $H_0$: "The text properties at generation $i$ are sampled from the same distribution as the text properties after generation 1", for each task (columns), property (rows) and models (colors). The grey shaded area represents p-values lower than 0.05. Over most instances, p-values decrease over generation and become close to 0, indicating that multi-turn transmissions lead to significantly different distributions compared to single-turn interactions.
• Figure 4: Attractors strength and position. The heigth of the bars represent the position (top row) and strength (bottom row) of theoretical attractors estimated using the method described in Section \ref{['Method_attractors']}, for each property (columns), task, and model. Less constrained tasks, such as Continue, appear to produce stronger attractors than more constrained tasks, such as Rephrase. Attractors appear to be stronger for toxicity than for length. Finally, we can notice that the position of attractors appears to vary between models.
• Figure 5: Effect of temperature (a) and fine-tuning (b) on attractors. (a) Attractor positions (top row) and strength (bottow row) for different values on temperature (x-axis), for model Llama3-8B-Instruct. The main visible effect is that increasing temperature increases attraction strength for tasks Rephrase and Take Inspiration, but not for Continue. (b) Attractor positions (top row) and strength (bottow row) for Base and Instruct versions of Mixtral-8x7B and Llama3-70B. Fine-tuning appears to increase the strength of attraction for toxicity, increases the position of the attractor for difficulty, and decreases the position of the attractor for length.