Across 1,980 five-agent LLM runs on citizen-assembly topics, LLM groups match human procedural talk but show one-third the perspective diversity, weak topic-dependent consistency gains, and reversed convergence dynamics.
A modified Hegselmann-Krause model for interacting voters and political parties
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abstract
The Hegselmann--Krause model is a prototypical model for opinion dynamics. It models the stochastic time evolution of an agent's or voter's opinion in response to the opinion of other like-minded agents. The Hegselmann--Krause model only considers the opinions of voters; we extend it here by incorporating the dynamics of political parties which influence and are influenced by the voters. We show in numerical simulations for $1$- and $2$-dimensional opinion spaces that, as for the original Hegselmann--Krause model, the modified model exhibits opinion cluster formation as well as a phase transition from disagreement to consensus. We provide an analytical sufficient condition for the formation of unanimous consensus in which voters and parties collapse to the same point in opinion space in the deterministic case. Using mean-field theory, we further derive an approximation for the critical noise strength delineating consensus from non-consensus in the stochastically driven modified Hegselmann--Krause model. We compare our analytical findings with simulations of the modified Hegselmann--Krause model.
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2026 1verdicts
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The Deliberative Deficit: An Empirical Critique of LLMs in Democratic Discourse
Across 1,980 five-agent LLM runs on citizen-assembly topics, LLM groups match human procedural talk but show one-third the perspective diversity, weak topic-dependent consistency gains, and reversed convergence dynamics.