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The naming game (NG) is a classic model for studying the emergence and evolution of language within a population. In this article, we extend the traditional NG model to encompass multiple committed opinions and investigate the system dynamics on the complete graph with an arbitrarily large population and random networks of finite size. For the fully connected complete graph, the homogeneous mixing condition enables us to use mean-field theory to analyze the opinion evolution of the system. However, when the number of opinions increases, the number of variables describing the system grows exponentially. To mitigate this, we focus on a special scenario where the largest group of committed agents compete with a motley of committed groups, each of which is smaller than the largest one, while initially, most of uncommitted agents hold one unique opinion. This scenario is chosen for its recurrence in diverse societies and its potential for complexity reduction by unifying agents from smaller committed groups into one category. Our investigation reveals that when the size of the largest committed group reaches the critical threshold, most of uncommitted agents change their beliefs to this opinion, triggering a phase transition. Further, we derive the general formula for the multiopinion evolution using a recursive approach, enabling investigation into any scenario. Finally, we employ agent-based simulations to reveal the opinion evolution and dominance transition in random graphs. Our results provide insights into the conditions under which the dominant opinion emerges in a population and the factors that influence these conditions.
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This content will become publicly available on August 1, 2026
Oscillatory and excitable dynamics in an opinion model with group opinions
In traditional models of opinion dynamics, each agent in a network has an opinion and changes in opinions arise from pairwise (i.e., dyadic) interactions between agents. However, in many situations, groups of individuals possess a collective opinion that can differ from the opinions of their constituent individuals. In this paper, we study the effects of group opinions on opinion dynamics. We formulate a hypergraph model in which both individual agents and groups of three agents have opinions, and we examine how opinions evolve through both dyadic interactions and group memberships. We find for some parameter values that the presence of group opinions can lead to oscillatory and excitable opinion dynamics. In the oscillatory regime, the mean opinion of the agents in a network has self-sustained oscillations. In the excitable regime, finite-size effects create large but short-lived opinion swings (as in social fads). We develop a mean-field approximation of our model and obtain good agreement with direct numerical simulations. We also show—both numerically and via our mean-field description—that oscillatory dynamics occur only when the numbers of dyadic and polyadic interactions of the agents are not completely correlated. Our results illustrate how polyadic structures, such as groups of agents, can have important effects on collective opinion dynamics.
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- Award ID(s):
- 2205967
- PAR ID:
- 10655890
- Publisher / Repository:
- Physical Review E
- Date Published:
- Journal Name:
- Physical Review E
- Volume:
- 112
- Issue:
- 2
- ISSN:
- 2470-0045
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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