- Open Access
Group adaptation drives opinion dynamics in higher-order networks
APS Open Sci. 1, 000028 – Published 26 May, 2026
DOI: https://doi.org/10.1103/gcz4-wwb3
Abstract
In modern interconnected societies, opinions and beliefs can quickly spread across large populations, giving rise to collective behaviors such as the adoption of social norms or polarization. The interest in these phenomena led to the formulation of many models aiming at reproducing relevant emergent properties from simple mechanisms of interactions between individuals. In particular, opinion dynamics models mimic how the opinions of individuals on a given topic may evolve when they interact, and study the conditions for global consensus or polarization. Most models assume that these interactions occur between pairs of agents, typically on a fixed network structure. However, discussions leading to opinion changes can occur in groups, and these groups can also undergo adaptive changes and modifications if their members disagree. Here, we propose a bounded confidence model of opinion dynamics taking into account these two mechanisms: A group discussion can lead to a global agreement among all group members, if their opinions are close enough, while a strong divergence of opinions within a group leads to its splitting, followed by merging of the resulting subgroups with other groups. We systematically study the outcome of this model as a function of the tolerance of agents for reaching an agreement. Strikingly, adaptivity seems to suppress important effects induced by group interactions, and to restore a phenomenology close to the one obtained with pairwise interactions. We show that adaptivity, which allows the formation of large groups, prevents the transition to a fragmented state at small tolerance. Moreover, it restores a phase transition from a polarized state to consensus, which would otherwise disappear due to group effects in a nonadaptive bounded confidence model with group interactions. Overall, our work shows that both adaptivity and group interactions shape the structure of social ties and the global opinion dynamics in a population.
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References (53)
- H. Xia, H. Wang, and Z. Xuan, Opinion dynamics: A multidisciplinary review and perspective on future research, Int. J. Knowl. Syst. Sci. 2, 72 (2011).
- H. Noorazar, Recent advances in opinion propagation dynamics: A 2020 survey, Eur. Phys. J. Plus 135, 521 (2020).
- C. Castellano, S. Fortunato, and V. Loreto, Statistical physics of social dynamics, Rev. Mod. Phys. 81, 591 (2009).
- M. Starnini, F. Baumann, T. Galla, D. Garcia, G. Iñiguez, M. Karsai, J. Lorenz, and S.-W. Katarzyna, Opinion dynamics: Statistical physics and beyond, Rev. Mod. Phys. (2026), doi:10.1103/j1zg-ddqv.
- G. Caldarelli et al., The physics of news, rumors, and opinions, arXiv:2510.15053.
- G. Deffuant, D. Neau, F. Amblard, and G. Weisbuch, Mixing beliefs among interacting agents, Adv. Complex Syst. 03, 87 (2000).
- M. Shirzadi, E. Cruciani, and A. N. Zehmakan, Opinion dynamics: A comprehensive overview, arXiv:2511.00401.
- A. F. Peralta, J. Kertész, and G. Iñiguez, Opinion dynamics in social networks: From models to data, in Handbook of Computational Social Science, editd by T. Yasseri (Edward Elgar Publishing Limited, Cheltenham, UK, 2025), pp. 384–406.
- J. Lorenz, Continuous opinion dynamics under bounded confidence: A survey, Int. J. Mod. Phys. C 18, 1819 (2007).
- H. Noorazar, K. R. Vixie, A. Talebanpour, and Y. Hu, From classical to modern opinion dynamics, Int. J. Mod. Phys. C 31, 2050101 (2020).
- H. Liang, Y. Yang, and X. Wang, Opinion dynamics in networks with heterogeneous confidence and influence, Physica A 392, 2248 (2013).
- H. Z. Brooks, P. S. Chodrow, and M. A. Porter, Emergence of polarization in a sigmoidal bounded-confidence model of opinion dynamics, SIAM J. Appl. Dyn. Syst. 23, 1442 (2024).
- X. F. Meng, R. A. Van Gorder, and M. A. Porter, Opinion formation and distribution in a bounded-confidence model on various networks, Phys. Rev. E 97, 022312 (2018).
- A. Barrat, M. Barthelemy, and A. Vespignani, Dynamical Processes on Complex Networks (Cambridge University Press, Cambridge, 2008).
- S. C. Fennell, K. Burke, M. Quayle, and J. P. Gleeson, Generalized mean-field approximation for the Deffuant opinion dynamics model on networks, Phys. Rev. E 103, 012314 (2021).
- A. Dubovskaya, S. C. Fennell, K. Burke, J. P. Gleeson, and D. O’Kiely, Analysis of mean-field approximation for Deffuant opinion dynamics on networks, SIAM J. Appl. Math. 83, 436 (2023).
- M. S. Levendusky, J. N. Druckman, and A. McLain, How group discussions create strong attitudes and strong partisans, Res. Polit. 3, 2053168016645137 (2016).
- F. Battiston et al., Networks beyond pairwise interactions: Structure and dynamics, Phys. Rep. 874, 1 (2020).
- F. Battiston et al., Higher-order interactions shape collective human behaviour, Nat. Hum. Behav. 9, 2441 (2025).
- I. Iacopini, G. Petri, A. Barrat, and V. Latora, Simplicial models of social contagion, Nat. Commun. 10, 2485 (2019).
- G. F. de Arruda, G. Petri, and Y. Moreno, Social contagion models on hypergraphs, Phys. Rev. Res. 2, 023032 (2020).
- I. Iacopini, G. Petri, A. Baronchelli, and A. Barrat, Group interactions modulate critical mass dynamics in social convention, Commun. Phys. 5, 64 (2022).
- A. Civilini, O. Sadekar, F. Battiston, J. Gómez-Gardeñes, and V. Latora, Explosive cooperation in social dilemmas on higher-order networks, Phys. Rev. Lett. 132, 167401 (2024).
- A. Hickok, Y. Kureh, H. Z. Brooks, M. Feng, and M. A. Porter, A bounded-confidence model of opinion dynamics on hypergraphs, SIAM J. Appl. Dyn. Syst. 21, 1 (2022).
- L. Neuhäuser, A. Mellor, and R. Lambiotte, Multibody interactions and nonlinear consensus dynamics on networked systems, Phys. Rev. E 101, 032310 (2020).
- R. Sahasrabuddhe, L. Neuhäuser, and R. Lambiotte, Modelling non-linear consensus dynamics on hypergraphs, J. Phys.: Complexity 2, 025006 (2021).
- H. Schawe and L. Hernández, Higher order interactions destroy phase transitions in Deffuant opinion dynamics model, Commun. Phys. 5, 32 (2022).
- P. Holme and M. E. J. Newman, Nonequilibrium phase transition in the coevolution of networks and opinions, Phys. Rev. E 74, 056108 (2006).
- B. Kozma and A. Barrat, Consensus formation on adaptive networks, Phys. Rev. E 77, 016102 (2008).
- U. Kan, M. Feng, and M. A. Porter, An adaptive bounded-confidence model of opinion dynamics on networks, J. Complex Netw. 11, 415 (2023).
- C. Nardini, B. Kozma, and A. Barrat, Who's talking first? Consensus or lack thereof in coevolving opinion formation models, Phys. Rev. Lett. 100, 158701 (2008).
- I. Iacopini, M. Karsai, and A. Barrat, The temporal dynamics of group interactions in higher-order social networks, Nat. Commun. 15, 7391 (2024).
- L. Horstmeyer and C. Kuehn, Adaptive voter model on simplicial complexes, Phys. Rev. E 101, 022305 (2020).
- G. Burgio, G. St-Onge, and L. Hébert-Dufresne, Characteristic scales and adaptation in higher-order contagions, Nat. Commun. 16, 4589 (2025).
- M. Mancastroppa, M. Karsai, and A. Barrat, Adaptive behaviors neutralize bistable explosive transitions in higher-order contagion, APS Open Sci. (2026), doi:10.1103/1sgn-k3fk.
- M. Mancastroppa, M. Karsai, and A. Barrat, Higher-order adaptive behaviors outperform pairwise strategies in mitigating contagion dynamics, arXiv:2602.05915.
- In the following, we will use equivalently the terms nodes and agents, as well as group and hyperedge (or hyperlink).
- G. Cencetti, F. Battiston, B. Lepri, and M. Karsai, Temporal properties of higher-order interactions in social networks, Sci. Rep. 11, 7028 (2021).
- A. P. Hare, A study of interaction and consensus in different sized groups, Am. Sociol. Rev. 17, 261 (1952).
- See Supplemental Material at https://link.aps.org/supplemental/10.1103/gcz4-wwb3 for further analysis and variations of the model.
- C. Agostinelli, M. Mancastroppa, and A. Barrat, Higher-order dissimilarity measures for hypergraph comparison, J. Complex Netw. 14, cnaf048 (2026).
- SocioPatterns collaboration (2008), http://www.sociopatterns.org/.
- M. Génois and A. Barrat, Can co-location be used as a proxy for face-to-face contacts? EPJ Data Sci. 7, 11 (2018).
- P. Sapiezynski, A. Stopczynski, D. D. Lassen, and S. Lehmann, Interaction data from the Copenhagen networks study, Sci. Data 6, 315 (2019).
- R. Mastrandrea, J. Fournet, and A. Barrat, Contact patterns in a high school: A comparison between data collected using wearable sensors, contact diaries and friendship surveys, PLoS One 10, e0136497 (2015).
- G. J. Li and M. A. Porter, Bounded-confidence model of opinion dynamics with heterogeneous node-activity levels, Phys. Rev. Res. 5, 023179 (2023).
- G. J. Li, J. Luo, and M. A. Porter, Bounded-confidence models of opinion dynamics with adaptive confidence bounds, SIAM J. Appl. Dyn. Syst. 24, 994 (2025).
- D. Centola, J. Becker, D. Brackbill, and A. Baronchelli, Experimental evidence for tipping points in social convention, Science 360, 1116 (2018).
- M. Mancastroppa, I. Iacopini, G. Petri, and A. Barrat, Hyper-cores promote localization and efficient seeding in higher-order processes, Nat. Commun. 14, 6223 (2023).
- S. Moor-Smith and D. Carpentras, Testing the validity of multiple opinion dynamics models, arXiv:2602.00876.
- D. Centola and A. Baronchelli, The spontaneous emergence of conventions: An experimental study of cultural evolution, Proc. Natl. Acad. Sci. USA 112, 1989 (2015).
- A. F. Ashery, L. M. Aiello, and A. Baronchelli, Emergent social conventions and collective bias in LLM populations, Sci. Adv. 11, eadu9368 (2025).
- C. Agostinelli, Code repository (2026), https://github.com/cosimoagostinelli/H-or_adaptive_Deffuant.