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This research proposes a quantum framework for modeling opinion dynamics that addresses limitations in classical theories regarding cognitive ambivalence and order effects. By representing agent states as density matrices, the study introduces novel metrics like quantum coherence to explain survey response dependencies on question ordering. The work establishes theoretical bridges between social network science and quantum physics without relying on physical qubits or hardware implementation.
A quantum model of opinion dynamics on networks
arXiv:2607.01452v2 Announce Type: replace-cross Abstract: Classical models of opinion dynamics represent individual opinions as scalar or vector values governed by the classical probability theory, either as deterministic quantities or random variables. This framework does not account for empirically observed phenomena such as cognitive ambivalence (where an individual simultaneously holds conflicting views) and order effects (where survey responses depend on the order in which questions are asked). We propose a quantum model of opinion dynamics in which each agent's cognitive state is represented by a density matrix that encodes both the expressed opinion and cognitive ambivalence. Survey questions become non-commuting self-adjoint operators, which provides a principled explanation for order effects. Our model also identifies quantities without classical counterparts, including quantum coherence and pairwise opinion covariances. Under a product state approximation, the quantum model reduces to the classical Friedkin--Johnsen opinion model. We test the framework on synthetic and real-world networks and observe that pairwise correlations follow network-dependent transient dynamics but converge to the same steady state regardless of the network, and that quantum coherence decays exponentially at a rate independent of the network.
Abstract:Classical models of opinion dynamics represent individual opinions as scalar or vector values governed by the classical probability theory, either as deterministic quantities or random variables. This framework does not account for empirically observed phenomena such as cognitive ambivalence (where an individual simultaneously holds conflicting views) and order effects (where survey responses depend on the order in which questions are asked). We propose a quantum model of opinion dynamics in which each agent's cognitive state is represented by a density matrix that encodes both the expressed opinion and cognitive ambivalence. Survey questions become non-commuting self-adjoint operators, which provides a principled explanation for order effects. Our model also identifies quantities without classical counterparts, including quantum coherence and pairwise opinion covariances. Under a product state approximation, the quantum model reduces to the classical Friedkin--Johnsen opinion model. We test the framework on synthetic and real-world networks and observe that pairwise correlations follow network-dependent transient dynamics but converge to the same steady state regardless of the network, and that quantum coherence decays exponentially at a rate independent of the network.
Physics and Society (physics.soc-ph); Social and Information Networks (cs.SI); Probability (math.PR); Quantum Physics (quant-ph)
arXiv:2607.01452 [physics.soc-ph]
(or arXiv:2607.01452v2 [physics.soc-ph] for this version)
https://doi.org/10.48550/arXiv.2607.01452 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 279 words
