Bridging Simple and Complex Contagions in Belief Dynamics: A Voter Model Extension
Franco, Jo�o
Franco, Jo�o
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Abstract
The standard voter model of belief dynamics - how beliefs form and evolve - assumes that individuals consistently express their internal beliefs and that these beliefs can change from one period to another. However, social norms and conformity pressures often lead individuals to either withhold beliefs or express beliefs that are contrary to their own, while internally held beliefs may exhibit inertia due to psychological mechanisms such as social hysteresis. Our extension of the voter model distinguishes between expressed beliefs, following simple contagion dynamics, and internal beliefs, that update through complex contagion mechanisms. Individuals hold binary beliefs on a given topic (a = �Against,� f = �in Favour�) but may express the opposite (af = holding �Against� but expressing �In Favour�). Expressed beliefs update through simple contagion based on the beliefs expressed by neighbours in the previous period, with contagion strength mediated by alignment with one�s internal belief (c when aligned and c? when misaligned), reflecting the potential burden of expressing beliefs contrary to those internally held. Internal beliefs update based on neighbours� expressed beliefs but follow a q-voter model, capturing complex contagion dynamics and belief inertia. Mean-field approximations reveal that when individuals face higher contagion pressure to express beliefs contrary to their internal ones (c? > c), the symmetry typical of voter models breaks down, enabling minority beliefs to persist at higher proportions than their initial frequency in the long term. These effects are robust across a range of initial conditions. Future work will explore how network structure and belief withholding shape the interplay between simple and complex contagion in real-world contexts.
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Date
1/1/2026
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Graduate Student
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Oral Presentation
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Complex Systems and Data Science
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College of Engineering and Mathematical Sciences
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Mathematical Science (Religion)