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arXiv · 2610.16053

A Shy Voter Model: Entropy Flux in Opinion Formation

Cook Hyun Kim·Sangjoon Park·B. Kahng
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Abstract

Some voters conceal their opinions, causing a mismatch between visible and private opinions in polls. Conventional voter models do not account for such concealment. Here, we introduce a shy voter model that incorporates a hidden state in addition to two visible states, as an extension of the conventional majority-rule voter model. The model exhibits continuous and hybrid transitions, yielding a rich phase diagram organized by the hidden fraction, i.e., the fraction of voters in the hidden state. For a large hidden fraction, the system undergoes a hybrid transition from the ordered state to the symmetric (disordered) state, whereas for a small hidden fraction, it exhibits a continuous transition, with a tricritical point separating the two regimes. Near criticality, both the order-parameter variance and the susceptibility diverge. The hidden fraction also governs the entropy flux, a quantity that is not directly observable in real-world situations. Thus, opinion concealment qualitatively reshapes opinion dynamics, while the present framework provides a basis for further extensions toward more realistic forms of social interactions.

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Cook Hyun Kim, Sangjoon Park, B. Kahng. 2026-10-12. A Shy Voter Model: Entropy Flux in Opinion Formation. https://arxiv.org/abs/2610.16053

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