A Shy Voter Model: Entropy Flux in Opinion Formation
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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BibTeX
@misc{kim2026voter,
title = {{A Shy Voter Model: Entropy Flux in Opinion Formation}},
author = {Cook Hyun Kim and Sangjoon Park and B. Kahng},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.16053},
eprint = {2610.16053},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.16053},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Shy Voter Model: Entropy Flux in Opinion Formation
AU - Cook Hyun Kim
AU - Sangjoon Park
AU - B. Kahng
PY - 2026
DA - 2026/10/12
PB - arXiv
DO - 10.48550/arxiv.2610.16053
UR - https://arxiv.org/abs/2610.16053
AB - 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.
ER -