Consensus, Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence
Abstract
:1. Introduction
- Socially motivated: to determine the role of the size of the influence group on the emerging social behavior (consensus, polarization, hysteresis, etc.).
2. Model
- Choose a target agent , where is a discrete uniform distribution in the interval ,
- Choose , where is a continuous uniform distribution in the interval , to determine the type of social response,
- If then independence: or 3 with equal probabilities ,
- Otherwise conformity:
- (a)
- Select at random without repetition q agents from neighbors of the target agent—they form the source of influence, called also the q-panel, and are indexed by .
- (b)
- If the q-panel is unanimous, i.e., and the BC requirement is fulfilled, then .
3. Mean-Field Approach
- For the CG we are able to obtain exact analytical results within MFA.
- To understand the role of BC in three-state qVM, we need to use the same structure as in [24], in which three-state qVM without BC was considered—that is, CG.
4. Results
4.1. Trajectories
- disagreement:
- ,
- central dominance:
- ,
- extreme dominance:
- or and
- polarization:
- .
4.2. Stationary States
4.3. Phase Portraits
- (2)
- polarization + central dominance,
- (1)
- disagreement + central dominance and
- (0)
- disagreement.
- (5)
- polarization + central dominance + extreme dominance,
- (4)
- disagreement + central dominance + extreme dominance,
- (3)
- extreme dominance + central dominance,
- (2)
- polarization + central dominance,
- (1)
- disagreement + central dominance and
- (0)
- disagreement.
5. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Doniec, M.; Lipiecki, A.; Sznajd-Weron, K. Consensus, Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence. Entropy 2022, 24, 983. https://doi.org/10.3390/e24070983
Doniec M, Lipiecki A, Sznajd-Weron K. Consensus, Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence. Entropy. 2022; 24(7):983. https://doi.org/10.3390/e24070983
Chicago/Turabian StyleDoniec, Maciej, Arkadiusz Lipiecki, and Katarzyna Sznajd-Weron. 2022. "Consensus, Polarization and Hysteresis in the Three-State Noisy q-Voter Model with Bounded Confidence" Entropy 24, no. 7: 983. https://doi.org/10.3390/e24070983