Opinion Evolution in Divided Community
Abstract
:1. Introduction
2. Models and Methods
2.1. Modelling Framework
- A binary opinion model with a single trait.
- q-voter model with conformity and anti-conformity as the general modeling framework.
- Double clique topology as the underlying social network.
- Conformity between agents within a clique and anti-conformity in the interactions between the cliques.
- Pick a target agent at random.
- Choose randomly q neighbors of the target (possibility of repetition).
- If all the q neighbors are in the same state, the target changes its state accordingly.
- Otherwise, the target changes its state with probability .
2.2. Independence of Agents
2.3. Quenched and Annealed Disorder Models
2.4. Updating Rules of the Models
- Pick a target agent at random (uniformly from nodes).
- Draw a random number form a uniform distribution, .
- If (i.e., with probability h), the agent is independent:
- (a)
- Change its state with probability . To this end, draw a random number f from a uniform distribution, :
- if , change the state of the target, i.e., ,
- otherwise, do nothing.
- (b)
- Go to step 1.
- If (i.e., with probability ), the agent is subject to social influence:
- (a)
- Randomly choose a group of q distinct neighbors of the target node:
- Quenched model
- simply look at the actual neighbors of the target (sampling with replacement).
- Annealed model
- first decide to which clique every member of the influence group will belong (with probability to the target’s clique, with p to the other one), then randomly choose the member from the appropriate clique.
- (b)
- Convert the states of the group members to signals. Assume that the signals of the neighbors from target’s clique are equal to their states. Invert the states when from the other clique.
- (c)
- Calculate the total signal of the influence group by summing up the individual signals of its members.
- (d)
- If the total signal is equal to (i.e., all group members emit the same signal), the target changes its opinion accordingly (see Figure 2). Otherwise, nothing happens.
- Go to step 1.
2.5. Quantities of Interest
2.6. Transition Probabilities and Dynamical System
- a target from clique A is chosen (probability ),
- the target is in state (probability ),
- it flips due to independence (probability ) or follows an influence group emitting signal .
- A target from clique A is chosen (probability ).
- The target is in state (probability ).
- It flips due to independence (probability ) or follows an influence group emitting signal .
3. Results
3.1. Direction Fields and Stationary Points
3.2. Time Evolution of the System
3.3. Impact of Independence on the System
4. Discussion
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Meaning | ||
---|---|---|
Positive consensus (all agents in clique X in state ) | ||
Partial positive consensus (majority of agents in clique X in state ) | ||
No ordering in clique X | ||
Partial negative consensus (majority of agents in clique X in state ) | ||
Negative consensus (all agents in clique X in state ) |
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Weron, T.; Szwabiński, J. Opinion Evolution in Divided Community. Entropy 2022, 24, 185. https://doi.org/10.3390/e24020185
Weron T, Szwabiński J. Opinion Evolution in Divided Community. Entropy. 2022; 24(2):185. https://doi.org/10.3390/e24020185
Chicago/Turabian StyleWeron, Tomasz, and Janusz Szwabiński. 2022. "Opinion Evolution in Divided Community" Entropy 24, no. 2: 185. https://doi.org/10.3390/e24020185
APA StyleWeron, T., & Szwabiński, J. (2022). Opinion Evolution in Divided Community. Entropy, 24(2), 185. https://doi.org/10.3390/e24020185