Abstract:
In this paper, we propose a new model for binary opinion dynamics in a (fully connected) structurally balanced network. In a structurally balanced network, agents are cla...Show MoreMetadata
Abstract:
In this paper, we propose a new model for binary opinion dynamics in a (fully connected) structurally balanced network. In a structurally balanced network, agents are classified into two clusters and two agents in the same cluster (resp. different clusters) are connected with a positive (resp. negative) edge. Initially, every agent is assigned with one of the two opinions randomly. In every time slot, three agents are randomly selected to have their opinions updated. If the three agents belong to the same cluster, the majority rule (MR) is used to update their opinions. On the other hand, if the three agents belong to two different clusters, with probability p, a consensus is reached by the MR, and with probability 1 - p, a polarization (in line with the signs of the three edges) is reached. The probability p, called the rationality probability, plays a significant role for measuring how rational the agents in a network behave when they encounter different opinions. By applying a fluid limit theorem for jump Markov processes, we derive a system of differential equations for the density functions of opinions for large networks. We show that the equilibrium points corresponding to consensus and polarization are the only stable equilibrium points. All other equilibrium points are all unstable. As such, as time goes on, the network eventually reaches a consensus or a polarization, depending on the rationality probability and the initial state of the network.
Published in: IEEE Transactions on Computational Social Systems ( Volume: 3, Issue: 4, December 2016)
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- IEEE Keywords
- Index Terms
- Structural Balance ,
- Binary Opinion ,
- Differential Equations ,
- Markov Chain ,
- System Of Equations ,
- Large Networks ,
- Equilibrium Point ,
- Time Slot ,
- System Of Differential Equations ,
- Stable Equilibrium Point ,
- Opinion Dynamics ,
- Straight Line ,
- Political Parties ,
- United States Of America ,
- Transition Probabilities ,
- Eigenvalues Of Matrix ,
- Poisson Process ,
- Different Signs ,
- Saddle Point ,
- Probable Cases ,
- Major Parties ,
- Basin Of Attraction ,
- Absorption Probability ,
- Major Political Parties ,
- Unit Square ,
- Vertices In The Network ,
- Democratic Countries ,
- Global Consensus ,
- Real Parts Of The Eigenvalues ,
- Members Of Congress
- Author Keywords
Keywords assist with retrieval of results and provide a means to discovering other relevant content. Learn more.
- IEEE Keywords
- Index Terms
- Structural Balance ,
- Binary Opinion ,
- Differential Equations ,
- Markov Chain ,
- System Of Equations ,
- Large Networks ,
- Equilibrium Point ,
- Time Slot ,
- System Of Differential Equations ,
- Stable Equilibrium Point ,
- Opinion Dynamics ,
- Straight Line ,
- Political Parties ,
- United States Of America ,
- Transition Probabilities ,
- Eigenvalues Of Matrix ,
- Poisson Process ,
- Different Signs ,
- Saddle Point ,
- Probable Cases ,
- Major Parties ,
- Basin Of Attraction ,
- Absorption Probability ,
- Major Political Parties ,
- Unit Square ,
- Vertices In The Network ,
- Democratic Countries ,
- Global Consensus ,
- Real Parts Of The Eigenvalues ,
- Members Of Congress
- Author Keywords