Consensus and Polarization of Binary Opinions in Structurally Balanced Networks

被引:17
作者
Lee, Duan-Shin [1 ]
Chang, Cheng-Shang [2 ]
Liu, Ying [3 ]
机构
[1] Natl Tsing Hua Univ, Dept Comp Sci, Hsinchu 30013, Taiwan
[2] Natl Tsing Hua Univ, Dept Elect Engn, Hsinchu 30013, Taiwan
[3] Premise Technol Inc, Hsinchu 30075, Taiwan
关键词
Clusterable network; consensus; majority rule (MR); opinion dynamics; polarization; social network; structural balance;
D O I
10.1109/TCSS.2016.2628051
中图分类号
TP3 [计算技术、计算机技术];
学科分类号
0812 ;
摘要
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.
引用
收藏
页码:141 / 150
页数:10
相关论文
共 21 条
[1]   Is polarization a myth? [J].
Abramowitz, Alan I. ;
Saunders, Kyle L. .
JOURNAL OF POLITICS, 2008, 70 (02) :542-555
[2]  
[Anonymous], 2006, WALRAS PARETO LECT
[3]   Social balance on networks: The dynamics of friendship and enmity [J].
Antal, T. ;
Krapivsky, P. L. ;
Redner, S. .
PHYSICA D-NONLINEAR PHENOMENA, 2006, 224 (1-2) :130-136
[4]  
Baccelli F, 2014, IEEE DECIS CONTR P, P3408, DOI 10.1109/CDC.2014.7039917
[5]   A New Partisan Voter [J].
Bafumi, Joseph ;
Shapiro, Robert Y. .
JOURNAL OF POLITICS, 2009, 71 (01) :1-24
[6]   Partisans without Constraint: Political Polarization and Trends in American Public Opinion [J].
Baldassarri, Delia ;
Gelman, Andrew .
AMERICAN JOURNAL OF SOCIOLOGY, 2008, 114 (02) :408-446
[7]   Statistical physics of social dynamics [J].
Castellano, Claudio ;
Fortunato, Santo ;
Loreto, Vittorio .
REVIEWS OF MODERN PHYSICS, 2009, 81 (02) :591-646
[8]  
Chen P., J PHYS A, V38, P7239
[9]   Improved bound for complexity of matrix multiplication [J].
Davie, A. M. ;
Stothers, A. J. .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2013, 143 (02) :351-369
[10]  
Easley D., 2010, NETWORKS CROWDS MARK