Majority rule dynamics between a double coalition and a third opinion: coalition profit models and majority coalition ties

2020 ◽  
pp. 105971231989548
Author(s):  
Felipe Gayosso Martínez ◽  
Alexander Balankin
Keyword(s):  
Majority Rule ◽  
Social Dynamics ◽  
Opinion Dynamics ◽  
Network Size ◽  
Opinion Formation ◽  
Random Choice ◽  
Rule Model ◽  
Rule Dynamics ◽  
Lattice Network ◽  
Consensus Time

This article explores the opinion dynamics of a double coalition opinion against a third opinion under majority rule updates on odd fixed size connected groups. For this purpose, coalition benefit criteria and three opinion formation models which extend the 2-state majority rule model on lattices are introduced. The proposed models focus on the coalition profit of its constituent coalition opinions and cover the possible final scenarios from coalition alliance perspective: either minor opinion or major opinion is favored, or dynamics do not favor to any coalition opinion. Opinion exchanges take place on a torus embedded lattice network of a 3-state system having in consideration tie configurations and two rules to break them: either by random choice or leaving ties unaltered. Models were analyzed in the statistical mechanics spirit through Monte Carlo simulations without node replacement. Estimations for coalition benefits, the growth of coalition ties, and consensus probabilities are reported. The loss of coalition strengths due to coalition ties and its indecision is indicated. In particular, the logistic decay of consensus probability is due to the logistic adaptive growth of coalition ties. Scaling behaviors for consensus time and coalition ties in terms of network size are suggested. The results of numerical simulations are discussed in the context of social influence and social dynamics.

Phase transition and universality of the three-one spin interaction based on the majority-rule model

2021 ◽  
pp. 2150115
Author(s):  
Roni Muslim ◽  
Rinto Anugraha ◽  
Sholihun Sholihun ◽  
Muhammad Farchani Rosyid
Keyword(s):  
Phase Transition ◽  
Critical Point ◽  
Majority Rule ◽  
Mean Field ◽  
Opinion Dynamics ◽  
Universality Class ◽  
Spin Interaction ◽  
Population Number ◽  
Infinite Population ◽  
Rule Model

In this work, we study the opinion dynamics of majority-rule model on a complete graph with additional social behavior namely anticonformity. We consider four spins with three-one interaction; three spins persuade the fourth spin in the population. We perform analytical and numerical calculations to find the critical behavior of the system. From both, we obtained the agreement results, e.g. the system undergoes a second-order phase transition and the critical point of the system only depends on the population number. In addition, the critical point decays exponentially as the number population increases. For the infinite population, the obtained critical point is [Formula: see text], which agrees well with that of the previous work. We also obtained the critical exponents [Formula: see text] and [Formula: see text] of the model, thus, the model is in the same universality class with the mean-field Ising.

scholarly journals Do zealots increase or decrease the polarization of social networks?

2019 ◽  
Vol 8 (4) ◽  
Author(s):  
Snehal M Shekatkar
Keyword(s):  
Social Networks ◽  
Social Network ◽  
Majority Rule ◽  
Initial Conditions ◽  
Opinion Dynamics ◽  
Network Density ◽  
Configuration Model ◽  
Rule Model ◽  
Total Fraction ◽  
Topological Characteristics

Abstract Zealots are the vertices in a social network who do not change their opinions under social pressure and are crucial to the study of opinion dynamics on complex networks. In this article, we study the effect of zealots on the polarization dynamics of a deterministic majority rule model using the configuration model as a substrate. To this end, we propose a novel quantifier, called ‘correlated polarization’, for measuring the amount of polarization in the network when vertices can exist in two opposite states. The quantifier takes into account not only the fraction of vertices with each opinion but also how they are connected to each other. We then show that the presence of zealots does not have a fixed effect on the polarization, and can change it in positive, negative or neutral way depending upon their topological characteristics like degree, their total fraction in the network, density and degree heterogeneity of the network and the type of initial conditions of the dynamics. Our results particularly highlight the importance of the role played by the initial conditions in drifting the polarization towards lower or higher values as the total number of zealots is increased.

scholarly journals Voter and Majority Dynamics with Biased and Stubborn Agents

2020 ◽  
Vol 181 (4) ◽  
pp. 1239-1265
Author(s):  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar ◽  
Rahul Roy
Keyword(s):  
Majority Rule ◽  
Branching Processes ◽  
Mean Field ◽  
Opinion Dynamics ◽  
Majority Opinion ◽  
Rule Model ◽  
Interacting Agents ◽  
The Mean ◽  
Fully Connected ◽  
Mean Time

Abstract We study binary opinion dynamics in a fully connected network of interacting agents. The agents are assumed to interact according to one of the following rules: (1) Voter rule: An updating agent simply copies the opinion of another randomly sampled agent; (2) Majority rule: An updating agent samples multiple agents and adopts the majority opinion in the selected group. We focus on the scenario where the agents are biased towards one of the opinions called the preferred opinion. Using suitably constructed branching processes, we show that under both rules the mean time to reach consensus is $$\varTheta (\log N)$$ Θ ( log N ) , where N is the number of agents in the network. Furthermore, under the majority rule model, we show that consensus can be achieved on the preferred opinion with high probability even if it is initially the opinion of the minority. We also study the majority rule model when stubborn agents with fixed opinions are present. We find that the stationary distribution of opinions in the network in the large system limit using mean field techniques.

EFFECTS OF HETEROGENEOUS INFLUENCE OF INDIVIDUALS ON THE GLOBAL CONSENSUS

2010 ◽  
Vol 21 (08) ◽  
pp. 1011-1019 ◽  
Author(s):  
YING-TING LIN ◽  
HAN-XIN YANG ◽  
ZHI-HAI RONG ◽  
BING-HONG WANG
Keyword(s):  
Small World ◽  
Opinion Dynamics ◽  
Network Size ◽  
Power Exponent ◽  
Scale Free ◽  
Global Consensus ◽  
Optimal Value ◽  
Consensus Time ◽  
The Relationship

We propose an opinion dynamics model to study the effects of heterogeneous influence of individuals on the global consensus. Each individual is assigned a weight that is proportional to the power of its degree, where the power exponent α is an adjustable parameter. Interestingly, it is found that there exists an optimal value of α leading to the shortest consensus time for scale-free networks, random networks and small-world networks. Other quantities, such as the probability that an individual's initial opinion becomes the final opinion as a function of degree, the evolution of the number of opinion clusters, as well as the relationship between average consensus time and the network size, are also studied. Our results are helpful for understanding the role of heterogeneous influence in the opinion dynamics.

Opinion Dynamics Optimization by Varying Susceptibility to Persuasion via Non-Convex Local Search

2021 ◽  
Vol 16 (2) ◽  
pp. 1-34
Author(s):  
Rediet Abebe ◽  
T.-H. HUBERT Chan ◽  
Jon Kleinberg ◽  
Zhibin Liang ◽  
David Parkes ◽  
...  
Keyword(s):  
Local Search ◽  
Objective Function ◽  
Iterative Process ◽  
Large Scale ◽  
Opinion Dynamics ◽  
Theoretical Models ◽  
Global Optimum ◽  
Local Optimum ◽  
Opinion Formation ◽  
Long Line

A long line of work in social psychology has studied variations in people’s susceptibility to persuasion—the extent to which they are willing to modify their opinions on a topic. This body of literature suggests an interesting perspective on theoretical models of opinion formation by interacting parties in a network: in addition to considering interventions that directly modify people’s intrinsic opinions, it is also natural to consider interventions that modify people’s susceptibility to persuasion. In this work, motivated by this fact, we propose an influence optimization problem. Specifically, we adopt a popular model for social opinion dynamics, where each agent has some fixed innate opinion, and a resistance that measures the importance it places on its innate opinion; agents influence one another’s opinions through an iterative process. Under certain conditions, this iterative process converges to some equilibrium opinion vector. For the unbudgeted variant of the problem, the goal is to modify the resistance of any number of agents (within some given range) such that the sum of the equilibrium opinions is minimized; for the budgeted variant, in addition the algorithm is given upfront a restriction on the number of agents whose resistance may be modified. We prove that the objective function is in general non-convex. Hence, formulating the problem as a convex program as in an early version of this work (Abebe et al., KDD’18) might have potential correctness issues. We instead analyze the structure of the objective function, and show that any local optimum is also a global optimum, which is somehow surprising as the objective function might not be convex. Furthermore, we combine the iterative process and the local search paradigm to design very efficient algorithms that can solve the unbudgeted variant of the problem optimally on large-scale graphs containing millions of nodes. Finally, we propose and evaluate experimentally a family of heuristics for the budgeted variant of the problem.

Majority Rule Based Opinion Dynamics with Biased and Stubborn Agents

2016 ◽  
Vol 44 (1) ◽  
pp. 385-386
Author(s):  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar ◽  
Rahul Roy
Keyword(s):  
Majority Rule ◽  
Opinion Dynamics ◽  
Rule Based
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