scholarly journals Answer to the Commentary on "A note on the consensus time of mean-field majority-rule dynamics"

2009 ◽  
Vol 1 (0) ◽  
Author(s):  
Damián H. Zanette
Keyword(s):  
Majority Rule ◽  
Mean Field ◽  
Rule Dynamics ◽  
Consensus Time

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.

scholarly journals Majority rule dynamics in finite dimensions

2005 ◽  
Vol 71 (3) ◽  
Author(s):  
P. Chen ◽  
S. Redner
Keyword(s):  
Majority Rule ◽  
Rule 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 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.

On closed-loop equilibrium strategies for mean-field stochastic linear quadratic problems

2020 ◽  
Vol 26 ◽  
pp. 41
Author(s):  
Tianxiao Wang
Keyword(s):  
Optimal Control ◽  
Closed Loop ◽  
Optimal Control Problems ◽  
Mean Field ◽  
Open Loop ◽  
Time Inconsistency ◽  
Control Problems ◽  
Linear Quadratic ◽  
Linear Quadratic Optimal Control ◽  
Equilibrium Strategies

This article is concerned with linear quadratic optimal control problems of mean-field stochastic differential equations (MF-SDE) with deterministic coefficients. To treat the time inconsistency of the optimal control problems, linear closed-loop equilibrium strategies are introduced and characterized by variational approach. Our developed methodology drops the delicate convergence procedures in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. When the MF-SDE reduces to SDE, our Riccati system coincides with the analogue in Yong [Trans. Amer. Math. Soc. 369 (2017) 5467–5523]. However, these two systems are in general different from each other due to the conditional mean-field terms in the MF-SDE. Eventually, the comparisons with pre-committed optimal strategies, open-loop equilibrium strategies are given in details.

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