Majority Rule in Nonlinear Opinion Dynamics

Author(s):  
Michael Gabbay ◽  
Arindam K. Das
2016 ◽  
Vol 44 (1) ◽  
pp. 385-386
Author(s):  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar ◽  
Rahul Roy

2011 ◽  
Vol 5 (3-4) ◽  
pp. 305-327 ◽  
Author(s):  
Marco A. Montes de Oca ◽  
Eliseo Ferrante ◽  
Alexander Scheidler ◽  
Carlo Pinciroli ◽  
Mauro Birattari ◽  
...  

Author(s):  
Roni Muslim ◽  
Rinto Anugraha ◽  
Sholihun Sholihun ◽  
Muhammad Farchani Rosyid

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.


2019 ◽  
Vol 8 (4) ◽  
Author(s):  
Snehal M Shekatkar

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.


2020 ◽  
Vol 181 (4) ◽  
pp. 1239-1265
Author(s):  
Arpan Mukhopadhyay ◽  
Ravi R. Mazumdar ◽  
Rahul Roy

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.


2020 ◽  
pp. 105971231989548
Author(s):  
Felipe Gayosso Martínez ◽  
Alexander Balankin

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.


Author(s):  
Aris Anagnostopoulos ◽  
Luca Becchetti ◽  
Emilio Cruciani ◽  
Francesco Pasquale ◽  
Sara Rizzo

We investigate opinion dynamics in multi-agent networks when there exists a bias toward one of two possible opinions; for example, reflecting a status quo vs a superior alternative. Starting with all agents sharing an initial opinion representing the status quo, the system evolves in steps. In each step, one agent selected uniformly at random adopts with some probability a the superior opinion, and with probability 1 - a it follows an underlying update rule to revise its opinion on the basis of those held by its neighbors. We analyze the convergence of the resulting process under two well-known update rules, namely majority and voter. The framework we propose exhibits a rich structure, with a nonobvious interplay between topology and underlying update rule. For example, for the voter rule we show that the speed of convergence bears no significant dependence on the underlying topology, whereas the picture changes completely under the majority rule, where network density negatively affects convergence. We believe that the model we propose is at the same time simple, rich, and modular, affording mathematical characterization of the interplay between bias, underlying opinion dynamics, and social structure in a unified setting.


2020 ◽  
Vol 287 (1938) ◽  
pp. 20201802
Author(s):  
Claudia Winklmayr ◽  
Albert B. Kao ◽  
Joseph B. Bak-Coleman ◽  
Pawel Romanczuk

Groups of organisms, from bacteria to fish schools to human societies, depend on their ability to make accurate decisions in an uncertain world. Most models of collective decision-making assume that groups reach a consensus during a decision-making bout, often through simple majority rule. In many natural and sociological systems, however, groups may fail to reach consensus, resulting in stalemates. Here, we build on opinion dynamics and collective wisdom models to examine how stalemates may affect the wisdom of crowds. For simple environments, where individuals have access to independent sources of information, we find that stalemates improve collective accuracy by selectively filtering out incorrect decisions (an effect we call stalemate filtering). In complex environments, where individuals have access to both shared and independent information, this effect is even more pronounced, restoring the wisdom of crowds in regions of parameter space where large groups perform poorly when making decisions using majority rule. We identify network properties that tune the system between consensus and accuracy, providing mechanisms by which animals, or evolution, could dynamically adjust the collective decision-making process in response to the reward structure of the possible outcomes. Overall, these results highlight the adaptive potential of stalemate filtering for improving the decision-making abilities of group-living animals.


2020 ◽  
Author(s):  
Claudia Winklmayr ◽  
Albert B. Kao ◽  
Joseph B. Bak-Coleman ◽  
Pawel Romanczuk

ABSTRACTGroups of organisms, from bacteria to fish schools to human societies, depend on their ability to make accurate decisions in an uncertain world. Most models of collective decision-making assume that groups reach a consensus during a decision-making bout, often through simple majority rule. In many natural and sociological systems, however, groups may fail to reach consensus, resulting in stalemates. Here, we build on opinion dynamics and collective wisdom models to examine how stalemates may affect the wisdom of crowds. For simple environments, where individuals have access to independent sources of information, we find that stalemates improve collective accuracy by selectively filtering out incorrect decisions. In complex environments, where individuals have access to both shared and independent information, this effect is even more pronounced, restoring the wisdom of crowds in regions of parameter space where large groups perform poorly when making decisions using majority rule. We identify network properties that tune the system between consensus and accuracy, providing mechanisms by which animals, or evolution, could dynamically adjust the collective decision-making process in response to the reward structure of the possible outcomes. Overall, these results highlight the adaptive potential of stalemale filtering for improving the decision-making abilities of group-living animals.


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