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 PLOS ONE , 2013, DOI: 10.1371/journal.pone.0078433 Abstract: Social influence is the process by which individuals adapt their opinion, revise their beliefs, or change their behavior as a result of social interactions with other people. In our strongly interconnected society, social influence plays a prominent role in many self-organized phenomena such as herding in cultural markets, the spread of ideas and innovations, and the amplification of fears during epidemics. Yet, the mechanisms of opinion formation remain poorly understood, and existing physics-based models lack systematic empirical validation. Here, we report two controlled experiments showing how participants answering factual questions revise their initial judgments after being exposed to the opinion and confidence level of others. Based on the observation of 59 experimental subjects exposed to peer-opinion for 15 different items, we draw an influence map that describes the strength of peer influence during interactions. A simple process model derived from our observations demonstrates how opinions in a group of interacting people can converge or split over repeated interactions. In particular, we identify two major attractors of opinion: (i) the expert effect, induced by the presence of a highly confident individual in the group, and (ii) the majority effect, caused by the presence of a critical mass of laypeople sharing similar opinions. Additional simulations reveal the existence of a tipping point at which one attractor will dominate over the other, driving collective opinion in a given direction. These findings have implications for understanding the mechanisms of public opinion formation and managing conflicting situations in which self-confident and better informed minorities challenge the views of a large uninformed majority.
 Physics , 2000, DOI: 10.1016/S0378-4371(00)00282-X Abstract: We study phase transitions in models of opinion formation which are based on the social impact theory. Two different models are discussed: (i) a cellular--automata based model of a finite group with a strong leader where persons can change their opinions but not their spatial positions, and (ii) a model with persons treated as active Brownian particles interacting via a communication field. In the first model, two stable phases are possible: a cluster around the leader, and a state of social unification. The transition into the second state occurs for a large leader strength and/or for a high level of social noise. In the second model, we find three stable phases, which correspond either to a paramagnetic'' phase (for high noise and strong diffusion), a ferromagnetic'' phase (for small nose and weak diffusion), or a phase with spatially separated domains'' (for intermediate conditions).
 Physics , 2010, DOI: 10.1016/j.cpc.2010.11.020 Abstract: In a previous paper we proposed a model to study the dynamics of opinion formation in human societies by a co-evolution process involving two distinct time scales of fast transaction and slower network evolution dynamics. In the transaction dynamics we take into account short range interactions as discussions between individuals and long range interactions to describe the attitude to the overall mood of society. The latter is handled by a uniformly distributed parameter $\alpha$, assigned randomly to each individual, as quenched personal bias. The network evolution dynamics is realized by rewiring the societal network due to state variable changes as a result of transaction dynamics. The main consequence of this complex dynamics is that communities emerge in the social network for a range of values in the ratio between time scales. In this paper we focus our attention on the attitude parameter $\alpha$ and its influence on the conformation of opinion and the size of the resulting communities. We present numerical studies and extract interesting features of the model that can be interpreted in terms of social behaviour.
 Computer Science , 2012, Abstract: We study the dynamics of the Naming Game as an opinion formation model on time-varying social networks. This agent-based model captures the essential features of the agreement dynamics by means of a memory-based negotiation process. Our study focuses on the impact of time-varying properties of the social network of the agents on the Naming Game dynamics. We investigate the outcomes of the dynamics on two different types of time-varying data - (i) the networks vary across days and (ii) the networks vary within very short intervals of time (20 seconds). In the first case, we find that networks with strong community structure hinder the system from reaching global agreement; the evolution of the Naming Game in these networks maintains clusters of coexisting opinions indefinitely leading to metastability. In the second case, we investigate the evolution of the Naming Game in perfect synchronization with the time evolution of the underlying social network shedding new light on the traditional emergent properties of the game that differ largely from what has been reported in the existing literature
 Computer Science , 2012, DOI: 10.1016/j.physa.2012.06.047 Abstract: We propose the PageRank model of opinion formation and investigate its rich properties on real directed networks of Universities of Cambridge and Oxford, LiveJournal and Twitter. In this model the opinion formation of linked electors is weighted with their PageRank probability. We find that the society elite, corresponding to the top PageRank nodes, can impose its opinion to a significant fraction of the society. However, for a homogeneous distribution of two opinions there exists a bistability range of opinions which depends on a conformist parameter characterizing the opinion formation. We find that LiveJournal and Twitter networks have a stronger tendency to a totalitar opinion formation. We also analyze the Sznajd model generalized for scale-free networks with the weighted PageRank vote of electors.
 Physics , 2010, Abstract: We propose a minimal model for the collective dynamics of opinion formation in the society, by modifying kinetic exchange dynamics studied in the context of income, money or wealth distributions in a society. This model has an intriguing spontaneous symmetry breaking transition.
 Physics , 2013, DOI: 10.1016/j.physa.2014.07.082 Abstract: The dynamical origin of opinion polarization in the real world is an interesting topic physical scientists may help to understand. To properly model the dynamics, the theory must be fully compatible with findings by social psychologists on microscopic opinion change. Here we introduce a generic model of opinion formation with homogeneous agents based on the well-known social judgment theory in social psychology by extending a similar model proposed by Jager and Amblard. The agents' opinions will eventually cluster around extreme and/or moderate opinions forming three phases in a two-dimensional parameter space that describes the microscopic opinion response of the agents. The dynamics of this model can be qualitatively understood by mean-field analysis. More importantly, first-order phase transition in opinion distribution is observed by evolving the system under a slow change in the system parameters, showing that punctuated equilibria in public opinion can occur even in a fully connected social network.
 Physics , 2006, DOI: 10.1142/S0129183107011431 Abstract: We have presented a numerical model of a collective opinion formation procedure to explain political phenomena such as two-party and multi-party systems in politics, political unrest, military coup d'etats and netizen revolutions. Nonlinear interaction with binary and independent decision making processes can yield various collective behaviors or collective political opinions. Statistical physics and nonlinear dynamics may provide useful tools to study various socio-political dynamics.
 Computer Science , 2012, DOI: 10.1103/PhysRevE.86.056106 Abstract: In the spirit of behavioral finance, we study the process of opinion formation among investors using a variant of the 2D Voter Model with a tunable social temperature. Further, a feedback acting on the temperature is introduced, such that social temperature reacts to market imbalances and thus becomes time dependent. In this toy market model, social temperature represents nervousness of agents towards market imbalances representing speculative risk. We use the knowledge about the discontinuous Generalized Voter Model phase transition to determine critical fixed points. The system exhibits metastable phases around these fixed points characterized by structured lattice states, with intermittent excursions away from the fixed points. The statistical mechanics of the model is characterized and its relation to dynamics of opinion formation among investors in real markets is discussed.
 Physics , 2009, DOI: 10.1103/PhysRevE.80.066119 Abstract: In human societies opinion formation is mediated by social interactions, consequently taking place on a network of relationships and at the same time influencing the structure of the network and its evolution. To investigate this coevolution of opinions and social interaction structure we develop a dynamic agent-based network model, by taking into account short range interactions like discussions between individuals, long range interactions like a sense for overall mood modulated by the attitudes of individuals, and external field corresponding to outside influence. Moreover, individual biases can be naturally taken into account. In addition the model includes the opinion dependent link-rewiring scheme to describe network topology coevolution with a slower time scale than that of the opinion formation. With this model comprehensive numerical simulations and mean field calculations have been carried out and they show the importance of the separation between fast and slow time scales resulting in the network to organize as well-connected small communities of agents with the same opinion.
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