Reaching Consensus on Social Networks

Research in sociology studies the effectiveness of social networks in achieving computational tasks. Typically the agents who are supposed to achieve a task are unaware of the underlying social network except their immediate friends. They have limited memory, communication, and coordination. These limitations result in computational obstacles in achieving otherwise trivial computational problems. One of the simplest problems studied in the social sciences involves reaching a consensus among players between two alternatives which are otherwise indistinguishable. In this paper we formalize the computational model of social networks. We then analyze the consensus problem as well as the problem of reaching a consensus which is identical to the majority of the original signals. In both models we seek to minimize the time it takes players to reach a consensus

Exploiting Asynchrony in Multi-agent Con-sensus to Change the Agreement Point

Reaching agreement by consensus is fundamental to the operation of distributed systems, such as sensor networks, social networks or multi-robot networks. In real systems, the resource limitations available to individual agents and communication delays typically result in asynchronous control models of discreet time for consensus. In this paper, we model the problem where a set of agents arrive at a consensus on the value of a variable of interest, being guided by one of them

The Dynamics of Public Opinion in Complex Networks

This paper studies the problem of public opinion formation and concentrates on the interplays among three factors: individual attributes, environmental influences and information flow. We present a simple model to analyze the dynamics of four types of networks. Our simulations suggest that regular communities establish not only local consensus, but also global diversity in public opinions. However, when small world networks, random networks, or scale-free networks model social relationships, the results are sensitive to the elasticity coefficient of environmental influences and the average connectivity of the type of network. For example, a community with a higher average connectivity has a higher probability of consensus. Yet, it is misleading to predict results merely based on the characteristic path length of networks. In the process of changing environmental influences and average connectivity, sensitive areas are discovered in the system. By sensitive areas we mean that interior randomness emerges and we cannot predict unequivocally how many opinions will remain upon reaching equilibrium. We also investigate the role of authoritative individuals in information control. While enhancing average connectivity facilitates the diffusion of the authoritative opinion, it makes individuals subject to disturbance from non-authorities as well. Thus, a moderate average connectivity may be preferable because then the public will most likely form an opinion that is parallel with the authoritative one. In a community with a scale-free structure, the influence of authoritative individuals keeps constant with the change of the average connectivity. Provided that the influence of individuals is proportional to the number of their acquaintances, the smallest percentage of authorities is required for a controlled consensus in a scale free network. This study shows that the dynamics of public opinion varies from community to community due to the different degree of impressionability of people and the distinct social network structure of the community.Public Opinion, Complex Network, Consensus, Agent-Based Model

Conformism-driven phases of opinion formation on heterogeneous networks: the q -voter model case

The q -voter model, a variant of the classic voter model, has been analyzed by several authors. While allowing us to study opinion dynamics, this model is also believed to be one of the most representative among the many defined in the wide field of sociophysics. Here, we investigate the consequences of conformity on the consensus reaching process, by numerically simulating a q -voter model with agents behaving either as conformists or nonconformists, embedded on heterogeneous network topologies (as small-world and scale-free). In fact, although it is already known that conformity enhances the reaching of consensus, the related process is often studied only on fully-connected networks, thus strongly limiting our full understanding of it. This paper represents a first step in the direction of analyzing more realistic social models, showing that different opinion formation phases, driven by the conformist agents density, are observable. As a result, we identify threshold values of the density of conformist agents, varying across different topologies and separating different regimes of our system, ranging from a disordered phase, where different opinions coexist, to a gradually more ordered phase, where consensus is eventually reached

Element-centric clustering comparison unifies overlaps and hierarchy

Clustering is one of the most universal approaches for understanding complex data. A pivotal aspect of clustering analysis is quantitatively comparing clusterings; clustering comparison is the basis for many tasks such as clustering evaluation, consensus clustering, and tracking the temporal evolution of clusters. In particular, the extrinsic evaluation of clustering methods requires comparing the uncovered clusterings to planted clusterings or known metadata. Yet, as we demonstrate, existing clustering comparison measures have critical biases which undermine their usefulness, and no measure accommodates both overlapping and hierarchical clusterings. Here we unify the comparison of disjoint, overlapping, and hierarchically structured clusterings by proposing a new element-centric framework: elements are compared based on the relationships induced by the cluster structure, as opposed to the traditional cluster-centric philosophy. We demonstrate that, in contrast to standard clustering similarity measures, our framework does not suffer from critical biases and naturally provides unique insights into how the clusterings differ. We illustrate the strengths of our framework by revealing new insights into the organization of clusters in two applications: the improved classification of schizophrenia based on the overlapping and hierarchical community structure of fMRI brain networks, and the disentanglement of various social homophily factors in Facebook social networks. The universality of clustering suggests far-reaching impact of our framework throughout all areas of science

Perception of trainers and students on the measures to be taken to solve the addiction of young people to social networks

Addictions to online social networks is a problem facing technological societies, and those most affected by this phenomenon are young people and teenagers. Among its effects are the decrease in academic performance and the increase in violent behavior. Given these facts, governments around the world are adopting mechanisms for their prevention. The present work describes the results of research focused on investigating the proposals that would be adopted by the members of the educational community to carry out preventive actions against the addiction and abuse of online social networks. The methodological design has been based on the intensive use of the Nominal Groups technique developed by Delbecq and Andrew in 1971 and which facilitates reaching consensus in a structured group process. The results show the high degree of coincidence among the participants stands out, which validates the usefulness of the measures, and that the addiction to social networks perceives it as a direct consequence of the addition to mobile phones and the Internet. Therefore, it seems necessary that prevention plans should have a generalized perspective that encompasses all three technologie

Accelerating consensus on co-evolving networks: the effect of committed individuals

Social networks are not static but rather constantly evolve in time. One of the elements thought to drive the evolution of social network structure is homophily - the need for individuals to connect with others who are similar to them. In this paper, we study how the spread of a new opinion, idea, or behavior on such a homophily-driven social network is affected by the changing network structure. In particular, using simulations, we study a variant of the Axelrod model on a network with a homophilic rewiring rule imposed. First, we find that the presence of homophilic rewiring within the network, in general, impedes the reaching of consensus in opinion, as the time to reach consensus diverges exponentially with network size $N$. We then investigate whether the introduction of committed individuals who are rigid in their opinion on a particular issue, can speed up the convergence to consensus on that issue. We demonstrate that as committed agents are added, beyond a critical value of the committed fraction, the consensus time growth becomes logarithmic in network size $N$. Furthermore, we show that slight changes in the interaction rule can produce strikingly different results in the scaling behavior of $T_c$. However, the benefit gained by introducing committed agents is qualitatively preserved across all the interaction rules we consider

The impact of noise and topology on opinion dynamics in social networks

We investigate the impact of noise and topology on opinion diversity in social networks. We do so by extending well-established models of opinion dynamics to a stochastic setting where agents are subject both to assimilative forces by their local social interactions, as well as to idiosyncratic factors preventing their population from reaching consensus. We model the latter to account for both scenarios where noise is entirely exogenous to peer influence and cases where it is instead endogenous, arising from the agents' desire to maintain some uniqueness in their opinions. We derive a general analytical expression for opinion diversity, which holds for any network and depends on the network's topology through its spectral properties alone. Using this expression, we find that opinion diversity decreases as communities and clusters are broken down. We test our predictions against data describing empirical influence networks between major news outlets and find that incorporating our measure in linear models for the sentiment expressed by such sources on a variety of topics yields a notable improvement in terms of explanatory power

The Naming Game in Social Networks: Community Formation and Consensus Engineering

We study the dynamics of the Naming Game [Baronchelli et al., (2006) J. Stat. Mech.: Theory Exp. P06014] in empirical social networks. This stylized agent-based model captures essential features of agreement dynamics in a network of autonomous agents, corresponding to the development of shared classification schemes in a network of artificial agents or opinion spreading and social dynamics in social networks. Our study focuses on the impact that communities in the underlying social graphs have on the outcome of the agreement process. 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. Further, we investigate agent-based network strategies to facilitate convergence to global consensus.Comment: The original publication is available at http://www.springerlink.com/content/70370l311m1u0ng3