Opinion Dynamics in the Presence of Increasing Agreement Pressure

A Comment on and Correction to: Opinion Dynamics in the Presence of Increasing Agreement Pressure

We identify counterexamples to the consensus result given in Semonsen et al. (2018). We resolve the counterexamples by replacing Lemma 5 in the given reference with a novel variation of the Banach fixed-point theorem, which explains both the numerical results in the reference and the counterexample(s) in this note and provides a sufficient condition for consensus in systems with increasing peer-pressure. This work is relevant for other papers that have used the proof technique from Semonsen et al. and establishes the veracity of their claims assuming the new sufficient condition.

Coevolutionary opinion dynamics with sparse interactions in open-ended societies

Opinion dynamics is a crucial topic in complex social systems. However, existing models rarely study limited information accessibility, sparse interactions, and the coevolution of opinion and an open-ended structure. In this paper, we propose the Sparse COevolutionary Open-Ended (SCOOE) model. We address the sparse interaction limitation through extrinsic collective interaction and intrinsic observation based on incomplete neighborhood information. We also consider the coevolution of opinion and open-ended structure by studying structure-opinion co-dynamics when dissidents are leaving and when newcomers with novel opinions are joining. From an opinion dynamics perspective, we find that the proposed mechanisms effectively form lean and fast decision strategies to reduce conflicts under uncertainty. The model is robust in boosting and enhancing a global consensus with only small odds of extreme results. The structure evolves toward a small-world network. We find that an emergent dialectic relationship exists between community segregation and community cohesion viewed from a structural dynamics perspective. We also study the influence of agent heterogeneity under different cognitive ability distributions.

Bounded Confidence Evolution of Opinions and Actions in Social Networks

Inspired by the continuous opinion and discrete action (CODA) model, bounded confidence and social networks, the bounded confidence evolution of opinions and actions in social networks is investigated and a social network opinions and actions evolutions (SNOAEs) model is proposed. In the SNOAE model, it is assumed that each agent has a CODA for a certain issue. Agents' opinions are private and invisible, that is, an individual agent only knows its own opinion and cannot obtain other agents' opinions unless there is a social network connection edge that allows their communication; agents' actions are public and visible to all agents and impact other agents' actions. Opinions and actions evolve in a directed social network. In the limitation of the bounded confidence, other agents' actions or agents' opinions noticed or obtained by network communication, respectively, are used by agents to update their opinions. Based on the SNOAE model, the evolution of the opinions and actions with bounded confidence is investigated in social networks both theoretically and experimentally with a detailed simulation analysis. Theoretical research results show that discrete actions can attract agents who trust the discrete action, and make agents to express extreme opinions. Simulation experiments results show that social network connection probability, bounded confidence, and the opinion threshold of action choice parameters have strong impacts on the evolution of opinions and actions. However, the number of agents in the social network has no obvious influence on the evolution of opinions and actions.

Resilient Consensus for Expressed and Private Opinions

This article proposes an opinion formation model featuring both a private and an expressed opinion for a given topic over dynamical networks. Each individual in the network has a private opinion, which is not known by others but evolves under local influence from the expressed opinions of its neighbors, and an expressed opinion, which varies under a peer pressure to conform to the local environment. We design the opinion sifting strategies which are purely distributed and provide resilience to a range of adversarial environment involving locally and globally bounded threats as well as malicious and Byzantine individuals. We establish the sufficient and necessary graph-theoretic criteria for normal individuals to attain opinion consensus in both directed-fixed and time-varying networks. Two classes of opinion clustering problems are introduced as an extension. By designing the resilient opinion separation algorithms, we develop necessary and sufficient criteria, which characterize the resilient opinion clustering in terms of the ratio of opinions as well as the difference of opinions. Numerical examples, including real-world jury deliberations, are presented to illustrate the effectiveness of the proposed approaches and test the correctness of our theoretical results.

Edge Convergence Problems on Signed Networks

This paper focuses on characterizing edge dynamics of signed networks subject to both cooperative and antagonistic interactions and copes with the state convergence problems of the resulting edge systems. To represent the two competitive classes of interactions that emerge in signed networks, signed digraphs are adopted and the relevant edge Laplacian matrices are introduced, with which an edge-based distributed protocol is presented. The relation between the edge Laplacian matrix and the structural balance (or unbalance) of a signed digraph is disclosed by taking advantage of properties of undirected cycles. Further, it is shown that for a signed network, the state of its edge system converges to a constant vector, regardless of whether its associated signed digraph is structurally balanced or unbalanced. This result does not need to impose the assumption upon the digon sign-symmetry of the signed digraph that is generally required by the node-based distributed protocols. In particular, the state convergence results of edges can be exploited to handle traditional bipartite consensus problems for the nodes of signed networks. Simulation examples are given to illustrate the effectiveness of the edge-based analysis method proposed for signed networks.