On the impact of agents with influenced opinions in the swarm social behavior

We consider a simplified version of the Taylor model, typically used in the collective dynamics of continuous exchange of opinions, to describe the properties of swarm formation in the presence of external sources of influence or prejudices affecting a number of agents in the network. Such external sources are responsible for the breakdown of the consensus equilibrium and directly influence certain other individuals in the network, which we denote as quasi-stubborn agents. These quasi-stubborn agents participate in consensus with other individuals, but are able to indirectly influence the opinions of the entire system. In particular, we show that the swarm in steady-state moves towards the convex hull of the opinions of the quasi-stubborn agents. This is an interesting result that allows a more accurate estimation of the final opinions in a social network. In the case of two prejudiced agents, an explicit expression of the stationary opinions is provided in terms of the Moore-Penrose inverse of the Laplacian of the graph. Numerical simulations are presented to illustrate the properties of the considered model

Mathematical Structures in Group Decision-Making on Resource Allocation Distributions.

Optimal decisions on the distribution of finite resources are explicitly structured by mathematical models that specify relevant variables, constraints, and objectives. Here we report analysis and evidence that implicit mathematical structures are also involved in group decision-making on resource allocation distributions under conditions of uncertainty that disallow formal optimization. A group's array of initial distribution preferences automatically sets up a geometric decision space of alternative resource distributions. Weighted averaging mechanisms of interpersonal influence reduce the heterogeneity of the group's initial preferences on a suitable distribution. A model of opinion formation based on weighted averaging predicts a distribution that is a feasible point in the group's implicit initial decision space

シャカイネットワークニオケルオピニオンダイナミクスノゴシップベースモデル

Emerico Aguilar & Yasumasa Fujisaki. "Reaching consensus via coordinated groups", SICE Journal of Control, Measurement, and System Integration, 14(1), 20-26 (2021). DOI: 10.1080/18824889.2021.1874673

Unique Nash equilibrium of a nonlinear model of opinion dynamics on networks with friction-inspired stubbornness

The modeling of opinion dynamics has seen much study in varying academic disciplines. Understanding the complex ways information can be disseminated is a complicated problem for mathematicians as well as social scientists. We present a nonlinear model of opinion dynamics that utilizes an environmental averaging protocol similar to the DeGroot and Freidkin-Johnsen models. Indeed, the way opinions evolve is complex and nonlinear effects ought to be considered when modelling. For this model, the nonlinearity destroys the translation invariance of the equations, as well as the convexity of the associated payout functions. The standard theory for well-posedness and convergence no longer applies and we must utilize the Brouwer topological degree and nonconvex analysis in order to achieve these results. Numerical simulations of the model reveal that the nonlinearity behaves similarly to the well-known Friedkin-Johnsen for so-called "reasonable" opinions, but better models the way agents that hold "extreme" opinions are more stubborn than their reasonable counterparts

Learning Hidden Influences in Large-Scale Dynamical Social Networks: A Data-Driven Sparsity-Based Approach, in Memory of Roberto Tempo

The processes of information diffusion across social networks (for example, the spread of opinions and the formation of beliefs) are attracting substantial interest in disciplines ranging from behavioral sciences to mathematics and engineering (see "Summary"). Since the opinions and behaviors of each individual are infl uenced by interactions with others, understanding the structure of interpersonal infl uences is a key ingredient to predict, analyze, and, possibly, control information and decisions [1]. With the rapid proliferation of social media platforms that provide instant messaging, blogging, and other networking services (see "Online Social Networks") people can easily share news, opinions, and preferences. Information can reach a broad audience much faster than before, and opinion mining and sentiment analysis are becoming key challenges in modern society [2]. The first anecdotal evidence of this fact is probably the use that the Obama campaign made of social networks during the 2008 U.S. presidential election [3]. More recently, several news outlets stated that Facebook users played a major role in spreading fake news that might have infl uenced the outcome of the 2016 U.S. presidential election [4]. This can be explained by the phenomena of homophily and biased assimilation [5]-[7] in social networks, which correspond to the tendency of people to follow the behaviors of their friends and establish relationships with like-minded individuals