A New Paradigm for the Modeling of Opinion Dynamics

Opinion dynamics study how social influence shapes individuals' opinions. Although it is widely adopted that individuals update their opinions by averaging the opinions of others, researchers might need to rethink this micro-foundation. We point out that the weighted-averaging mechanism features a non-negligible unrealistic implication, which limits its predictive power. We propose a novel opinion dynamics model, namely a weighted-median mechanism, that is grounded in the framework of cognitive dissonance theory and resolves the shortcomings of weighted averaging. This new microscopic mechanism characterizes the sophisticated nature of opinion dynamics and provides a parsimonious explanation for various empirically-observed macroscopic phenomena. Moreover, our model extends, for the first time, the applicability of opinion formation models to the setting of ordered multiple-choice issues.

  • W. Mei, F. Bullo, G. Chen, F. Dörfler, "Occam's Razor in Opinion Dynamics: The Weighted-Median Influence Process", manuscript and slides available.    PDF ]

Dynamic Models of Appraisal Networks and Team Learning​

Transactive memory system (TMS) is a well-established conceptual models of team structure and performance in organization science. To put it simply, TMS characterizes 1) the team members’ mutual perceptions of individual expertise; 2) the division of labor based on the collective knowledge on the distribution expertise. Despite the extensive qualitative and empirical studies revealing a strong positive relationship between the development of a team's TMS and team performance,  there is a dearth of mathematical formulation.

We propose a novel mathematical formalization of TMS as the team members’ interpersonal appraisals of individual skill levels. The development of TMS is thereby modeled as the dynamics of the appraisal network. Our models are grounded in replicator dynamics from evolutionary games, influence networks from mathematical sociology, and transactive memory systems from organization science.

  • W. Mei, N. E. Friedkin, K. Lewis, and F. Bullo, “Dynamical Models of Appraisal Networks Explaining Collective Learning,” IEEE TAC, conditionally accepted.

Discrete-time dynamic social balance

Social balance theory describes allowable and forbidden configurations of the topologies of signed directed social appraisal networks. According to the classic Heider's structural balance theory, in a structurally balanced network, the interpersonal relationships satisfy the following four famous aphorisms: "The friend of my friend is my friend; the friend of my enemy is my enemy; the enemy of my friend is my enemy; the enemy of my enemy is my friend". While the traditional studies of social balance mainly focus on the static theory, the dynamic social balance theory has recently attracted the interest of researchers.

We propose two novel discrete-time dynamic models leading to the bounded evolution of the interpersonal appraisals towards social balance. Our two models are based on two extensively-studied socio-psychological mechanisms respectively: the homophily mechanism and the influence mechanism.  For each model, we provide a comprehensive theoretical analysis of its dynamical behavior. Some simulation results revealing insightful interpretations are also presented. 

  • W. Mei, P. Cisneros-Velarde, N. E. Friedkin, and F. Bullo, “Dynamic Social Balance and Convergent Appraisals via Homophily and Influence Mechanisms,” submitted to Automatica.

Dynamics of Deterministic Epidemic Propagation over Networks

We review a class of deterministic nonlinear models for the propagation of infectious diseases over contact networks with strongly-connected topologies. We consider network SI, SIS, and SIR settings. In each setting, we provide a comprehensive nonlinear analysis of equilibria, stability properties, convergence, monotonicity, positivity, and threshold conditions.  These results are analogous  to those well-known for the scalar case.  We do not  only  review the  known results in  the  previous literature, but  also provide some  novel results to make the  analysis comprehensive and systematical.

  • W. Mei, S. Mohagheghi, S. Zampieri, and F. Bullo, “On the Dynamics of Deterministic Epidemic Propagation over Networks,” Annual Reviews in Control, to appear.

Competitive Propagation and Quality-Seeding Games

Various models have been proposed on the propagation of a single meme on networks. However, there is still a lack of more generalized models for the propagation of multiple memes. We propose a class of epidemic-like propagation models for multiple competing products over arbitrary social networks. We model two microscopic propagation mechanisms: social conversion and self-conversion. We establish how the interplay among the competing products influences the system's asymptotic state. Moreover, based on the competitive propagation models, we propose a class of dynamic games, in which the companies as the players invest on both seeding, e.g., advertisement and promotion, and improving their products’ quality. We characterize the Nash equilibrium and the system's evolution under the player's rational actions. Theoretical analysis reveals some strategic insights on the dynamic trade-off between seeding and quality. 

  • W. Mei and F. Bullo, “Competitive Propagation: Models, Asymptotic Behavior and Quality-Seeding Games,” IEEE Transactions on Network Science and Engineering, 4(2):83-99, 2017.