Group-based rewiring rules of binary opinion competition dynamics

Majority networks and local consensus algorithm

In this paper, we study consensus behavior based on the local application of the majority consensus algorithm (a generalization of the majority rule) over four-connected bi-dimensional networks. In this context, we characterize theoretically every four-vicinity network in its capacity to reach consensus (every individual at the same opinion) for any initial configuration of binary opinions. Theoretically, we determine all regular grids with four neighbors in which consensus is reached and in which ones not. In addition, in those instances in which consensus is not reached, we characterize statistically the proportion of configurations that reach spurious fixed points from an ensemble of random initial configurations. Using numerical simulations, we also analyze two observables of the system to characterize the algorithm: (1) the quality of the achieved consensus, that is if it respects the initial majority of the network; and (2) the consensus time, measured as the average amount of steps to reach convergence.

A general framework to link theory and empirics in opinion formation models

We introduce a minimal opinion formation model that is quite flexible and can reproduce a wide variety of the existing micro-influence assumptions and models. The model can be easily calibrated on real data, upon which it imposes only a few requirements. From this perspective, our model can be considered as a bridge, connecting theoretical studies on opinion formation models and empirical research on social dynamics. We investigate the model analytically by using mean-field approximation and numerically via Monte Carlo simulations. Our analysis is exemplified by recently reported empirical data drawn from an online social network. We demonstrate that the model calibrated on these data may reproduce fragmented and polarizing social systems. Furthermore, we manage to generate an artificial society that features properties quantitatively and qualitatively similar to those observed empirically at the macro scale. This ability became possible after we had advanced the model with two important communication features: selectivity and personalization algorithms.