Interacting Social Processes on Interconnected Networks

ALVAREZ-ZUZEK, L.; BRAUNSTEIN, L. A.; F. VAZQUEZ; LA ROCCA, C. E.

Taller; SoFiA: Latin American School on Data Analysis and Mathematical Modeling of Social Science; 2016

We propose and study a model for the interplay between two different dynamical processes ?one for opinion formation and the other for decision making? on two interconnected networks A and B. The opinion dynamics on network A corresponds to that of the M-model, where the state of each agent can take one of four possible values (S = −2, −1, 1, 2), describing its level of agreement on a given issue. The likelihood to become an extremist (S = ±2) or a moderate (S = ±1) is controlled by a reinforcement parameter r ≥ 0. The decision making dynamics on network B is akin to that of the Abrams-Strogatz model, where agents can be either in favor (S = +1) or against (S = −1) the issue. The probability that an agent changes its state is proportional to the fraction of neighbors that hold the opposite state raised to a power β. Starting from a polarized case scenario in which all agents of network A hold positive orientations while all agents of network B have a negative orientation, we explore the conditions under which one of the dynamics prevails over the other, imposing its initial orientation. We find that, for a given value of β, the two-network system reaches a consensus in the positive state (initial state of network A) when the reinforcement overcomes a crossover value r ∗ (β), while a negative consensus happens for r < r ∗ (β). In the r − β phase space, the system displays a transition at a critical threshold β c , from a coexistence of both orientations for β < β c to a dominance of one orientation for β > β c . We develop an analytical mean-field approach that gives an insight into these regimes and shows that both dynamics are equivalent along the crossover line (r ∗ , β ∗ ).