Interacting Social Processes on Interconnected Networks

Lucila G Alvarez-Zuzek, Cristian E La Rocca, Federico Vazquez and Lidia A Braunstein

PLOS ONE, 2016, vol. 11, issue 9, 1-17

Abstract: 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 βc. 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*).

Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:plo:pone00:0163593

DOI: 10.1371/journal.pone.0163593

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