Majority networks and consensus dynamics

Consensus is an emergent property of many complex systems, considering this as an absolute majority phenomenon. In this work we study consensus dynamics in grids (in silicon), where individuals (the vertices) with two possible opinions (binary states) interact with the eight nearest neighbors (Moore's neighborhood). Dynamics emerge once the majority rule drives the evolution of the system. In this work, we fully characterize the sub-neighborhoods on which the consensus may be reached or not. Given this, we study the quality of the consensus proposing two new measures, namely effectiveness and efficiency. We characterize attraction basins through the energy-like and magnetization-like functions similar to the Ising spin model.