Monotonicity of Social Opinion Dynamics on Large Networks

Motivated by the research on social opinion dynamics over large networks, a general framework for verifying the Monotonicity Property of multi-agent dynamics is introduced. This allows a derivation of sociologically meaningful sufficient conditions for monotonicity that are tailor-made for social opinion dynamics, which typically have high non-linearity. A key part of this framework is the definition of a partial order relation that is suitable for a large class of social opinion dynamics such as the generalized Naming games. Comparisons are made to previous techniques to verify monotonicity which fails on social opinion dynamics due to the high non-linearity of these systems. Using the results obtained, we extend many of the consequences of monotonicity to this class of social dynamics, including several corollaries on their asymptotic behavior, such as global convergence to consensus and tipping points of a minority fraction of zealots or leaders.