  To analyze the nuances of the root concept of neutral in social networks, we
focus on several related interpretations and suggest corresponding mathematical
models for each of them from the family of information-sharing multi-agents
network games known as Voter models and the Naming Games (NG). We solve the
case of the strong neutrals known as the middle-roaders for global quantities
such as expected times to consensus and local times. By using generating
functions and treating the two extreme and middle opinions in this modification
as a two balls, three urns version of the Voter model, we give closed-form
expressions for the eigenvalues and eigenvectors of its Markov propagator. This
modification of the two-opinions Naming Games is applicable to the roles and
behaviour of neutrals in social forums or blogs, and represent a significant
departure from the linguistic roots of the original NG.
