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To analyze the nuances of the root concept of neutral in social networks, wefocus on several related interpretations and suggest corresponding mathematicalmodels for each of them from the family of information-sharing multi-agentsnetwork games known as Voter models and the Naming Games (NG). We solve thecase of the strong neutrals known as the middle-roaders for global quantitiessuch as expected times to consensus and local times. By using generatingfunctions and treating the two extreme and middle opinions in this modificationas a two balls, three urns version of the Voter model, we give closed-formexpressions for the eigenvalues and eigenvectors of its Markov propagator. Thismodification of the two-opinions Naming Games is applicable to the roles andbehaviour of neutrals in social forums or blogs, and represent a significantdeparture from the linguistic roots of the original NG.

Information Sharing for Strong Neutrals on Social Networks - Exact Solutions for Consensus Times