Zealotry and Influence Maximization in the Voter Model: When to Target Partial Zealots?

In this paper, we study influence maximization in the voter model in the presence of biased voters (partial zealots) on complex networks. Under what conditions should an external controller with finite budget who aims at maximizing its influence over the system target partial zealots? Our analysis, based on both analytical and numerical results, shows a rich diagram of preferences and degree-dependencies of allocations to partial zealots and normal agents varying with the budget. We find that when we have a large budget or for low levels of zealotry, optimal strategies should give larger allocations to partial zealots and allocations are positively correlated with node degree. In contrast, for low budgets or highly-biased zealots, optimal strategies give higher allocations to normal agents, with some residual allocations to partial zealots, and allocations to both types of agents decrease with node degree. Our results emphasize that heterogeneity in agent properties strongly affects strategies for influence maximization on heterogeneous networks.