On the impact of zealots in a population of susceptible agents in a best-of-n problem within a heterogeneous network

Both humans and social animals live in groups and are frequently forced to choose between options with different qualities. When there are no leader agents controlling the group decision, consensus can be achieved through repeated interactions among group members. Various studies on collective decision-making illustrate how the dynamics of the opinions are determined by the structure of the social network and the methods that individuals use to share and update their opinion upon a social interaction. In this paper, we are interested in further exploring how cognitive, social, and environmental factors interactively contribute to determining the outcome of a collective best-of-n decision process involving asymmetric options, i.e., different costs and/or benefits for each option. We propose and study a novel model capturing those different factors, (i) the cognitive load in processing social information, (ii) the number of zealots (i.e., asocial agents who never change their opinion), (iii) the option qualities, (iv) the social connectivity structure, and (v) the degree centrality of the asocial agents (i.e., the number of neighbours). By using the heterogeneous mean-field approach, we study the impact of the above-mentioned factors in the decision dynamics. Our findings indicate that when susceptible agents, i.e., individuals who change their opinion to conform with others, use the voter model as a mechanism to update their opinion, both the number and the degree of connectivity of the zealots can lead the population to converge towards the lowest quality option. Instead, when susceptible agents use methods demanding a larger cognitive cost (e.g., the majority rule), the group is marginally impacted by the presence of zealots. The results of the analytical model are complemented and extended by agent-based simulations. Our analysis also shows that the network topology can modulate the influence of zealots on group dynamics. In fact, in homogeneous networks where all nodes have the same degree, any location of the zealots has similar impact on the group dynamics. Instead, when the network is heterogeneous, our simulations confirm the model predictions showing that placing the zealots in the network hubs (nodes with several neighbours) has a much larger impact than placing them in lower-degree nodes.