On the role of zealots in a best-of-n problem on a heterogeneous network

Abstract: Both humans and social animals live in groups and are frequently faced to choose between options with different qualities. When no leader agents are controlling the group decision, consensus can be achieved through repeated interactions among group members. Various studies on CDM illustrate how the dynamics of 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 error 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. By using the HMF approach, we study the impact of the above-mentioned factors in the decision dynamics. Our findings indicate that when susceptible agents 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 more cognitively demanding, 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.