How social contagions shape collective consensus in the presence of scale-free networks

Consensus-building can be considered a cornerstone of democratic societies and effective governance. Recently, it has been shown that social contagions can shape some forms of consensus-based collective decision-making (Horsevad et al., Nature Communications, (2022)13:1442). The topology of the network underpinning such processes plays a key role in promoting or hampering simple contagions—based on pairwise interactions—and complex contagions, which require social influence and reinforcement. However, considering the ubiquitous scalefreeness of most social networks, it becomes imperative to delve into how this particular characteristic of networks impacts the dynamics of social contagions and the subsequent group consensus. Two specific aspects are worth analyzing: (i) understanding the interplay between scalefreeness and the transition from a simple to a complex contagion, and (ii) exploring the specificities associated with highly clustered networks. Here, we consider two distinct collective decision-making processes: (1) the classical linear threshold model, and (2) the leader-follower consensus model—a paradigmatic approach to collective decision-making—to systematically explore the transition from simple to complex contagions in the presence of a tunable family of synthetic scale-free networks. In contrast to previous findings, our results show that scale-free networks can, under certain conditions, support the spread of complex contagions. These findings carry profound implications for the development of innovative strategies aimed at fostering consensus within social groups.