The role of heterarchical Simmelian ties in opinion dynamics with bounded confidence

This paper positions itself in the stream of literature that complements the classical theories of advocacy coalition with the studies of social networks and their structural properties. In particular, the paper aims at proposing a model that allows to further understand how a consensus à la DeGroot regarding a set of beliefs can be achieved considering not only the starting set of beliefs that each subject has, but also the relations that the subjects have with their neighbours within an organization. The novelty that this paper brings is twofold and regards, on the one hand, the way in which the structural statistics are specified and, on the other hand, the adaptation of the DeGroot model for the specific issue at hand. For what regards the structural statistics, we adopt a multilayer approach. For instance, by relying on the concept of Simmelian ties (Simmel, 1950), we further the discussion regarding the role that the strength of a tie plays in the transfer of information, communication and influence of opinions across a network. Additionally, by considering the formal structure of an organization and the personal relationships of its members, we want to propose a model that would allow to study the influence of opinions between subjects belonging to two different hierarchical levels and the role that Simmelian ties play in such a process. For what regards the opinion dynamics model (DeGroot, 1974), we first of all, suggest to make the trust that each subject poses on her neighbours’ opinion depend on the specific structural statistics and, additionally, on the distance of the beliefs themselves (Kozitsin, 2023). In such a way, the model can account for, on the one hand, the relational characteristics that each subject has and, on the other hand, for the role that homophily, confirmation biases and conformity plays in the trust subjects pose on others (Gargiulo and Yandica, 2017). Secondly, we go over the base assumption that characterize the DeGroot model and subsequent evolutions according to which a subject interacts with all her neighbours at each generic time-step t. On the contrary, by being information exchange at the base of the opinion dynamics and being it an information episode (Yale and Gilly, 1995), similarly to what is done to trust in bounded confidence studies (Cheng and Yu, 2019), we make the interaction between two subjects at a given time-step t depend on a probability that varies according to the characteristics of the tie between the subjects, the characteristics of the subjects (their sets of beliefs, their positions within the network). The introduction of stochastic interactions makes our model non-deterministc and allows to consider exogenous factors such as geographical distance. Eventually, computer simulations are conducted to study the collective opinion evolution, focusing on four key factors: whether a consensus is reached or whether we have a polarization, the characteristics of the dominant set of beliefs, who are the most influential subjects during the consensus formation process and the impact that the introduction of stochasticity has on the previous aspects.