A new adaptive two-layer model for opinion spread in hypergraphs: parameter sensitivity and estimation

Abstract: When opinion spread is studied, peer pressure is often modeled by interactions of more than two individuals (higher-order interactions). In our work, we introduce a two-layer random hypergraph model, in which hyperedges represent households and workplaces. Within this overlapping, adaptive structure, individuals react if their opinion is in majority in their groups. The process evolves through random steps: individuals can either change their opinion, or quit their workplace and join another one in which their opinion belongs to the majority. Based on computer simulations, our first goal is to describe the effect of the parameters responsible for the probability of changing opinion and quitting workplace on the homophily and speed of polarization. We also analyze the model as a Markov chain, and study the frequency of the absorbing states. Then, we quantitatively compare how different statistical and machine learning methods, in particular, linear regression, xgboost and a convolutional neural network perform for estimating these probabilities, based on partial information from the process, for example, the distribution of opinion configurations within households and workplaces. Among other observations, we conclude that all methods can achieve the best results under appropriate circumstances, and that the amount of information that is necessary to provide good results depends on the strength of the peer pressure effect.