Moral foundations in an interacting neural networks society: A statistical mechanics analysis

The moral foundations theory supports that people, across cultures, tend to consider a small number of dimensions when classifying issues on a moral basis. The data also show that the statistics of weights attributed to each moral dimension is related to self-declared political affiliation, which in turn has been connected to cognitive learning styles by the recent literature in neuroscience and psychology. Inspired by these data, we propose a simple statistical mechanics model with interacting neural networks classifying vectors and learning from members of their social neighbourhood about their average opinion on a large set of issues. The purpose of learning is to reduce dissension among agents when disagreeing. We consider a family of learning algorithms parametrized by δ, that represents the importance given to corroborating (same sign) opinions. We define an order parameter that quantifies the diversity of opinions in a group with homogeneous learning style. Using Monte Carlo simulations and a mean field approximation we find the relation between the order parameter and the learning parameter δ at a temperature we associate with the importance of social influence in a given group. In concordance with data, groups that rely more strongly on corroborating evidence sustain less opinion diversity. We discuss predictions of the model and propose possible experimental tests.