  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 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 neighborhood about their
average opinion on a large set of issues. The purpose of learning is to reduce
dissension among agents even when disagreeing. We consider a family of learning
algorithms parametrized by \delta, 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 \delta 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 sustains less opinion diversity. We discuss predictions
of the model and propose possible experimental tests.
