Sympatric Multiculturalism in Opinion Models

While social interactions tend to decrease differences in opinions, multiplicity of groups and individual
opinion differences persist in human societies. Axelrod identified homophily and social conformity seeking as basic
interactions that can lead to multiculturalism in spatial scenarios in models under certain special conditions.
We follow another route, where the social interactions between any two agents is given by the descent along the gradient of a cost function
deduced from a Bayesian learning formalism. The cost functions depends on a hyperparameter that estimates the trust of one agent on the
information provided by the other. If the expected value of the total cost function is relevant information, Maximum Entropy permits characterizing the state
of the society. Furthermore we introduce a dynamics on the trust parameters, which increases when agents concur and decreases
otherwise. We study the resulting phase diagram in the case of large number of interacting agents on a complete social graph, hence under sympatric conditions.
Simulations show that there is evolution of assortative
distrust in rich cultural environments measured by the diversity of the set of issues under discussions. High distrust leads to antilearning which leads
to multiple groups which hold different opinions on the set of issues. We simulate conditions of political pressure and interaction
that describe the House of Congress of Brazil and are able
to qualitatively replicate voting patterns through four presidential cycles during the years of $1994$ to $2010$.