Romualdo Pastor-SatorrasOpinion depolarization transtions in interdependent topics on heterogeneous social networks*

The presence of opinion polarization (i.e. two groups holding opposite and possibly extreme opinions in a population) has been extensively observed with  respect to several controversial topics, ranging from religion to political ideology. Modeling the process of reducing opinion polarization among the population, or depolarization, has been the object of much recent work. In most cases, such efforts address the simplest case of one-dimensional opinions with respect to a single topic. However, the process of opinion formation may invest multiple topics at the same time, requiring a proper multidimensional modeling framework for opinion dynamics. Here we present an analytically tractable model of opinion dynamics in a space of two interdependent topics, the so-called "Social Compass Model" (SCM). In the SCM, opinions are represented in polar coordinates, where the angle represents the orientation and the radius the conviction of individuals. We postulate a dynamics inspired by the classic Friedkin-Johnsen, in which the orientation of individuals, subject to an initial, preferred orientation and to social influence by peers, experience a depolarization phase transition for a sufficiently large social influence level. By means of a mean field analysis, we observe that the transition of the SCM is continuous for correlated initial opinions, while it has an discontinuous, explosive nature for uncorrelated initial opinions. These results are checked against numerical simulations using as initial opinions real data extracted form the American Nation Election Studies (ANES) surveys. Finally we discuss the effects of an complex networks pattern of contacts on the depolarization transition of the SCM model, and show how an heterogeneous pattern of interactions can decrease the over level of polarization.