On the Effects of Heterogeneous Logical Interdependencies in a Multi-Dimensional Opinion Dynamics Model

In this paper, we investigate a recently proposed opinion dynamics model which considers a network of individuals simultaneously discussing a set of logically interdependent topics. The logical interdependence between the topics is captured by a 'logic matrix'. Previous works have investigated the model under the assumption that all individuals have the same logic matrix, or that individuals have different logic matrices but each individual has some stubbornness, which are restrictive assumptions. In contrast, we investigate heterogeneous logic matrices for the individuals, and assume that no stubborn individuals are present. We show that such heterogeneity can lead to a stable system with persistent disagreement among the final opinions. This indicates heterogeneity in individuals' logical interdependence structures, and not just the stubbornness of individuals (as in the Friedkin-Johnsen model), may explain the phenomenon of strong diversity of opinions often observed in a strongly connected network: the opinions at equilibrium are not at a complete consensus and opinions in any cluster are similar but not equal