Measuring bi-polarization with argument graphs

Multi-agent models play a significant role in testing hypotheses about the unfolding of opinion dynamics in complex social networks. The model of the Argument Communication Theory of Bi-polarization (ACTB), developed by Maes and Flache (2013), shows that simple circulation of arguments among individuals in a group can determine strong differentiation of opinions (bi-polarization effects) even with a small degree of homophily. The ACTB model and similar ones have nevertheless one limitation: given a topic of discussion, only direct pro and con arguments for it are considered. This does not allow to account for the topology of a more complex debate, where arguments may also interact indirectly with the topic at stake. This gap can be filled by using Quantitative Bipolar Argument Frameworks (QBAF). More specifically, by applying measures of argument strength for QBAFs in order to calculate the agents' opinion. In the present paper we generalize the ACTB measure of opinion strength to acyclic bipolar graphs and compare it with other measures from the literature. We then present a revised version of the ACTB model, where the agents' knowledge bases are structured as subgraphs of an underlying global knowledge base (described as a QBAF). We first test that the predictions of the ACTB model are confirmed when the underlying QBAF contains only direct pro and con arguments for a topic. We then explore more complex topologies of debate with two additional batches of simulations. Our first results show that changing the topology, while keeping the same number of pro and con arguments, has no significant impact on bi-polarization dynamics.