A two-stage opinion formation model based on the extended XY-magnet interaction and socio-dynamic update mechanism

Abstract

We introduce herein a two stage model of opinion formation in a community of individuals which share strong interests within a permanent pair, and attend also a persuasion social process with others to finalize their attitudes. In the first step, individuals behave as member of their couples and seek to optimize respective satisfaction. Then, they modify their attitudes inherited from the first stage throughout a persuasion process and social influence. The first stage consists in an extension of a classical XY magnet model, and the calculation in this step are performed using statistical mechanics tools. At the end of this phase, each opinion agent has adapted its support Ox for the issue F and the agreement within their pair O = |O1 + O2|. The evaluated quantities Ox(i) depend on the magnetic-like system parameters J, T, F and on the extra parameter α(i) which embodies the dissimilarity of the system utility from the reference Hamiltonian. The set {Ox(i), O(i)} represents the opinion state of the community straightaway after the first stage, and is presented hereto with respective histogram. We observed that histograms of Ox(i) approximate to q-Gaussian distributions for moderate F/T ratio, and approaches to power law distributions for low F/T ratio. The histograms of the inner agreement O(i) do not fit well to a given distribution, and therefore, the social comportment which we identify hereto with this set, is not a stationary quantity under this approach. Next, the opinion quantities Ox(i) will pursue an update course as result of the persuasion process and social influence. We performed the calculation based on Deffuant and Heglesman models by using Ox(αi)F,J,T as initial opinion values. We observed that the final opinion fragmentation resulted lower than when using standard assumptions of those models and also, the time to consensus was shorter. Next, for the special case where there are only two output final opinion values, the lower one needs more iteration time steps to converge. In our approach, usually the lowest level opinion converge slower than higher ones. Finally, we have implemented a modified preferential attachment model to realize a network of the linked nodes based on the opinions Ox inherited from the early stage. We acknowledged the power law distribution of the grades of nodes, but in our case there are no disturbances in the queue of the histogram, which are common in the standard simulation for such networking process. As conclusion, having regard to every aspect and specifics, we believe that the proposed model would help on the understanding of the complexity of social conduct.