Opinion evolution analysis for short-range and long-range Deffuant-Weisbuch models

In this paper, we propose and then analyze two generalized Deffuant-Weisbuch (DW) models. The generalized models extend the conventional DW model by taking multiple choices in two different ways. First, we demonstrate the almost sure convergence of the agent opinions for the short-range multi-choice DW dynamics when only the opinions within confidence regions may be count in. Then we analyze dynamical behavior about the long-range multi-choice DW model when some opinions out of the confidence ranges are considered with a weighted combination. Moreover, both theoretical and simulation results show that the dynamical behaviors of the two models are totally different.