The facilitation and analytical support of argumentation-based collaborative decision making is the focus of this research. We model collaborative decision making as an argumentation process. We develop a connectionist modeling framework, a network representation formalism for argument structures, connectionist network mechanisms, and their models of computations to extract the behavior of argument structures. We use two examples from the case study literature to illustrate the concepts. Several interesting properties of the connectionist network models are observed from our computational results. We find that although the length of the computation is affected by parametric values, the final activation levels of the units are largely unaffected. We observe that the initial activation levels of the defeasible units seem to have no effect on their final activation levels. The proposed modeling approach generates valuable insights into the characteristics of specific argumentative discussions. While the intention of this work is not to introduce the connectionist paradigm as a means to bring arguments to a closure (resolution), we show that certain resolution mechanisms can be easily implemented under the connectionist framework.