Collective argumentation with topological restrictions: the case of aggregating abstract argumentation frameworks

Collective argumentation is the process of reaching a collective decision that is acceptable to the group in a debate. We introduce the notion of topological restriction to enrich the study of collective argumentation. Topological restrictions are rational constraints assumed to be satisfied by individual agents. We assume that in a debate, for every pair of arguments under consideration, every agent indicates whether the first argument attacks the second, i.e. an agent's argumentative stance is characterized as an argumentation framework, and only argumentation frameworks that satisfy topological restrictions are allowed. The topological restrictions we consider in this paper include various topological properties in the literature, such as acyclicity, symmetry, coherence and determinedness, as well as three topological restrictions that generalize classic social-choice-theoretic domain conditions. We show that when the profile of the argumentation frameworks provided by the agents satisfies topological restrictions, impossibility results during aggregation can be avoided. Furthermore, if a profile is topologically restricted with respect to restrictions that generalize domain conditions, then the majority rule preserves several desirable properties during aggregation.