Aggregating Alternative Extensions of Abstract Argumentation Frameworks: Preservation Results for Quota Rules

When confronted with the same abstract argumentation framework, specifying a set of arguments and an attack-relation between them, different agents may disagree on which arguments to accept, i.e., they may choose different extensions. In the context of designing systems to support collective argumentation, we may then wish to aggregate such alternative extensions into a single extension that appropriately reflects the views of the group as a whole. Focusing on a conceptually and computationally simple family of aggregation rules, the quota rules, we analyse under what circumstances relevant properties of extensions shared by all extensions reported by the individual agents will be preserved under aggregation. The properties we consider are the classical properties of argumentation semantics, such as being a conflict-free, a complete, or a preferred extension. We show that, while for some properties there are quota rules that guarantee their preservation, for the more demanding properties it is impossible to do so in general.