Guaranteeing Admissibility of Abstract Argumentation Frameworks with Rationality and Feasibility Constraints

Abstract

Abstract This paper considers the problem of under what circumstances an aggregation rule guarantees admissible sets of arguments that represent a good compromise between several extensions, i.e., sets of arguments of abstract argumentation frameworks each provided by a different individual. We start by showing that the preservation results of Dung’s admissibility, graded admissibility and strong admissibility during the aggregation of extensions are negative. To overcome such negative results, we define a model for extension aggregation that clearly separates the constraint supposed to be satisfied by individuals and the constraint that must be met by the collective decision. Using this model, we show that the majority rule guarantees admissible sets on profiles that satisfy a variant of Dung’s admissibility, as well as profiles of extensions with some specific characteristics.