Measuring the Impact of Arguments on Admissibility in Abstract Argumentation

This paper develops a measure of the influence of individual arguments in abstract argumentation frameworks. By applying ideas from power indices in coalitional game theory, the proposed measure-called admissibility impact value-quantifies the impact that individual arguments have on the set of admissible extensions of a given argumentation framework. It improves on existing impact measures in that it is more fine-grained and sensitive to small differences in the attack relations of argumentation frameworks. Special consideration is given to well-founded frameworks, where the improvements are particularly pronounced.