Michael Andreas Müller

Pro/Con-lists are one of the most common ways of summarising the main points of debates surrounding practical decisions. However, their simplicity has attracted criticism and argument graphs have been proposed as an alternative. Since graphs can easily become very complex, they tend to be difficult to use in everyday life. Our proposal, the Concern-Oriented REasoning (CORE) table, lies in-between the two. It improves on the drawbacks of pro/con-lists without having to go to graph-level complexity. We start by identifying and organising the main reasons for and against an action into a pro/con-list. We then add structure to the CORE-table by organising the main reasons according to their subject matter. Additional arguments surrounding the main reasons are then placed in designated spots based on their function.

We consider scenarios where a group of agents wish to simplify a given abstract argumentation framework—specifying a set of arguments and the attacks between them—by eliminating cycles in the attack-relation on the basis of their preferences over arguments. They do so by first aggregating their individual preferences into a collective preference order and then removing any attacks involved in a cycle that go against that order. Our analysis integrates insights from formal argumentation and social choice theory. We obtain sweeping impossibility results for essentially all standard methods of preference aggregation, showing that no Condorcet method and no positional scoring rule can uphold the fundamental principle expressing that views held by every single member of the group must be respected. But we also find that so-called representative-agent rules do offer this guarantee.

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.

We develop a novel argument scheme tailored to debates surrounding public votes on a state action. It can be used to propose reasons for voting “yes” or “no” and allows for natural reconstructions of such debates. These reconstructions are of particular use to voters trying to weigh the pros and cons of the proposed state action. The scheme for proposing reasons helps answering two questions: What changes will the proposed state action bring with it? And are these changes good or not? Using the scheme, we derive a three-layered structure of public debates surrounding votes that aides in constructing systematic and comprehensive overviews. The scheme for proposing reasons also lends itself to concise summaries for voter information and can be incorporated into more general deliberation dialogues.