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. (shrink)

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. (shrink)

An important appeal of strategy-proofness is the robustness that it implies. Under a strategy-proof voting rule, every individual has an optimal strategy independently of the behavior of all other voters, namely truth-telling. In particular, optimal play is robust with respect to the beliefs voters may have about the type and the behavior of the other voters. Following Blin and Satterthwaite (Economet J Economet Soc 45(4):881–888, 1977), we call this logically weaker property “belief-independence.” In this paper, we give a number of (...) examples of voting rules that are belief-independent but not strategy-proof. However, we also show that belief-independence implies strategy-proofness under a few natural additional conditions. The notion of belief-independence naturally leads to a the strengthening of strategy-proofness to “robust” strategy-proofness which requires that no voter whose true preference may come from a restricted domain can benefit by submitting any unrestricted preference ordering given any unrestricted preference profile for all other voters. There are examples of strategy-proof voting rules (on a restricted domain) that are not robustly strategy-proof, but under natural additional conditions the two properties are shown to be equivalent. (shrink)

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. (shrink)