Aggregation of Attack Relations: A Social-Choice Theoretical Analysis of Defeasibility Criteria
This paper analyzes the aggregation of different abstract attack relations over a common set of arguments. Each of those attack relations can be considered as the representation of a criterion of warrant. It is well known in the field of Social Choice Theory that if some “fairness” conditions are imposed over an aggregation of preferences, it becomes impossible to yield a result. When the criteria lead to acyclic attack relations, a positive result may ensue under the same conditions, namely that if the class of winning coalitions in an aggregation process by voting is a proper prefilter an outcome will exist. This outcome may preserve some features of the competing attack relations, such as the highly desirable property of acyclicity which can be associated with the existence of a single extension of an argumentation system. The downside of this is that, in fact, the resulting attack relation must be a portion common to the “hidden dictators” in the system, that is, all the attack relations that belong to all the winning coalitions.
KeywordsMajority Vote Aggregation Function Winning Coalition Weak Order Argumentation Framework
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