Ranking of Arguments Using Social Ranking Choice

In argumentation theory, semantics defined by Dung evaluate subsets of arguments by classifying each into two categories: accepted or rejected. This makes some applications (like online debate) more complex since many accepted arguments can be returned without any insight into the strength of each argument. Conversely to extension-based semantics, ranking-based semantics allow us to determine the strength of acceptability of each argument. However, this approach does not evaluate sets of arguments but each argument individually. In this paper, our goal is to classify the arguments more precisely than just accepting or rejecting them and, therefore, to find a total pre-order of arguments. For this purpose, we will present a method to, first, rank subsets of arguments using extension-based semantics and, then, apply power indices of social choice to this ranking to find a pre-order of arguments. Our approach has the advantage of combining extension-based semantics and lexicographic social ranking. Indeed, given two arguments, it allows us to state which one is more plausible than the other and if they are jointly acceptable or not.