Judgement aggregation in multi-agent argumentation

Given a set of conflicting arguments, there can exist multiple plausible opinions about which arguments should be accepted, rejected or deemed undecided. We study the problem of how multiple such judgements can be aggregated. We define the problem by adapting various classical social-choice-theoretic properties for the argumentation domain. We show that while argument-wise plurality voting satisfies many properties, it fails to guarantee the collective rationality of the outcome. We then present more general results, proving multiple impossibility results on the existence of any good aggregation operator. After characterizing the sufficient and necessary conditions for satisfying collective rationality, we study whether restricting the domain of argument-wise plurality voting to classical semantics allows us to escape the impossibility result. We close by mentioning a couple of graph-theoretical restrictions under which the argument-wise plurality rule does produce collectively rational outcomes. In addition to identifying fundamental barriers to collective argument evaluation, our results contribute to research at the intersection of the argumentation and computational social choice fields