Given a set of conflicting arguments, there can exist multiple plausibleopinions about which arguments should be accepted, rejected, or deemedundecided. We study the problem of how multiple such judgments can beaggregated. We define the problem by adapting various classicalsocial-choice-theoretic properties for the argumentation domain. We show thatwhile argument-wise plurality voting satisfies many properties, it fails toguarantee the collective rationality of the outcome, and struggles with ties.We then present more general results, proving multiple impossibility results onthe existence of any good aggregation operator. After characterising thesufficient and necessary conditions for satisfying collective rationality, westudy whether restricting the domain of argument-wise plurality voting toclassical semantics allows us to escape the impossibility result. We close bylisting graph-theoretic restrictions under which argument-wise plurality ruledoes produce collectively rational outcomes. In addition to identifyingfundamental barriers to collective argument evaluation, our results open up thedoor for a new research agenda for the argumentation and computational socialchoice communities.
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