Judgment 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 judgments 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, and struggles with ties.
We then present more general results, proving multiple impossibility results on
the existence of any good aggregation operator. After characterising 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
listing graph-theoretic restrictions under which argument-wise plurality rule
does produce collectively rational outcomes. In addition to identifying
fundamental barriers to collective argument evaluation, our results open up the
door for a new research agenda for the argumentation and computational social
choice communities.
