Interval Methods for Judgment Aggregation in Argumentation

ABSTRACT. Given a set of conflicting arguments, there can exist multiple plausible opinions about which arguments should be accepted, rejected, or deemed undecided. Recent work explored some operators for deciding how multiple such judgments should be aggregated. Here, we generalize this line of study by introducing a family of operators called *interval aggregation methods*, and show that they contain existing operators as instances. While these methods fail to output a complete labelling in general, we show that it is possible to *transform* a given aggregation method into one that *does* always yield collectively rational labellings. This employs the *down-admissible* and *up-complete* constructions of Caminada and Pigozzi. For interval methods, collective rationality is attained at the expense of a strong *Independence* postulate, but we show that an interesting weakening of the Independence postulate is retained by this transformation. Our results open up many new directions in the study of generalized judgment aggregation in argumentation