Judgment Aggregation in Multi-Agent Argumentation

TL;DR

This paper investigates how to aggregate conflicting arguments in multi-agent systems, revealing fundamental limitations and conditions for achieving collectively rational judgments using various voting methods.

Contribution

It adapts social-choice properties to argumentation, characterizes conditions for rational aggregation, and identifies graph restrictions that enable rational collective judgments.

Findings

Argument-wise plurality voting often fails to ensure rational outcomes.

Impossibility results show no perfect aggregation operator exists in general.

Graph-theoretic restrictions can enable rational aggregation with plurality rule.

Abstract

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.