Combining Voting and Abstract Argumentation to Understand Online Discussions

TL;DR

This work addresses how to interpret and summarize online discussions by modeling them as Approval-Based Social Argumentation Frameworks (ABSAFs), which couple abstract argumentation with voter approvals. The authors propose a formal representation of discussions, define representational objectives via 1-representation and core-representation, and develop a range of decision rules based on Ordered Weighted Averaging (OWA) as well as greedy variants to select a small, representative set of defendable viewpoints from the preferred extensions. They prove complexity bounds (e.g., $1$-Representability is $\mathsf{NP}$-complete; $1$-Core-Representability is $\Theta_{2}\mathsf{P}$-complete) and analyze justification properties (JR/SJR), showing that MaxCov satisfies JR while many OWA-based rules do not. Through experiments on synthetic ABSAFs, the study demonstrates that Utilitarian and Harmonic rules offer strong practical performance with good scalability when paired with greedy implementations, and it identifies MaxCov as favorable when justified representation is crucial. Overall, the framework provides a principled, explainable approach to extracting coherent, representative viewpoints from online deliberations and offers concrete guidance on method selection based on application goals.

Abstract

Online discussion platforms are a vital part of the public discourse in a deliberative democracy. However, how to interpret the outcomes of the discussions on these platforms is often unclear. In this paper, we propose a novel and explainable method for selecting a set of most representative, consistent points of view by combining methods from computational social choice and abstract argumentation. Specifically, we model online discussions as abstract argumentation frameworks combined with information regarding which arguments voters approve of. Based on ideas from approval-based multiwinner voting, we introduce several voting rules for selecting a set of preferred extensions that represents voters' points of view. We compare the proposed methods across several dimensions, theoretically and in numerical simulations, and give clear suggestions on which methods to use depending on the specific situation.

Figures (14)

• Figure 1: AF for the Canadian election reform discussion.
• Figure 2: Approval ballots (Canadian election reform data).
• Figure 3: Voter 2 approves undefendable arguments.
• Figure 4: Construction used in the proof of Theorem \ref{['thm:core-representability-completeness']}.
• Figure 5: Counterexample SJR.

Theorems & Definitions (39)

• Definition 1
• Definition 2
• Example 1
• Definition 3
• Definition 4
• Example 2
• Definition 5
• Example 3: Example \ref{['example:absaf']} continued
• Definition 6
• Proposition 0