Essays on judgment aggregation and argumentation

Résumé

This dissertation reports some new results on two emerging fields, judgment aggregation and abstract argumentation, within the aggregation literature. Judgment aggregation concerns the way of translating a group of people's opinions for a set of logically interconnected propositions into a consistent collective opinion. In a standard non-sequential framework, many impossibility theorems arise. I start from the fact that many real-life processes of arriving at consistent set of judgments are sequential, and crisp binary judgment sometimes fails to accommodate rich information of evaluation. In view of this, the foremost problem is how to determine the decision path, and what are desirable axioms and properties a reasonable method should satisfy in the sequential non-binary framework. I introduce three properties of determining the decision path, and explore the relationships among them. I also design three decision paths that constitute a general framework for well-known premise-based procedure and conclusion-based procedure in judgment aggregation, and show some of their properties. In abstract argumentation, where arguments are viewed as abstract entities with a binary defeat relation among them, a set of agents may assign individual members the right to determine the collective defeat relation on some pairs of arguments. I prove that even under a minimal condition of rationality, the assignment of rights to two or more agents is inconsistent with the unanimity principle, whereby unanimously accepted defeat or defend relation among arguments are collectively accepted. This result expands the domain of liberal impossibility beyond preference aggregation and judgment aggregation, and highlights this impossibility as an inherent tension between individual rights and collective consensus.