Judgment Aggregation : A Primer

Judgment aggregation is a mathematical theory of collective decision-making. It concerns the methods whereby individual opinions about logically interconnected issues of interest can, or cannot, be aggregated into one collective stance. Aggregation problems have traditionally been of interest for disciplines like economics and the political sciences, as well as philosophy, where judgment aggregation itself originates from, but have recently captured the attention of disciplines like computer science, artificial intelligence and multi-agent systems. Judgment aggregation has emerged in the last decade as a unifying paradigm for the formalization and understanding of aggregation problems. Still, no comprehensive presentation of the theory is available to date. This Synthesis Lecture aims at filling this gap presenting the key motivations, results, abstractions and techniques underpinning it. Table of Contents: Preface / Acknowledgments / Logic Meets Social Choice Theory / Basic Concepts / Impossibility / Coping with Impossibility / Manipulability / Aggregation Rules / Deliberation / Bibliography / Authors' Biographies / Index Cover Copyright Page Title Page Contents Preface Acknowledgments Logic Meets Social Choice Theory A Concise History of Social Choice Theory The Early History Modern Social Choice Theory A New Type of Aggregation From the Doctrinal Paradox to the Discursive Dilemma Preference Aggregation and Judgment Aggregation Further Topics Basic Concepts Preliminaries Agendas in Propositional Logic Judgment Sets and Profiles Aggregation Functions Examples: Aggregation Rules Agenda Conditions How Interconnected is an Agenda? Comparing Agenda Conditions Aggregation Conditions How Should an Aggregation Function Behave? On the `Meaning' of the Aggregation Conditions Further Topics Abstract Aggregation General Logics Impossibility What is the Majority Rule Like? Properties of Propositionwise Majority Characterizing Propositionwise Majority An Impossibility Theorem Winning Coalitions Winning Coalitions as Ultrafilters Dictators The Theorem (Ultra)filters, Dictators and Oligarchs Impossibility of Non-Oligarchic Aggregation Proof: from Ultrafilters to Filters Impossibility via (Ultra)filters Further Topics Other Impossibility Results Infinite Agendas and Infinite Voters Judgment Aggregation vs. Preference Aggregation Coping with Impossibility Relaxing Universal Domain Unidimensional Alignment Value-Restriction Relaxing the Output Conditions Abstention Quota Rules Relaxing Independence The Premise-Based Approach The Sequential Priority Approach The Distance-Based Rules Further Topics More Domain Restrictions Dropping Consistency Other Distance-Based Rules Judgment Aggregation and Abstract Argumentation Manipulability Types of Manipulation Agenda Manipulation Vote Manipulation Manipulability: Definition and Characterization Sincere and Insincere Manipulation Non-Manipulable Aggregation: Impossibility Auxiliary Results The Impossibility Theorem Further Topics: Manipulation Beyond Impossibility Results The Possibility of Non-Manipulable Aggregation Strategy-Proof Judgment Aggregation Complexity as a Safeguard Against Manipulation Aggregation Rules Introduction Rules Based on the Majoritarian Judgment Set Rules Based on the Weighted Majoritarian Judgment Set Rules Based on the Removal or Change of Individual Judgments Further Topics Deliberation Deliberation and Opinion Pooling Probabilistic Judgments A Stochastic Model of Deliberation Opinion Pooling and Judgment Aggregation Deliberation as Judgment Transformation Deliberation and Voting Judgment Transformation Functions Examples of Transformation Functions Limits of Judgment Transformation Conditions on Transformation Functions An Impossibility Result Further Topics and Open Issues Bibliography Authors' Biographies Index