SYSU Lectures on the Theory of Aggregation, April 2014

This series of lectures will provide an introduction to the theory of aggregation, ranging from classical results in social choice theory to some recent work conducted in Amsterdam. No specific technical background will be required to follow these lectures. Slides and papers covering material closely related to each lecture are linked below.

Lecture 1: Preference and Judgment Aggregation. This opening lecture will be an introduction to social choice theory, and more specifically to the frameworks of preference aggregation and judgment aggregation (a.k.a. logical aggregation). Topics to be covered will include basic aggregation rules, the Condorcet paradox, the discursive dilemma, May's Theorem, Arrow's Theorem, and the List-Pettit Theorem.

Lecture 2: Binary Aggregation with Integrity Constraints. Binary aggregation deals with situations where several individuals each make a yes/no choice regarding a number of issues and these choices then need to be aggregated into a collective choice. Depending on the application at hand, different combinations of yes/no may be considered rational. We can use an integrity constraint, modelled in terms of a formula of propositional logic, to define the set of those rational choices. We will see how to embed other aggregation frameworks into this framework and then focus on the interplay of the propositional language used to express integrity constraints and the axiomatic properties of the aggregation rules that can be guaranteed to respect those constraints.

Lecture 3: Graph Aggregation. Graph aggregation is the problem of computing a single collective graph that best represents the information inherent in a profile of several individual graphs over a common set of vertices. This may be considered a generalisation of classical preference aggregation, given that preferences, as typically understood in social choice theory, are directed graphs that are transitive and complete. In this lecture, we will use this more general perspective to arrive at a proof of a generalisation of Arrow's Theorem.

Lecture 4: Collective Annotation. The principles of aggregation theory can be applied to improve the utility of crowdsourcing tools. Crowdsourcing, which is used in fields such as computer vision and computational linguistics, allows us to efficiently label large amounts of data using nonexpert annotators. The individual annotations collected then need to be aggregated into a single collective annotation that can serve as a new gold standard. In this lecture, I will introduce the framework of collective annotation, formulate several concrete aggregation rules in this framework, and discuss their performance on data collected in three crowdsourcing exercises in the domain of computational linguistics.