Mini Course on the Theory of Aggregation at LIP6, March 2016

This mini course will provide an introduction to the theory of aggregation, ranging from the presentation of classical results in social choice theory to the discussion of some recent research conducted in Amsterdam. The first lecture will focus on the use of the axiomatic method in preference aggregation and then discuss a generalisation to obtain a framework for graph aggregation, which has additional applications in a variety of fields, including clustering and abstract argumentation. The second lecture will focus on judgment aggregation and then discuss applications to the collective annotation of crowdsourced data. 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 Graph Aggregation. This lecture will be an introduction to voting theory and preference aggregation using the axiomatic method. We will cover a number of basic aggregation rules, the Condorcet paradox, May's Theorem, and Arrow's Theorem. In the second part of the lecture we will discuss recent work on generalising the framework of preference aggregation to graph aggregation, which besides modelling elections also has applications in fields such a clustering and abstract argumentation.

Lecture 2: Judgment Aggregation and Collective Annotation. Judgment aggregation deals with situations where several individuals each make a yes/no choice regarding a number of propositions and these choices then need to be aggregated into a collective choice. Applications range from legal theory to multiagent systems and crowdsourcing. In this lecture we will review a formal framework for judgment aggregation, the doctrinal paradox, a basic impossibility theorem, and the embedding of preference aggregation into judgment aggregation. In the second part of the lecture we will see how to use aggregation rules to process noisy data collected through crowdsourcing and report on a case study with data from computational linguistics.