Compact Course: Judgment Aggregation: An Introductory Afternoon (29 May 2017)
by Christian List (LSE)
Idea & Motivation
The aim of this compact course is to introduce the theory of judgment aggregation. Judgment-aggregation theory addresses the question of how the judgments of several individuals (experts, committee members, voters, but also theories or criteria) can be aggregated into overall collective judgments. The interest in this question was originally prompted by the observation that majority voting does not always secure consistent collective judgments, which raises the question of whether other aggregation rules perform better.
In this course, I will begin by explaining the paradoxes that first motivated the field. I will then introduce the formal model of judgment aggregation, which combines ideas from social choice theory with ideas from logic. Using this model, I will explain some of the central impossibility results that have been proved in the area, most notably the judgment-aggregation variant of Arrow's famous impossibility theorem. I will relate these to classic results in social choice theory, and explore possible escape routes from them. This provides us with a taxonomy of the logical space of possible judgment-aggregation rules.
If time permits, I will relate the problem of judgment aggregation to some related problems, such as probability aggregation (i.e., how can the subjective probabilities that different experts assign to some events be aggregated into coherent collective probability assignments to these events?). I will also comment on a number of possible applications of judgment aggregation theory. Illustrative areas of application include: (i) the problem of peer disagreement, (ii) the super-valuation theory of vagueness, and (iii) the relationship between quantitative and qualitative beliefs.
Stephan Hartmann (LMU Munich/MCMP)