CHAPTER 19 Judgment Aggregation

Abstract

The chapter surveys the recent and fast‐growing literature on the aggregation of logically interrelated propositions, following List and Pettit's formalization of the “doctrinal paradox”. The classical preference aggregation problem is a special case in which propositions take the form of binary preference judgments (“alternative x is better than alternative y”). The first part of the chapter focuses on aggregation methods that satisfy an Arrowian independence condition (“propositionwise aggregation”). In the independent case, the literature has produced a number of general characterization results that precisely demarcate the circumstances in which satisfactory aggregation is possible from those in which it is not Arrow's impossibility theorem and Gibbards oligarchy theorem are special cases of these results. The independence condition is, however, not uncontroversial and the second part of the chapter considers various relaxations of it. Judgment aggregation is still a very active field and the chapter concludes with an outlook on what we believe are important topics for future research.

Advances in Knowledge Representation, Logic Programming, and Abstract Argumentation

“…Before describing some concrete families of such methods in the next sections, we take a look at a few desirable postulates for aggregation methods. These are inspired by and appropriately modified from postulates studied in the AF case in [3] (which, in turn, have been mostly inspired by postulates from the judgment aggregation literature [11,12]). Free variables in these postulates, e.g., D, v in the first three postulates below, are implicitly universally quantified.…”

“…The question is, can we aggregate these opinions into a single group interpretation that represents the opinion of the group as a whole? In the AF setting, this question (which can be thought of as a special case of the problem of judgment aggregation [11,12]) has been investigated in [3]. There, a general family of methods for aggregating complete AF labellings called interval methods was defined and studied.…”

Judgement Aggregation and Distributed Thinking

“…This impossibility result has kicked off the research into questions of judgement aggregation and has led to a flourishing, often technically advanced literature (see List and Puppe, 2009, for a survey). The theorem is important because it systematizes the special case of the discursive dilemma and shows that any form of judgement aggregation over a sufficiently complex agenda fails to meet all the described desiderata together.…”

A Complete Conclusion-Based Procedure for Judgment Aggregation

“…Furthermore, the problem of aggregating individual judgments is not restricted to majority voting, but it applies to all aggregation procedures satisfying some seemingly desirable conditions. For an overview, the reader is referred to [13].…”