Complexity Results for Aggregating Judgments using Scoring or Distance-Based Procedures

Judgment aggregation is an abstract framework for studying collective decision making by aggregating individual opinions on logically related issues. Important types of judgment aggregation methods are those of scoring and distance-based methods, many of which can be seen as generalizations of voting rules. An important question to investigate for judgment aggregation methods is how hard it is to find a collective decision by applying these methods. In this article we study the complexity of this "winner determination" problem for some scoring and distance-based judgment aggregation procedures. Such procedures aggregate judgments by assigning values to judgment sets. Our work fills in some of the last gaps in the complexity landscape for winner determination in judgment aggregation. Our results reaffirm that aggregating judgments is computationally hard and strongly point towards the necessity of analyzing approximation methods or parameterized algorithms in judgment aggregation.