Reliable Methods of Judgment Aggregation

Journal of Logic and …, 2010

Lecture Notes in Computer Science, 2010

Judgment aggregation is a recent formal discipline that studies how to aggregate individual judgments on logically connected propositions to form collective decisions on the same propositions. Despite the apparent simplicity of the problem, the aggregation of individual judgments can result in an inconsistent outcome. This seriously troubles this research field. Expert panels, legal courts, boards, and councils are only some examples of group decision situations that confront themselves with such aggregation problems. So far, the existing framework and procedures considered in the literature are idealized. Our goal is to enrich standard judgment aggregation by allowing the individuals to agree or disagree on the decision rule. Moreover, the group members have the possibility to abstain or express neutral judgments. This provides a more realistic framework and, at the same time, consents the definition of an aggregation procedure that escapes the inconsistent group outcome.

2009

Abstract The aggregation of consistent individual judgments on logically interconnected propositions into a collective judgment on those propositions has recently drawn much attention. Seemingly reasonable aggregation procedures, such as propositionwise majority voting, cannot ensure an equally consistent collective conclusion. In this paper, we motivate that quite often, we do not only want to make a factually right decision, but also to correctly evaluate the reasons for that decision.

Algorithmic Decision Theory, 2009

Judgment aggregation is a formal theory reasoning about how a group of agents can aggregate individual judgments on connected propositions into a collective judgment on the same propositions. Three procedures for successfully aggregating judgments sets are: premise-based procedure, conclusion-based procedure and distance-based merging. The conclusion-based procedure has been little investigated because it provides a way to aggregate the conclusions, but not the premises, thus it outputs an incomplete judgment set. The goal of this paper is to present a conclusion-based procedure outputting complete judgment sets.

Journal of Logic and Computation, 2009

The theory of belief revision and merging has recently been applied to judgement aggregation. In this article I argue that judgements are best aggregated by merging the evidence on which they are based, rather than by directly merging the judgements themselves. This leads to a three-step strategy for judgement aggregation. First, merge the evidence bases of the various agents using some method of belief merging. Second, determine which degrees of belief one should adopt on the basis of this merged evidence base, by applying objective Bayesian theory. Third, determine which judgements are appropriate given these degrees of belief by applying a decision-theoretic account of rational judgement formation.

Games and Economic Behavior, 2014

We analyse the problem of aggregating judgments over multiple issues from the perspective of efficient aggregation of voters' private information. While new in judgment aggregation theory, this perspective is familiar in a different body of literature about voting between two alternatives when voters' disagreements stem (fully or partly) from conflicts of information rather than interests. Combining the two literatures, we consider a simple judgment aggregation problem and model the private information underlying voters' judgments. We analyse the resulting strategic incentives and determine which voting rules lead to collective judgments that efficiently use all private information, assuming that voters share a preference for true collective judgments. We find that in certain, but not all cases a quota rule should be used, which decides on each issue according to whether the proportion of 'yes' votes exceeds a particular quota.

Cooperative Approaches, 2011

Computational Intelligence, 2017

Judgment aggregation deals with the problem of how collective judgments on logically connected propositions can be formed based on individual judgments on the same propositions. The existing literature on judgment aggregation mainly focuses on the anonymity condition requiring that individual judgments be treated equally. However, in many real-world situations, a group making collective judgments may assign individual members or subgroups different priorities to determine the collective judgment. Based on this consideration, this paper relaxes the anonymity condition by giving a hierarchy over individuals so as to investigate how the judgment from each individual affects the group judgment in such a hierarchical environment. Moreover, we assume that an individual can abstain from voting on a proposition and the collective judgment on a proposition can be undetermined, which means that we do not require completeness at both individual and collective levels. In this new setting, we first identify an impossibility result and explore a set of plausible conditions in terms of abstentions. Secondly, we develop an aggregation rule based on the hierarchy of individuals and show that the aggregation rule satisfies those plausible conditions. The computational complexity of this rule is also investigated. Finally, we show that the proposed rule is (weakly) oligarchic over a subset of agenda. This is by no means a negative result. In fact, our result reveals that with abstentions, oligarchic aggregation is not necessary to be a single-level determination but can be a multiple-level collective decision-making, which partially explains its ubiquity in the real world.

SYNTHESE-DORDRECHT-, 2006

… of the 9th International Conference on …, 2010

A conflicting knowledge base can be seen abstractly as a set of arguments and a binary relation characterising conflict among them. There may be multiple plausible ways to evaluate conflicting arguments. In this paper, we ask: given a set of agents, each with a legitimate subjective evaluation of a set of arguments, how can they reach a collective evaluation of those arguments? After formally defining this problem, we extensively analyse an argument-wise plurality voting rule, showing that it suffers a fundamental limitation. ...