A Hierarchical Approach to Judgment Aggregation with Abstentions

Lecture Notes in Computer Science, 2014

Similar to Arrow's impossibility theorem for preference aggregation, judgment aggregation has also an intrinsic impossibility for generating consistent group judgment from individual judgments. Removing some of the pre-assumed conditions would mitigate the problem but may still lead to too restrictive solutions. It was proved that if completeness is removed but other plausible conditions are kept, the only possible aggregation functions are oligarchic, which means that the group judgment is purely determined by a certain subset of participating judges. Instead of further challenging the other conditions, this paper investigates how the judgment from each individual judge affects the group judgment in an oligarchic environment. We explore a set of intuitively demanded conditions under abstentions and design a feasible judgment aggregation rule based on the agents' hierarchy. We show this proposed aggregation rule satisfies the desirable conditions. More importantly, this rule is oligarchic with respect to a subset of agenda instead of the whole agenda due to its literal-based characteristics.

Lecture Notes in Computer Science, 2013

This paper presents a quasi-lexicographic judgment aggregation rule based on the hierarchy of judges. We do not assume completeness at both individual and collective levels, which means that a judge can abstain from a proposition and the collective judgment on a proposition can be undetermined. We prove that the proposed rule is (weakly) oligarchic. This is by no means a negative result. In fact, our result demonstrates that with abstentions, oligarchic aggregation is not necessarily a single level determination but can be a multiple-level democracy, which partially explains its pervasiveness in the real world.

Social Choice and Welfare, 2012

In the theory of judgment aggregation, it is known for which agendas of propositions it is possible to aggregate individual judgments into collective ones in accordance with the Arrow-inspired requirements of universal domain, collective rationality, unanimity preservation, non-dictatorship and propositionwise independence. But it is only partially known (e.g., only in the monotonic case) for which agendas it is possible to respect additional requirements, notably non-oligarchy, anonymity, no individual veto power, or extended unanimity preservation. We fully characterize the agendas for which there are such possibilities, thereby answering the most salient open questions about propositionwise judgment aggregation. Our results build on earlier results by Nehring and Puppe (Strategy-proof social choice on single-peaked domains: possibility, impossibility and the space between, 2002), Nehring

Journal of Artificial Intelligence Research, 2012

We analyse the computational complexity of three problems in judgment aggregation: (1) computing a collective judgment from a profile of individual judgments (the winner determination problem); (2) deciding whether a given agent can influence the outcome of a judgment aggregation procedure in her favour by reporting insincere judgments (the strategic manipulation problem); and (3) deciding whether a given judgment aggregation scenario is guaranteed to result in a logically consistent outcome, independently from what the judgments supplied by the individuals are (the problem of the safety of the agenda). We provide results both for specific aggregation procedures (the quota rules, the premise-based procedure, and a distance-based procedure) and for classes of aggregation procedures characterised in terms of fundamental axioms.

The aim of judgment aggregation is to make collective decisions based on the judgments of individual agents. Some rationality conditions governing the expected behavior of the aggregation function must be considered. However, impossibility theorems show that designing an aggregation function satisfying all desirable properties is not feasible. While some rationality conditions are very natural ones, other ones are more disputable. We show that this is the case of the systematicity condition that prevents from electing issues with more votes than others. We rather promote a neutrality and a swap optimality condition. Swap optimality ensures that among two possible results, the one with the best support (number of votes) is chosen. We propose a new family of judgment aggregation methods based on the support (number of votes) that receives each issue.

Social Choice and Welfare, 2008

Several recent results on the aggregation of judgments over logically connected propositions show that, under certain conditions, dictatorships are the only propositionwise aggregation functions generating fully rational (i.e., complete and consistent) collective judgments. A frequently mentioned route to avoid dictatorships is to allow incomplete collective judgments. We show that this route does not lead very far: we obtain oligarchies rather than dictatorships if instead of full rationality we merely require that collective judgments be deductively closed, arguably a minimal condition of rationality, compatible even with empty judgment sets. We derive several characterizations of oligarchies and provide illustrative applications to Arrowian preference aggregation and Kasher and Rubinstein's group identi…cation problem.

Lecture Notes in Computer Science, 2015

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.

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.