A Complete Conclusion-Based Procedure for Judgment Aggregation

Many voting rules are based on minimization or maximization principle. Likewise, in the field of logic-based knowledge representation and reasoning, many belief change or inconsistency handling operators make use of minimization. Surprisingly, minimization has not played a major role in the field of judgment aggregation, in spite of its proximity to voting theory and logic-based knowledge representation and reasoning. Here we make a first step in the study of judgment aggregation rules based on minimization, and propose a classification of judgment aggregation rules based on some minimization or maximization principle. We distinguish four families. The rules of the first family compute the collective judgment for each issue, using proposition-wise majoritarian aggregation, and then restore consistency using some minimal change principle. The rules of the second family proceed in a similar way but take into account the strength of the majority on each issue. Those of the third family consist in restoring the consistency of the majoritarian judgment by removing or changing some individual judgments in a minimal way. Finally, those of the fourth family are based on some predefined distance between judgment sets, and look for a consistent collective judgment minimizing the overall distance to the individual judgment sets. For each family we propose a few typical rules. While most of these rules are new, a few ones correspond to rules * A preliminary version of this paper appeared in the

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“…Proof: See again the counterexample that can be found in [30], which we presented in the proof of Proposition 16.…”

Section: Resultsmentioning

confidence: 86%

Judgment aggregation rules based on minimization

Lang

Pigozzi

Slavkovik

et al. 2011

Proceedings of the 13th Conference on Theoretical Aspects of Rationality and Knowledge

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“…Tie-breaking problems in judgment aggregation are the focus of our ongoing research. The CCBP from [20] also satisfies anonimity. Whether this is a desirable property for a group of artificial agents depends entirely on whether the group is democratic or the opinions of some agents are more important.…”

Section: Judgment Aggregation For Bdi Agentsmentioning

confidence: 99%

“…However, the conclusion-based aggregation can be supplemented with an additional procedure that completes the produced set of judgments when necessary. Such aggregation procedure is the complete conclusion-based procedure (CCBP) developed in [20]. This CCBP satisfies universal domain and is collectively rational.…”

Section: Judgment Aggregation For Bdi Agentsmentioning

confidence: 99%

Group Intention Is Social Choice with Commitment

Boella

Pigozzi

Slavkovik

et al. 2011

Lecture Notes in Computer Science

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Abstract. A collaborative group is commonly defined as a set of agents, which share information and coordinate activities while working towards a common goal. How do groups decide which are their common goals and what to intend? According to the much cited theory of Cohen and Levesque, an agent intends g if it has chosen to pursue goal g and it has committed itself to making g happen. Following the same line of reasoning, a group intention should be a collectively chosen goal with commitment. The literature often considers a collective goal to be one of those individual goals that are shared by all members. This approach presumes that a group goal is also an individual one and that the agents can act as a group if they share the beliefs relevant to this goal. This is not necessarily the case. We construct an abstract framework for groups in which common goals are determined by social choice. Our framework uses judgment aggregation to choose a group goal and a multi-modal multi-agent logic to define commitment and revision strategies for the group intentions.

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“…The distance-based direct aggregators satisfy universal domain and non-dictatorship by design, however it is safe to conjecture that they will not satisfy ZPP for the same reason that distance-based classical aggregators do not satisfy unanimity [31] -for an agenda with sufficiently many issues, a judgment set that does not contain the unanimously likely judgment might end up being "closer" to the profile.…”

Section: Properties Of Aggregatorsmentioning

confidence: 99%

Aggregating Probabilistic Judgments

Ivanovska¹,

Slavkovik²

2019

Electron. Proc. Theor. Comput. Sci.

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In this paper we explore the application of methods for classical judgment aggregation in pooling probabilistic opinions on logically related issues. For this reason, we first modify the Boolean judgment aggregation framework in the way that allows handling probabilistic judgments and then define probabilistic aggregation functions obtained by generalization of the classical ones. In addition, we discuss essential desirable properties for the aggregation functions and explore impossibility results.

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A Complete Conclusion-Based Procedure for Judgment Aggregation

Cited by 12 publications

References 15 publications

Judgment aggregation rules based on minimization

Judgment aggregation rules based on minimization

Group Intention Is Social Choice with Commitment

Aggregating Probabilistic Judgments

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