Approximately classic judgement aggregation

Ilan Nehama

doi:10.1007/s10472-013-9358-6

Approximately classic judgement aggregation

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Abstract

This paper analyzes judgement aggregation problems in which a group of agents independently votes on a set of complex propositions subject to an interdependency constraint. It considers the issue of judgement aggregation from the perspective of approximation; that is, it generalizes the classic framework of judgement aggregation by relaxing the two main constraints assumed in the literature, Consistency and Independence. In doing so, it also considers mechanisms that only approximately satisfy these constraints, that is, satisfy them up to a small fraction of the inputs. The main question raised is whether the relaxation of these constraints significantly alters the class of aggregation mechanisms that meet the two (relaxed) constraints. The main result of this paper is that in the case of a subclass of a natural class of aggregation problems termed "truth-functional agendas," the set of aggregation mechanisms that meet the constraints does not extend nontrivially when the constraints are relaxed. This paper also shows connections between this new general framework and the works on approximation of preference aggregation as well as the field of Property Testing and particularly linear testing of Boolean functions.

Original language	English
Pages (from-to)	91-134
Number of pages	44
Journal	Annals of Mathematics and Artificial Intelligence
Volume	68
Issue number	1-3
DOIs	https://doi.org/10.1007/s10472-013-9358-6
State	Published - Jul 2013
Externally published	Yes

Bibliographical note

Funding Information:
Previous versions of this work were presented at Bertinoro Workshop on Frontiers in Mechanism Design 2010, Third International Workshop on Computational Social Choice (COMSOC) 2010, Computation and Economics Seminar at the Hebrew University, Computation and Incentives in Social Choice (Dagstuhl Seminar 12101), The Fourth Congress of the Game Theory Society (GAMES) 2012, The Eleventh Meeting of the Society for Social Choice and Welfare (SSCW) 2012, and Workshop on Internet and Network Economics (WINE) 2011 [46]. The author would like to thank the participants in these workshops and two anonymous referees for their comments. Research was supported by a grant from the Israeli Science Foundation (ISF) and by the Google Inter-university Center for Electronic Markets and Auctions.

Keywords

Approximate aggregation
Computational judgement aggregation
Computational social choice
Dependency index
Inconsistency index
Judgement aggregation
Truth-functional agendas

ASJC Scopus subject areas

Artificial Intelligence
Applied Mathematics

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10.1007/s10472-013-9358-6

Cite this

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abstract = "This paper analyzes judgement aggregation problems in which a group of agents independently votes on a set of complex propositions subject to an interdependency constraint. It considers the issue of judgement aggregation from the perspective of approximation; that is, it generalizes the classic framework of judgement aggregation by relaxing the two main constraints assumed in the literature, Consistency and Independence. In doing so, it also considers mechanisms that only approximately satisfy these constraints, that is, satisfy them up to a small fraction of the inputs. The main question raised is whether the relaxation of these constraints significantly alters the class of aggregation mechanisms that meet the two (relaxed) constraints. The main result of this paper is that in the case of a subclass of a natural class of aggregation problems termed {"}truth-functional agendas,{"} the set of aggregation mechanisms that meet the constraints does not extend nontrivially when the constraints are relaxed. This paper also shows connections between this new general framework and the works on approximation of preference aggregation as well as the field of Property Testing and particularly linear testing of Boolean functions.",

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Approximately classic judgement aggregation

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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