Approximate judgement aggregation

Ilan Nehama

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

4 Scopus citations

Abstract

In this paper we analyze judgement aggregation problems in which a group of agents independently votes on a set of complex propositions that has some interdependency constraint between them (e.g., transitivity when describing preferences). We consider the issue of judgement aggregation from the perspective of approximation. That is, we generalize the previous results by studying approximate judgement aggregation. We relax the main two constraints assumed in the current literature, Consistency and Independence and consider mechanisms that only approximately satisfy these constraints, that is, satisfy them up to a small portion of the inputs. The main question we raise is whether the relaxation of these notions significantly alters the class of satisfying aggregation mechanisms. The recent works for preference aggregation of Kalai, Mossel, and Keller fit into this framework. The main result of this paper is that, as in the case of preference aggregation, in the case of a subclass of a natural class of aggregation problems termed 'truth-functional agendas', the set of satisfying aggregation mechanisms does not extend non-trivially when relaxing the constraints. Our proof techniques involve boolean Fourier transform and analysis of voter influences for voting protocols. The question we raise for Approximate Aggregation can be stated in terms of Property Testing. For instance, as a corollary from our result we get a generalization of the classic result for property testing of linearity of boolean functions.

Original languageEnglish
Title of host publicationInternet and Network Economics - 7th International Workshop, WINE 2011, Proceedings
PublisherSpringer Verlag
Pages302-313
Number of pages12
ISBN (Print)9783642255090
StatePublished - 2011
Externally publishedYes
Event7th International Workshop on Internet and Network Economics, WINE 2011 - Singapore, Singapore
Duration: 11 Dec 201114 Dec 2011

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7090 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference7th International Workshop on Internet and Network Economics, WINE 2011
Country/TerritorySingapore
CitySingapore
Period11/12/1114/12/11

Funding

The research was supported by a grant from the Israeli Science Foundation (ISF) and by the Google Inter-university center for Electronic Markets and Auctions.

FundersFunder number
Google Inter-university center for Electronic Markets and Auctions
Israel Science Foundation

    Keywords

    • approximate aggregation
    • computational social choice
    • dependency index
    • discursive dilemma
    • doctrinal paradox
    • inconsistency index
    • truth-functional agendas

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