Incoherent majorities: the McGarvey problem in judgement aggregation
type: Item
instance of: scholarly article
title: Incoherent majorities: the McGarvey problem in judgement aggregation
zbMATH Open document ID: 1246.91044
author: Klaus Nehring
author: Marcus Pivato
published in: Discrete Applied Mathematics
publication date: 2011-10-27T00:00:00Z
review text: `Judgement aggregation' is a model of social choice where the space of social alternatives is the set of consistent truth-valuations (`judgements') on a family of logically interconnected propositions. It is well-known that propositionwise majority voting can yield logically inconsistent judgements. In this paper authors show that, for a variety of spaces, propositionwise majority voting can yield any possible judgement. By considering the geometry of sub-polytopes of the Hamming cube, they also estimate the number of voters required to achieve all possible judgements. These results generalize the classic results of \textit{D. C. McGarvey} [Econometrica 21, 608--610 (1953)] and \textit{R. Stearns} [Am. Math. Mon. 66, 761--763 (1959; Zbl 0090.25101)].
reviewed by: Simona Settepanella
Mathematics Subject Classification ID: 91B14
Mathematics Subject Classification ID: 91B12
zbMATH DE Number: 5964687
zbMATH Keywords: judgement aggregation
zbMATH Keywords: majority voting
zbMATH Keywords: McGarvey
zbMATH Keywords: stearns
zbMATH Keywords: 0/1 polytope
MaRDI profile type: Publication
full work available at URL: j.dam.2011.03.014
OpenAlex ID: W2169640500
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DOI: 10.1016/J.DAM.2011.03.014
description: scientific article; zbMATH DE number 5964687