Collective judgement: combining individual value judgements
type: Item
instance of: scholarly article
title: Collective judgement: combining individual value judgements
zbMATH Open document ID: 1035.39014
DOI: 10.1016/S0165-4896(98)00030-4
author: Ákos Münnich
author: Gyula Maksa
author: Robert J. Mokken
published in: Mathematical Social Sciences
publication date: 1999-09-23T00:00:00Z
review text: The mathematical part of the paper, preceded by a wide-ranging introduction, and followed by remarks on Arrow's paradox and by a 63 item bibliography, offers the continuous and in each variable strictly increasing solutions of the bisymmetry equation \[ B[B(x_{11},\dots ,x_{1n}),\dots ,B(x_{n1},\dots ,x_{nn})]=B[B(x_{11},\dots ,x_{n1}), \dots ,B(x_{1n},\dots ,x_{nn})]. \] The result has been announced in \textit{J. Aczél}'s 1948 paper [Bull. Am. Math. Soc. 54, 392--400 (1948; Zbl 0030.02702)] but proved only for \(n=2\). As application an axiomatization of group decision making is offered, where the group consists of \(n^2\) evaluators and their decision is aggregated from those of \(n\) subsets of \(n\) members each.
reviewed by: János Aczél
Mathematics Subject Classification ID: 39B12
Mathematics Subject Classification ID: 39B22
Mathematics Subject Classification ID: 91C20
zbMATH DE Number: 1319691
zbMATH Keywords: functional equations
zbMATH Keywords: bisymmetry
zbMATH Keywords: aggregation
zbMATH Keywords: collective judgement
zbMATH Keywords: decision making
MaRDI profile type: Publication
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full work available at URL: s0165-4896(98)00030-4
OpenAlex ID: W2124702972
Wikidata QID: Q127320202
description: scientific article; zbMATH DE number 1319691