The median procedure for n-trees
type: Item
instance of: scholarly article
title: The median procedure for n-trees
zbMATH Open document ID: 0617.62066
DOI: 10.1007/BF01894194
published in: Journal of Classification
publication date: 1986-01-01T00:00:00Z
review text: One approach to produce a consensus of several classifications constructed for a set of objects is to produce a reasonable-looking method and then seek to discover those properties that characterize it. In the present paper this is made by giving an axiomatic characterization of the median procedure for n-trees. Let (X,d) be a metric space. The function \(M: X^ k\to 2^ X\) defined by \[ M(x_ 1,...,x_ k)=\{x\in X:\sum^{k}_{j>1}d(x,x_ j)\quad is\quad \min imum\} \] is called the median procedure. Axioms are presented that characterize M when X is a certain class of trees (hierarchical classification), and d is the symmetric difference metric. The median complete multiconsensus function (CMF) is shown to be the unique CMF that is efficient, stable on clusters, consistent, symmetric, and quasi-Condorcet.
Mathematics Subject Classification ID: 62H30
zbMATH DE Number: 4001233
zbMATH Keywords: majority rule
zbMATH Keywords: consensus
zbMATH Keywords: axiomatic characterization
zbMATH Keywords: median procedure
zbMATH Keywords: n-trees
zbMATH Keywords: hierarchical classification
zbMATH Keywords: symmetric difference metric
zbMATH Keywords: median complete multiconsensus function
author: J. P. Barthélemy
author: F. R. McMorris
MaRDI profile type: Publication
cites work: Medians in median graphs
cites work: The median procedure in cluster analysis and social choice theory
cites work: Consensus n-trees
cites work: A Consistent Extension of Condorcet’s Election Principle
full work available at URL: https://doi.org/10.1007/bf01894194
OpenAlex ID: W2000034617
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description: scientific article; zbMATH DE number 4001233