Faithful consensus methods for n-trees
type: Item
instance of: scholarly article
title: Faithful consensus methods for n-trees
zbMATH Open document ID: 0539.62073
DOI: 10.1016/0025-5564(82)90043-8
published in: Mathematical Biosciences
publication date: 1983-01-01T00:00:00Z
review text: In this article are introduced and compared some new consensus methods for n-trees. Let the system of classifications of a fixed finite set be given in the form of the system \({\mathcal T}^ k_ n\) (tree primary classifications are given by hierarchical clusterings). A consensus rule is a function from \({\mathcal T}^ k_ n\) to \({\mathcal T}_ n\) (tree representing resulting clustering). A consensus rule is said to be faithful if a condition of betweenness is fulfilled. That means for any choice of the sets \(X_ i\) from the tree \(T_ i\) there exists some cluster B satisfying: \(\cap^{k}_{i=1}X_ i\subseteq B\subseteq \cup^{k}_{i=1}X_ i.\) Besides the betweenness axiom there are other reasonable properties of consensus rules as neutrality, monotonicity, Pareto axiom etc. A number of examples illustrates various consensus rules satisfying these axioms. The main result of this paper is the following: Only trivial consensus rules are simultaneously faithful and neutral.
Mathematics Subject Classification ID: 62H30
zbMATH DE Number: 3858218
zbMATH Keywords: faithfulness
zbMATH Keywords: n-trees
zbMATH Keywords: hierarchical clusterings
zbMATH Keywords: consensus rule
zbMATH Keywords: betweenness axiom
zbMATH Keywords: neutrality
zbMATH Keywords: monotonicity
zbMATH Keywords: Pareto axiom
author: Dean A. Neumann
reviewed by: Ludovit Niepel
MaRDI profile type: Publication
full work available at URL: 0025-5564(82)90043-8
OpenAlex ID: W2024470772
cites work: The median procedure in cluster analysis and social choice theory
cites work: Q4085109
cites work: Q5671815
cites work: Consensus n-trees
cites work: Consensus functions defined on trees
cites work: An Axiomatic Theory of Tournament Aggregation
cites work: Q5635232
description: scientific article; zbMATH DE number 3858218