Cancellation conditions for finite two-dimensional additive measurement
type: Item
instance of: scholarly article
title: Cancellation conditions for finite two-dimensional additive measurement
zbMATH Open document ID: 1015.91057
author: Peter Fishburn
published in: Journal of Mathematical Psychology
publication date: 2003-07-09T00:00:00Z
review text: The author partially settles a delicate issue in two-component additive conjoint measurement theory. It is known that a weak order on a finite set \(X_1\times X_2\) admits an additive real-valued order-preserving representation if and only if it satisfies a denumerable set of cancellation conditions \(C(k),\;k=2,3,\dots\). The question of concern here is, given cardinalities \(m,n\) of \(X_1,X_2\), what is the number \(f(m,n)\) of cancellation conditions that need to be checked? Apart for some known special cases of small \((m,n)\), the existing result for general \((m,n)\) is that \(f(m,n)\leq m+n-1\). The present paper shows that for all odd \(m\) and \(n\) greater than \(11\) one also has \(f(m,n)\geq m+n-10\). Thus for large odd \(m,n\), one needs to check approximately \(m+n\) cancellation conditions.
reviewed by: Salvatore Modica
Mathematics Subject Classification ID: 91C05
Mathematics Subject Classification ID: 91E45
zbMATH DE Number: 1749370
zbMATH Keywords: finite additive conjoint structures
zbMATH Keywords: cancellation conditions
MaRDI profile type: Publication
full work available at URL: jmps.1999.1285
OpenAlex ID: W2049329889
Wikidata QID: Q52088535
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DOI: 10.1006/JMPS.1999.1285
description: scientific article; zbMATH DE number 1749370