Signed orders, choice probabilities, and linear polytopes
type: Item
instance of: scholarly article
title: Signed orders, choice probabilities, and linear polytopes
zbMATH Open document ID: 1051.91085
author: Peter Fishburn
published in: Journal of Mathematical Psychology
publication date: 2001-01-01T00:00:00Z
review text: The number of subsets of a finite set can be huge and it is unreasonable to suppose that an individual can order these subsets. On the other hand, one can consider what the author calls signed orders. Given a set \(S=\{1,\dots,b\}\), there is a set \(S^*=\{1^*,\dots,n^*\}\) and the order is defined over \(S\cup S^*\). The elements of \(S^*\) signify exclusion from the subset. For instance, a linear signed order for \(n=3\) given by \(1\succ 2^*\succ 3\succ 3^*\succ 2\succ 1^*\) would mean that the first priority is to have 1 in some committee, the second priority is to have 2 excluded from the committee etc. In this paper, the author studies the relationship between binary choice probabilities \(p(x,y)\) for distinct \(x,y\in S\cup S^*\) and probability distributions on the set of all linear signed orders on \(S\cup S^*\). In particular, he searches for necessary and sufficient conditions for the existence of a probability distribution \(P\) on the set \(L_n\) of linear signed orders such that \(p(x,y)=\Sigma\{P(l): l\in L_n\) and \(xly\}\). The cases where \(n=2\) and \(n=3\) are dealt with.
Mathematics Subject Classification ID: 91C05
zbMATH DE Number: 1749373
zbMATH Keywords: binary choice probabilities
zbMATH Keywords: probability distributions
zbMATH Keywords: linear signed orders
Wikidata QID: Q52068551
reviewed by: Maurice Salles
describes a project that uses: LOLIB
MaRDI profile type: Publication
full work available at URL: jmps.1999.1288
OpenAlex ID: W1973971930
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DOI: 10.1006/JMPS.1999.1288
description: scientific article; zbMATH DE number 1749373