Random relations, random utilities, and random functions
type: Item
instance of: scholarly article
title: Random relations, random utilities, and random functions
zbMATH Open document ID: 1004.91071
published in: Journal of Mathematical Psychology
publication date: 2002-07-04T00:00:00Z
review text: The aim of the paper is to extend the first author's earlier results, and to complement and reformulate closely related work, by analyzing the relationship between three fundamental ways of mathematically representing judgements and preferences. The paper significantly extends the following three approaches considered in the paper to modelling the preference, judgement, and choice behaviour of a population: (1) The development of the random junction approach, which has often been used implicitly in the random utility literature, and is now made explicit. This is an effective extension to the existing literature on probabilistic choice models in general, and can be viewed as very similar to the random relation approach. Another useful feature of the random function approach is that it enables to state probabilistic versions of some results from the (deterministic) representational theory of measurement in a natural way. (2) The second approach involves the development of extended results from valued \(m\)-ary relations to relational structures and finite-valued relations. (3) The third important extension consists of the two illustrative examples that are exposed in detail. The obtained theoretical results are comprehensibly applied to probabilistic models of magnitude estimation, probabilistic extensive measurement, probabilistic metric spaces, and (binary) subjective expected utility.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 91E45
Mathematics Subject Classification ID: 91B16
zbMATH DE Number: 1763487
zbMATH Keywords: theory of measurement
zbMATH Keywords: representation of judgements and preferences
zbMATH Keywords: probabilistic choice models
zbMATH Keywords: probabilistic extensive measurement
zbMATH Keywords: subjective expected utility
author: Michel Regenwetter
author: A. A. J. Marley
MaRDI profile type: Publication
full work available at URL: jmps.2000.1357
OpenAlex ID: W2061532330
Wikidata QID: Q57086481
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DOI: 10.1006/JMPS.2000.1357
description: scientific article; zbMATH DE number 1763487