{"title":"Stochastic additive differences","authors":"Yutaka Nakamura","doi":"10.1016/j.jmp.2022.102744","DOIUrl":null,"url":null,"abstract":"<div><p><span>Properties of a binary choice probability function </span><span><math><mi>p</mi></math></span> defined on multiattributed outcomes are studied to represent <span><math><mi>p</mi></math></span><span> as a transformation of additive difference evaluations of chosen and unchosen outcomes into the unit interval. We use an algebraic assumption to obtain an additive difference representation, but allow for restricting strict increasingness of the transformation to the subset of the domain on which transformed values are strictly between 0 and 1. We also apply a topological assumption to axiomatize the cases of homogeneous product sets in the context of finite-state decision making under uncertainty.</span></p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"113 ","pages":"Article 102744"},"PeriodicalIF":2.2000,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Psychology","FirstCategoryId":"102","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022249622000827","RegionNum":4,"RegionCategory":"心理学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
Properties of a binary choice probability function defined on multiattributed outcomes are studied to represent as a transformation of additive difference evaluations of chosen and unchosen outcomes into the unit interval. We use an algebraic assumption to obtain an additive difference representation, but allow for restricting strict increasingness of the transformation to the subset of the domain on which transformed values are strictly between 0 and 1. We also apply a topological assumption to axiomatize the cases of homogeneous product sets in the context of finite-state decision making under uncertainty.
期刊介绍：
The Journal of Mathematical Psychology includes articles, monographs and reviews, notes and commentaries, and book reviews in all areas of mathematical psychology. Empirical and theoretical contributions are equally welcome.
Areas of special interest include, but are not limited to, fundamental measurement and psychological process models, such as those based upon neural network or information processing concepts. A partial listing of substantive areas covered include sensation and perception, psychophysics, learning and memory, problem solving, judgment and decision-making, and motivation.
The Journal of Mathematical Psychology is affiliated with the Society for Mathematical Psychology.
Research Areas include:
• Models for sensation and perception, learning, memory and thinking
• Fundamental measurement and scaling
• Decision making
• Neural modeling and networks
• Psychophysics and signal detection
• Neuropsychological theories
• Psycholinguistics
• Motivational dynamics
• Animal behavior
• Psychometric theory
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