{"title":"Quasi-separable preferences","authors":"Wei-zhi Qin, Hendrik Rommeswinkel","doi":"10.1007/s11238-023-09962-8","DOIUrl":null,"url":null,"abstract":"<p>Utility functions often lack additive separability, presenting an obstacle for decision theoretic axiomatizations. We address this challenge by providing a representation theorem for utility functions of quasi-separable preferences of the form <span>\\(u(x,y,z)=f(x,z) + g(y,z)\\)</span> on subsets of topological product spaces. These functions are additively separable only when holding <i>z</i> fixed but are cardinally comparable for different values of <i>z</i>. We then generalize the result to spaces with more than three dimensions and provide applications to belief elicitation, inequity aversion, intertemporal choice, and rank-dependent utility.</p>","PeriodicalId":47535,"journal":{"name":"Theory and Decision","volume":"7 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2023-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theory and Decision","FirstCategoryId":"96","ListUrlMain":"https://doi.org/10.1007/s11238-023-09962-8","RegionNum":4,"RegionCategory":"经济学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"ECONOMICS","Score":null,"Total":0}
引用次数: 0
Abstract
Utility functions often lack additive separability, presenting an obstacle for decision theoretic axiomatizations. We address this challenge by providing a representation theorem for utility functions of quasi-separable preferences of the form \(u(x,y,z)=f(x,z) + g(y,z)\) on subsets of topological product spaces. These functions are additively separable only when holding z fixed but are cardinally comparable for different values of z. We then generalize the result to spaces with more than three dimensions and provide applications to belief elicitation, inequity aversion, intertemporal choice, and rank-dependent utility.
期刊介绍：
The field of decision has been investigated from many sides. However, research programs relevant to decision making in psychology, management science, economics, the theory of games, statistics, operations research, artificial intelligence, cognitive science and analytical philosophy have remained separate. Theory and Decision is devoted to all aspects of decision making belonging to such programs, but addresses also possible cross-fertilizations between these disciplines which would represent effective advances in knowledge. The purpose of the journal is to let the engineering of choice gradually emerge both for individual and for collective decision making. Formalized treatments will be favoured, to the extent that they provide new insights into the issues raised and an appropriate modeling of the situation considered. Due to its growing importance, expermentation in decision making as well as its links to the cognitive sciences will be granted special attention by Theory and Decision.
Of particular interest are: Preference and belief modeling,
Experimental decision making under risk or under uncertainty,
Decision analysis, multicriteria decision modeling,
Game theory, negotiation theory, collective decision making, social choice,
Rationality, cognitive processes and interactive decision making,
Methodology of the decision sciences. Applications to various problems in management and organization science, economics and finance, computer-supported decision schemes, will be welcome as long as they bear on sufficiently general cases. Analysis of actual decision making processes are also relevant topics for the journal, whether pertaining to individual, collective or negotiatory approaches; to private decisions or public policies; to operations or to strategic choices.
Officially cited as: Theory Decis
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