{"title":"单峰偏好的结构","authors":"Alexander Karpov","doi":"10.1016/j.jmp.2023.102817","DOIUrl":null,"url":null,"abstract":"<div><p>The paper studies a variety of domains of preference orders that are closely related to single-peaked preferences. We develop recursive formulas for the number of single-peaked preference profiles and the number of preference profiles that are single-peaked on a circle. The number of Arrow’s single-peaked preference profiles is found for three, four, and five alternatives. Random sampling applications are discussed. For restricted tier preference profiles, a forbidden subprofiles characterization and an exact enumeration formula are obtained. It is also shown that each Fishburn’s preference profile is single-peaked on a circle preference profile, and Fishburn’s preference profiles cannot be characterized by forbidden subprofiles.</p></div>","PeriodicalId":50140,"journal":{"name":"Journal of Mathematical Psychology","volume":"117 ","pages":"Article 102817"},"PeriodicalIF":2.2000,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Structure of single-peaked preferences\",\"authors\":\"Alexander Karpov\",\"doi\":\"10.1016/j.jmp.2023.102817\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The paper studies a variety of domains of preference orders that are closely related to single-peaked preferences. We develop recursive formulas for the number of single-peaked preference profiles and the number of preference profiles that are single-peaked on a circle. The number of Arrow’s single-peaked preference profiles is found for three, four, and five alternatives. Random sampling applications are discussed. For restricted tier preference profiles, a forbidden subprofiles characterization and an exact enumeration formula are obtained. It is also shown that each Fishburn’s preference profile is single-peaked on a circle preference profile, and Fishburn’s preference profiles cannot be characterized by forbidden subprofiles.</p></div>\",\"PeriodicalId\":50140,\"journal\":{\"name\":\"Journal of Mathematical Psychology\",\"volume\":\"117 \",\"pages\":\"Article 102817\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2023-12-01\",\"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/S0022249623000731\",\"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}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Psychology","FirstCategoryId":"102","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022249623000731","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}
The paper studies a variety of domains of preference orders that are closely related to single-peaked preferences. We develop recursive formulas for the number of single-peaked preference profiles and the number of preference profiles that are single-peaked on a circle. The number of Arrow’s single-peaked preference profiles is found for three, four, and five alternatives. Random sampling applications are discussed. For restricted tier preference profiles, a forbidden subprofiles characterization and an exact enumeration formula are obtained. It is also shown that each Fishburn’s preference profile is single-peaked on a circle preference profile, and Fishburn’s preference profiles cannot be characterized by forbidden subprofiles.
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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