Structure of single-peaked preferences

IF 2.2 4区心理学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

Journal of Mathematical Psychology Pub Date : 2023-12-01 DOI:10.1016/j.jmp.2023.102817

Alexander Karpov

引用次数: 0

Abstract

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.

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单峰偏好的结构

本文研究了与单峰偏好密切相关的各种偏好顺序领域。我们建立了单峰偏好轮廓数和圆上单峰偏好轮廓数的递推公式。我们找到了三个、四个和五个备选方案的阿罗单峰偏好轮廓数。讨论了随机抽样的应用。对于限制层偏好剖面，得到了禁止子剖面特征和精确枚举公式。同时还证明了每个费什伯恩偏好轮廓都是圆偏好轮廓上的单峰，而且费什伯恩偏好轮廓不能用禁止子轮廓来表征。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematical Psychology 医学-数学跨学科应用

CiteScore

3.70

自引率

11.10%

发文量

审稿时长

20.2 weeks

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