Algebraic and Stochastic Models of Structures Arising in Utility Theory and Psychophysics

这项研究继续并扩展了研究者和合作者A.A.J.Marley关于测量心理属性的早期理论工作，如商品的效用和物理信号(如光或声音)的主观强度。这项研究将用代数术语描述影响属性的自变量的基本结构，如(1)通过“主观大于”的排序，(2)同时或快速连续地面对两个商品或刺激的操作，(3)在效用或心理物理学中将刺激作为偏离现状或阈值的处理，以及(4)使用类似于在量值产生方法中发现的“区间比率”的判断。这个项目将解释违反支配地位的行为，例如赌博本身的效用，收益和损失混合赌博的特殊性，以及将理论从二元赌博扩展到一般赌博的各种原则。该项目还将尝试将一些代数理论推广到概率版本。效用模型被广泛用于为决策者提供建议，主观期望效用也是贝叶斯统计方法的关键部分。感官测量广泛应用于各种工业环境中。然而，这些应用主要是基于经验总结，其理论基础最近受到了质疑。该项目将在多个应用领域推进理论和方法的发展。它还将进一步发展基本测量理论的概率版本，从而扩大这种方法对许多社会和行为科学调查的价值。

This research continues and extends earlier theoretical work of the investigator and of collaborator A. A. J. Marley on the measurement of psychological attributes such as the utility of goods and the subjective intensity of physical signals such as lights or sounds. The research will describe the underlying structure of independent variables that affect the attribute in such algebraic terms as (1) the ordering by "subjectively greater than," (2) operations like being presented with two goods or stimuli at once or in quick succession, (3) treatments of stimuli as deviations from the status quo in utility or from threshold in psychophysics, and (4) use of judgements of "ratios of intervals" similar to those found in magnitude production methods. This project will account for violations of dominance, such as the utility of gambling per se, peculiarities of mixed gambles of gains and losses, and various principles to extend the theory from binary gambles to general ones. The project also will attempt to generalize some of the algebraic theories to probabilistic versions.Utility models are extensively used in providing advice to decision makers and subjective expected utility also is a key part of Bayesian statistical methods. Sensory measurement is used widely in a variety of industrial settings. Yet these applications are based primarily on empirical generalizations whose theoretical basis has recently been brought into doubt. This project will advance theory and methods in many application areas. It also will further the development of a probabilistic version of fundamental measurement theory, thereby expanding the value of this approach for many social and behavioral science inquiries.