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

这项研究涉及对不确定和有风险的选项之间的选择和判断的建模。它既包括一种已被积极研究多年但仍有可能进行重要改进的代数建模，也包括适应此类选择和判断中明显存在的某种不一致行为的概率建模。四个代数问题是：(1)提供一般线性加权效用表示的基本行为模型(公理化)。虽然许多模型都是这种类型的，但对导致这种类型的行为特性仍然缺乏普遍的理解。例如，需要对Birnbaum的注意转移交换模型进行行为表述。(2)更深层次地理解两次赌博是独立实现的假设，这是这些理论中经常引用的。(3)虽然经常被提及，但很少有人理解不确定性本身的用处或坏处。根据Meginniss(1976)在风险背景下的非公理工作，研究者与其他人合作一直致力于公理化，该公理产生线性加权效用加上常量乘以标准的熵度量。这需要进一步澄清和发展。(4)开发更全面的混合收益和亏损模型，这些模型通常会被推迟，以支持更简单的情况，要么全部收益，要么全部亏损。关于概率模型，研究人员的方法旨在补充和改进现有的文献，这些文献主要集中在一维测量的随机模拟上。问题的关键是处理相互关联的结构，如赌博及其联合收受，特别是获得相当于将两个结构相互关联的(代数分布)定律的随机版本。解决这类问题的尝试一直不是很令人满意，除了最近对预期效用的概率版本进行了复杂的公理化。这项研究将影响考察不确定情况下个人决策的科学，包括经济学、管理学、心理学和统计学。感官心理物理学家也应该受益，因为效用理论的正式结果可以应用于主观强度的测量，有时经过修改。效用理论发展的社会重要性在很大程度上在于决策分析师向投资和医药等领域的客户提供的建议。到目前为止，这类建议通常是基于主观预期效用等理性理论。随着对传统理论未能捕捉到人们目标的方式有了更深入的理解，我们可以预期会有相当大的改进。

The research concerns the modeling of choices between, and judgments about, uncertain and risky options. It involves both algebraic modeling of a sort that has been actively studied for many years, but where important improvements are still possible, and probabilistic modeling to accommodate the somewhat inconsistent behavior apparent in such choices and judgments. Four of the algebraic problems are: (1) Provide a fundamental behavioral model (axiomatization) of the general linear weighted utility representation. Although many models are of this type, a general understanding of the behavioral properties that give rise to it still is lacking. For instance, a behavioral formulation of Birnbaum's Transfer of Attention Exchange model is needed. (2) Understand at a deeper level the assumption that two gambles are independently realized, which is often invoked in these theories. (3) Although often mentioned, little has been done to understand the utility or disutility of uncertainly itself. Following non-axiomatic work of Meginniss (1976) in the context of risk, the investigator in collaboration with others has been working on an axiomatization that yields a linear weighted utility plus a constant times a standard measure of entropy. This needs further clarification and development. (4) Develop more fully models of mixed gains and losses, which often are postponed in favor of the simpler cases of either all gains or all losses. Turning to probabilistic models, the investigators' approach is designed to supplement and improve the existing literature that focuses mainly on the random analogue of one-dimensional measurement. The crux of the problem is to deal with interlocked structures, such as gambles and their joint receipt, and, in particular, to gain what amounts to a random version of the (algebraic distribution) laws that interlock two structures. Attempts to resolve this type of problem have not been very satisfactory, except for the recent sophisticated axiomatization of a probabilistic version of expected utility.This research will impact the sciences, including economics, management science, psychology, and statistics, that examine individual decision making under uncertainty. Sensory psychophysicists also should benefit because the formal results of utility theory can be applied, sometimes with modifications, to the measurement of subjective intensity. The social importance of the developments in utility theory lies largely in the advice that is given by decision analysts to clients in areas such as investment and medicine. Up to now, such advice has typically been based on rational theories such as subjective expected utility. With a deeper understanding of the ways in which traditional theories have failed to capture people's goals, we can expect considerably improved advising.