Cube and Disk Models for best-worst tasks and status-quo options

对(人类)决策过程进行建模是心理学及相关领域最热门的问题之一。虽然许多方法都是静态的，但学者们越来越多地接受动态选择模型可能会进一步瓦解选择过程。一种思路是基于这样的假设，即决策的产生是随着时间的推移积累信息的结果，直到达到决策标准(阈值)。这些模型通常被称为序贯抽样模型，并被形式化为随机过程，已被应用于各种心理学研究领域，其中最主要的是涉及二元选择选项，一个是“正确的”，另一个是“不正确的”，给定特定的任务。这种方法已经扩展到优先选择的情况，最近又扩展到有三个选择选择的选择情况，最重要的是考虑了所谓的语境效应(吸引、相似、妥协)。Mallahi-Karai和Diederich(2019,2021)针对具有任意数量备选方案的一般选择情况提出了两个模型。这些模型是基于更高维空间中的维纳过程。所谓的立方体模型是为了在任意有限数量的备选方案中进行选择而设计的；圆盘模型可以被视为涉及三个备选方案的立方体模型的修改，其中一个被认为是维持现状的方案。在这个项目中，我们试图(1)将这两个模型推广和应用到所谓的最佳-最差比例情形，即一个人面对三个或三个以上的选择方案时，需要识别最佳和最差选择方案，以及一个维持现状的选择方案，即决策者不需要采取行动，而是维持当前或以前的决策；(2)对模型进行实证检验；(3)将理论和经验结果与现有的两个模型，并行线性弹道累加器模型和2N-ary Choice Tree模型进行比较。

Modeling the processes underlying (human) decision making is one of the most topical issues in psychology and related areas. While many approaches are static, there is growing acceptance among scholars that dynamic choice models might add to unraveling the choice process. One line of thought is based on the assumption that decisions arise as a result of accumulating information over time until a decision criterion (threshold) is met. These models, often called sequential sampling models and formalized as stochastic processes, have been applied to various psychological research areas, foremost involving binary choice options, one being "correct" and the other being "incorrect" given the specified task. The approach has been extended to preferential choice situations and, more recently, to choice situations with three choice alternatives, foremost to account for so-called context effects (attraction, similarity, compromise). Mallahi-Karai and Diederich (2019, 2021) proposed two models for general choice situations with an arbitrary number of alternatives. These models are based on a Wiener process in a higher-dimensional space. The so-called cube model was designed for making a choice between any finite number of alternatives; the disk model can be viewed as a modification of the cube model involving three alternatives, one of which considered as a status-quo option. In this project, we seek (1) to extend and apply both models to the so-called best-worst scaling situation, that is, a person faced with three or more choice alternatives is required to identify the best and the worst choice option, and to a status-quo choice setting, that is, the decision maker is not required to act but maintains the current or previous decision; (2) to test the models empirically; and (3) to compare the theoretical and empirical results with two current models, the parallel Linear Ballistic Accumulator model and the 2N-ary Choice Tree model.