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和相关领域最热门的问题之一。虽然许多方法是静态的，但学者们越来越多地接受动态选择模型可能有助于揭示选择过程。一种思路是基于这样的假设，即决策是随着时间的推移而积累信息的结果，直到满足决策标准（阈值）。这些模型，通常被称为顺序抽样模型，并形式化为随机过程，已应用于各种心理学研究领域，主要涉及二元选择选项，一个是“正确的”，另一个是“不正确的”给定的特定任务。该方法已扩展到优先选择情况，最近，有三个选择选项的选择情况，最重要的是考虑所谓的环境效应（吸引力，相似性，妥协）。Mallahi-Karai和Diederich（2019,2021）提出了两个具有任意数量选择的一般选择情况模型。这些模型基于高维空间中的维纳过程。所谓的立方体模型是为了在有限的选项中做出选择而设计的；磁盘模型可以看作是多维数据集模型的一个修改，涉及三个备选方案，其中一个被认为是一个维持现状的选项。在这个项目中，我们寻求(1)将这两个模型扩展并应用于所谓的最佳-最差缩放情况，即一个人面临三个或更多的选择选项，需要确定最佳和最差的选择选项，以及维持现状的选择设置，即决策者不需要采取行动，但保持当前或先前的决定；(2)对模型进行实证检验；(3)比较当前两种模型（并联线性弹道蓄能器模型和2N-ary选择树模型）的理论和实证结果。

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.