The 2N-ary Choice Tree model for choices between multiple options with multiple attributes: Further developments and empirical test.

多方案决策问题的两个主要计算模型--多方案决策场理论（MDFT）和泄漏竞争累加器（LCA）模型--主要集中在同时考虑三种情境效应：相似性、妥协性和吸引力。当第三个备选方案被添加到两个选择集时，可能会出现这些效果。这两个模型都可以解释为一个四层神经网络。这些模型的预测只能通过模拟得出。在这里，我们提出了一种替代方法，其中包括一些假设之前，并试图克服这些模型的一些计算问题。 本提案的主要目标有四个方面。在理论部分，本文试图（1）进一步发展和探索多项选择的替代决策模型（2N-ary Choice Tree，2NCT），具有基于树结构而不是基于神经网络的多个属性;（2）提供选择概率和选择响应时间的分析解决方案，而不是仅依赖于模拟，此外，提供允许有效模型拟合过程的算法。在实证部分，该建议旨在（3）开发一种新的设备，用于进行具有多个选项和属性的选择实验，（4）设计实验，以测试模型的方式，而不仅仅是产生三个上下文效应。第一个系列涉及三种选择方案，主要涉及在新设备上复制三种背景效应，并测试产生这些效应的2NCT模型假设。此外，在时间约束下的决策进行了研究，以测试模型的动态方面更详细。第二个系列涉及三个以上的替代品，包括幻影诱饵。

The two leading computational models for multi-alternative decision problems -- multi-alternative Decision Field Theory (MDFT) and the Leaky Competing Accumulator (LCA) model -- primarily focus on accounting simultaneously for three context effects: similarity, compromise and attraction. These effects may occur when a third alternative is added to a choice set of two. Both models can be interpreted as a neural network with four layers. Predictions of these models have only been derived via simulations. Here, we propose an alternative approach, which includes some of the assumptions made previously and try to overcome some of the computational problems these models have. The main goal of the present proposal is fourfold. For the theoretical part, it seeks to (1) further develop and explore an alternative decision model for multiple choice options (2N-ary Choice Tree, 2NCT), with multiple attributes based on a tree structure rather than on neural nets; (2) provide an analytical solution for choice probabilities and choice response times rather than relying on simulations only and, in addition, provide algorithms allowing for efficient model fitting procedures. For the empirical part, the proposal seeks to (3) develop a new device for conducting choice experiments with multiple alternatives and attributes and, therewith, (4) design experiments that test the model in ways that go beyond producing merely the three context effects.Two series of experiments are planned. The first series involves three choice alternatives and is mainly concerned with replicating the three context effects on the new device and testing the 2NCT model assumptions for producing the effects. Furthermore, decision making under time constraints are investigated to test the dynamic aspects of the model in more detail. The second series is concerned with more than three alternatives including phantom decoys.