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--主要集中于同时考虑三种情境效应：相似性、折衷和吸引力。当将第三个选项添加到两个选项集中时，这些效果可能会发生。这两个模型都可以解释为具有四层结构的神经网络。对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，它包括了前面所做的一些假设，并试图克服这些模型所存在的一些计算问题。本提案的主要目标有四个。在理论部分，它试图(1)进一步发展和探索多项选择选项的替代决策模型(2N-ary Choice Tree，2NCT)，该模型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解析解，而不是仅仅依赖于模拟；此外，还提供了允许高效模型拟合过程的算法。对于实证部分，该提案试图(3)开发一种新的装置来进行具有多个选项和属性的选择实验，并据此(4)设计实验，以超越仅产生三个上下文效应的方式来测试模型。第一个系列涉及三个选择方案，主要涉及在新设备上复制三个上下文效应，并测试产生效果的2NCT模型假设。此外，还研究了时间约束下的决策问题，以更详细地检验模型的动态特性。第二个系列涉及三种以上的选择，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.