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

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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.