Comparing the 2N-ary Choice Tree model and the Cube model for best-worst choice situations with three choice alternatives

The 2N-ary Choice Tree (2NCT) model (Wollschlaeger and Diederich, 2012, 2020) and the Cube model (Mallahi-Karai and Diederich, 2019, 2023) are dynamic-stochastic approaches for decision making situations with multiple alternatives. The 2NCT model is a dynamic stochastic model formalized as a random walk on a tree. It shares several features of other stochastic models on decision making such as including initial biases for any of the choice alternatives, updating preferences over time or initiation of a response when a decision criterion is met . Its distinct assumption is that it establishes two counters for each alternative for tracking evidences in favor of choosing a specific alternative and a negative counter for tracking evidence against choosing that alternative. It provides a mechanism to predict a preference order of the the offered alternative The multi-episode Cube model postulates that best–worst choice task is the outcome of sequential choices made in a number of episodes allowing the alternatives to be ranked from best to worst or from worst to best. The underlying model is a multivariate Wiener process with drift issued from a point in the unit cube, where episodes are defined in terms of a sequence of stopping times. Both models make predictions with respect to choice probabilities and (mean) choice response times. It is shown how the models can be implemented using Markov chains and how they are tested on data.