The 2N-ary Choice Tree Model for N-Alternative Preferential Choice

Abstract

The 2N-ary choice tree model accounts for response times and choice probabilities in multi-alternative preferential choice. It implements pairwise comparison of alternatives on weighted attributes into an information sampling process which, in turn, results in a preference process. The model provides expected choice probabilities and response time distributions in closed form for optional and fixed stopping times. The theoretical background of the 2N-ary choice tree model is explained in detail with focus on the transition probabilities that take into account constituents of human preferences such as expectations, emotions, or socially influenced attention. Then it is shown how the model accounts for several context-effects observed in human preferential choice like similarity, attraction, and compromise effects and how long it takes, on average, for the decision. The model is extended to deal with more than three choice alternatives. A short discussion on how the 2N-ary choice tree model differs from the multi-alternative decision field theory and the leaky competing accumulator model is provided