The Limit of Rationality in Choice Modeling: Formulation, Computation, and Implications

Abstract

Customer preferences may not be rational, so we focus on quantifying the limit of rationality (LoR) in choice modeling applications. We define LoR as the cost of approximating the observed choice fractions from a collection of offer sets with those from the best-fitting probability distribution over rankings. Computing LoR is intractable in the worst case. To deal with this challenge, we introduce two new concepts, rational separation and choice graph, through which we reduce the problem to solving a dynamic program on the choice graph and express the computational complexity in terms of the structural properties of the graph. By exploiting the graph structure, we provide practical methods to compute LoR efficiently for a large class of applications. We apply our methods to real-world grocery sales data and identify product categories for which going beyond rational choice models is necessary to obtain an acceptable performance.

Keywords: Limit of Rationality, Choice Modeling, Rank Aggregation