The generalized stochastic preference choice model

Abstract

We propose a new discrete choice model, called the generalized stochastic preference (GSP) model, that incorporates non-rationality into the stochastic preference (SP) choice model, also known as the rank-based model. Our model can capture several context-dependent choice behaviors that cannot be represented by any SP model, such as the well-documented compromise and attraction effects, while still including the SP model as a special case. The GSP model is defined as a distribution over consumer types, where each type extends the choice behavior of rational types in the SP model. We build on existing methods for estimating the SP model and propose an iterative estimation algorithm for the GSP model that finds new types by solving an integer linear program in each iteration. We further show that our proposed notion of non-rationality can be incorporated into other choice models, like the random utility maximization (RUM) model class as well as any of its subclasses. As a concrete example, we introduce the non-rational extension of the classical MNL model, which we term the generalized MNL (GMNL) model and present an efficient expectation-maximization (EM) algorithm for estimating it. \av{For the GSP model, we demonstrate that the worst-case performance guarantee of revenue-ordered assortments is significantly worse than for the SP model. For the GMNL model, we establish that assortment optimization with totally unimodular constraints is NP-hard to approximate to within a factor of $O(n^{1-\epsilon})$ for any $\epsilon > 0$, where $n$ is the number of products.} Finally, numerical evaluation on synthetic and real choice data shows that the GMNL and GSP models can outperform their rational counterparts in out-of-sample prediction accuracy.