Consider or Choose? The Role and Power of Consideration Sets

Consideration sets play a crucial role in discrete choice modeling, where customers are commonly assumed to go through a two-stage decision making process. Specifically, customers are assumed to form consideration sets in the first stage and then use a second-stage choice mechanism to pick the product with the highest utility from the consideration sets. Recent studies mostly aim to propose more powerful choice mechanisms based on advanced non-parametric models to improve prediction accuracy. In contrast, this paper takes a step back from exploring more complex second-stage choice mechanisms and instead focus on how effectively we can model customer choice relying only on the first-stage consideration set formation. To this end, we study a class of nonparametric choice models that is only specified by a distribution over consideration sets and has a bounded rationality interpretation. We denote it as the consideration set model. Intriguingly, we show that this class of choice models can be characterized by the axiom of symmetric demand cannibalization, which enables complete statistical identification. We further consider the model's downstream assortment planning as an application. We first present an exact description of the optimal assortment, proving that it is revenue-ordered based on the blocks defined by the consideration sets. Despite this compelling structure, we establish that the assortment optimization problem under this model is NP-hard even to approximate. This result shows that accounting for consideration sets in the model inevitably results in inapproximability in assortment planning, even though the consideration set model uses the simplest possible uniform second-stage choice mechanism. Finally, using a real-world dataset, we show the tremendous power of the first-stage consideration sets when modeling customers' decision-making processes.