  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.
