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.

翻译：考虑集在离散选择模型中扮演着关键角色，通常假设顾客会经历两阶段的决策过程。具体而言，假设顾客在第一阶段形成考虑集，随后在第二阶段通过选择机制从考虑集中挑选效用最高的产品。近期研究大多旨在基于先进的非参数模型提出更强大的选择机制以提高预测精度。与此相反，本文暂缓探索更复杂的第二阶段选择机制，转而聚焦于仅依靠第一阶段考虑集形成过程来有效建模顾客选择的能力。为此，我们研究一类仅由考虑集上的分布定义且具有有限理性解释的非参数选择模型，并将其称为考虑集模型。有趣的是，我们证明该类选择模型可通过对称需求侵蚀公理进行刻画，从而实现完全的统计识别。我们进一步探讨了该模型在下游品类规划中的应用。首先，我们给出了最优品类的精确描述，证明其基于考虑集定义的区块具有收益排序特性。尽管存在这一引人注目的结构，我们证实即使在该模型下近似求解品类优化问题也是NP难的。这一结果表明，在模型中纳入考虑集必然导致品类规划问题的不可近似性，即使考虑集模型采用了最简单的均匀第二阶段选择机制。最后，通过真实数据集，我们展示了第一阶段考虑集在建模顾客决策过程中的强大解释力。