Efficient Choice Designs for a Consider-Then-Choose Model

Existing research on choice designs focuses exclusively on compensatory models that assume that all available alternatives are considered in the choice process. In this paper, we develop a method to construct efficient designs for a two-stage, consider-then-choose model that involves a noncompensatory screening process at the first stage and a compensatory choice process at the second stage. The method applies to both conjunctive and disjunctive screening rules. Under certain conditions, the method also applies to the subset conjunctive and disjunctions of conjunctions screening rules. Based on the local design criterion, we conduct a comparative study of compensatory and conjunctive designs--the former are optimized for a compensatory model and the latter for a two-stage model that uses conjunctive screening in its first stage. We find that conjunctive designs have higher level overlap than compensatory designs. This occurs because level overlap helps pinpoint screening behavior. Higher overlap of conjunctive designs is also accompanied by lower orthogonality, less level balance, and more utility balance. We find that compensatory designs have a significant loss of design efficiency when the true model involves conjunctive screening at the consideration stage. These designs also have much less power than conjunctive designs in identifying a true consider-then-choose process with conjunctive screening. In contrast, when the true model is compensatory, the efficiency loss from using a conjunctive design is lower. Also, conjunctive designs have about the same power as compensatory designs in identifying a true compensatory choice process. Our findings make a strong case for the use of conjunctive designs when there is prior evidence to support respondent screening.