Complex design problems are typically decomposed into smaller design problems that are solved by domain-specific experts who must then coordinate their solutions into a satisfactory system-wide solution. In set-based collaborative design, collaborating engineers coordinate themselves by communicating multiple design alternatives at each step of the design process. The goal in set-based collaborative design is to spend additional resources exploring multiple options in the early stages of the design process, in exchange for less iteration in the latter stages, when iterative rework tends to be most expensive. Several methods have been proposed for representing sets of designs, including intervals, surrogate models, fuzzy membership functions, and probability distributions. In this paper, we introduce the use of Bayesian networks for capturing sets of promising designs, thereby classifying the design space into satisfactory and unsatisfactory regions. The method is compared to intervals in terms of its capacity to accurately classify satisfactory design regions as a function of the number of available data points. A simplified, multilevel design problem for an unmanned aerial vehicle is presented as the motivating example.