Design space reduction decisions made in set-based design use perceptions of feasibility to eliminate unfavorable design solutions from consideration. Perceptions are formed with incomplete information, leaving them susceptible to change if new and conflicting information is made available later in the design process. This paper considers how new information originating from newly sampled design points can alter perceptions of feasibility and introduces a probabilistic and an entropic strategy for quantifying the risk of prematurely eliminating potential design solutions. Emergent designs of automated set-based design simulations gauging this risk are evaluated against ones neglecting it for an analogous design problem. The Python-based simulations have different disciplines randomly explore their design spaces and generate reasonable space reduction propositions, and then they give a design manager the opportunity to check the fragility of reduced design spaces before finalizing any reductions. Gathered results indicate that both the probabilistic and entropic models are able to effectively delay design decisions and help disciplines maintain a higher diversity of design solutions while designer understanding is still growing. Both models effectively delay risky space reductions and encourage a more gradual reduction of design spaces compared to simulations not including fragility checks. Furthermore, as the entropic model takes a more holistic approach by working with the history of perceptions formed in a discipline's design space rather than just the newest perceptions, space remaining and diversity results show it slightly outperforming the probabilistic model.