Design decisions often require input from multiple stakeholders or require balancing multiple design requirements. However, leading axiomatic approaches to decision-based design suggest that combining preferences across these elements is virtually guaranteed to result in irrational outcomes. This has led some to conclude that a single “dictator” is required to make design decisions. In contrast, proponents of heuristic approaches observe that aggregate decisions are frequently made in practice, and argue that this widespread usage justifies the value of these heuristics to the engineering design community. This paper demonstrates that these approaches need not be mutually exclusive. Axiomatic approaches can be informed by empirically motivated restrictions on the way that individuals can order their preferences. These restrictions are represented using “anigrafs”—structured relationships between alternatives that are represented using a graph–theoretic formalism. This formalism allows for a computational assessment of the likelihood of irrational outcomes. Simulation results show that even minimal amounts of structure can vastly reduce the likelihood of irrational outcomes at the level of the group, and that slightly stronger restrictions yield probabilities of irrational preferences that never exceed 5%. Next, an empirical case study demonstrates how anigrafs may be extracted from survey data, and a model selection technique is introduced to examine the goodness-of-fit of these anigrafs to preference data. Taken together, these results show how axiomatic consistency can be combined with empirical correspondence to determine the circumstances under which “dictators” are necessary in design decisions.