Chaotic responses to COVID-19, political polarization, and pervasive misinformation raise the question of whether some or many individuals exercise irrational moral judgment. We provide the first mathematically correct test for transitivity of moral preferences. Transitivity is the most prominent rationality criterion of the behavioral, biological, and economic sciences. However, transitivity is conceptually, mathematically, and statistically difficult to evaluate empirically. We tested three parsimonious, order-constrained, probabilistic characterizations: First, the weak utility model treats an individual’s choices as noisy reflections of a single, deterministic, underlying transitive preference; second, a variant severely limits the allowable response noise; and third, by the general random utility hypothesis, individuals’ choices reveal uncertain, but transitive, moral preferences. Among 28 individuals, everyone’s data were consistent with the weak utility model and general random utility model, thus supporting both operationalizations. Tightening the bounds on error rates in noisy responses yielded a poorly performing model, thus rejecting the model according to which choices are highly consistent with a single transitive preference. Bayesian model selection favored probabilistic transitive preferences and hence the equivalent random utility hypothesis. This suggests that there is some order underlying the apparent chaos: Rather than presume widespread disregard for moral principles, policymakers may build on navigating and reconciling extreme heterogeneity compounded with individual uncertainty.