Transitivity of preferences: when does it matter?

We define necessary and sufficient conditions on prices and incomes under which quantity choices can violate SARP (Strong Axiom of Revealed Preference) but not WARP (Weak Axiom of Revealed Preference). As SARP extends WARP by additionally imposing transitivity on the revealed preference relation, this effectively defines the conditions under which transitivity adds bite to the empirical analysis. For finite datasets, our characterization takes the form of a triangular condition that must hold for all three-element subsets of normalized prices, and which is easy to verify in practice. For infinite datasets, we formally establish an intuitive connection between our characterization and the concept of Hicksian aggregation. We demonstrate the practical use of our conditions through two empirical illustrations.