Transitivity of preferences: when does it matter?

We define the empirical conditions on prices and incomes under which transitivity of preferences has specific testable implications. In particular, we set out necessary and sufficient requirements for budget sets under which consumption choices can violate SARP (Strong Axiom of Revealed Preferences) but not WARP (Weak Axiom of Revealed Preferences). As SARP extends WARP by additionally imposing transitive preferences, this effectively defines the conditions under which transitivity is separately testable. Our findings have considerable practical relevance, as transitivity conditions are known to substantially aggravate the computational burden of empirical revealed preference analysis. Our characterization takes the form of triangular conditions that must hold for all three-element subsets of normalized prices, and which are easy to verify in practice. We demonstrate their practical use through two short empirical applications.