(Functional)Characterizations vs (Finite)Tests: Partially Unifying Functional and Inequality-Based Approaches to Testing

Historically, testing if decision-makers obey certain choice axioms using choice data takes two distinct approaches. The 'functional' approach observes and tests the entire 'demand' or 'choice' function, whereas the 'revealed preference(RP)' approach constructs inequalities to test finite choices. I demonstrate that a statistical recasting of the revealed enables uniting both approaches. Specifically, I construct a computationally efficient algorithm to output one-sided statistical tests of choice data from functional characterizations of axiomatic behavior, thus linking statistical and RP testing. An application to weakly separable preferences, where RP characterizations are provably NP-Hard, demonstrates the approach's merit. I also show that without assuming monotonicity, all restrictions disappear. Hence, any ability to resolve axiomatic behavior relies on the monotonicity assumption.