In light of the interest in axiomatic models of decision making in recent years, one is led to ask, in what ways do axiomatic derivations advance positive economics? If economists are interested in predicting how people behave, without a pretense to change individual decision making, how can they benefit from representation theorems, which are no more than equivalence results? We address these questions. We propose several ways in which representation results can be useful and discuss their potential implications for axiomatic decision theory.