# Working Papers

### How Strong is the Weak Axiom?

I characterize those abstract choice environments for which the satisfaction of the weak axiom of revealed preference suffices for the strong rationalizability of any choice correspondence. Roughly, this requires that all circuits on a certain graph defined from the budget collection of the environment are able to be broken in an intuitive way. I additionally provide a notion of local integrability for arbitrary choice correspondences, and prove an ordinal variant of the Hurwicz-Uzawa integrability theorem that holds in the full generality of the abstract choice model. Using this, I show that the weak axiom implying the strong rationalizability of any choice correspondence for a given environment is jointly equivalent to (i) the weak axiom implying a generalization of Slutsky symmetry, and (ii) a sampling richness condition that I interpret as an ex-ante measure of the informativeness of the choice environment. I give applications to the study of inconsistency indices for choice data.