  We consider the problem of rationalizing choice data by a preference
satisfying an arbitrary collection of invariance axioms. Examples of such
axioms include quasilinearity, homotheticity, independence-type axioms for
mixture spaces, constant relative/absolute risk and ambiguity aversion axioms,
stationarity for dated rewards or consumption streams, separability, and many
others. We provide necessary and sufficient conditions for invariant
rationalizability via a novel approach which relies on tools from the
theoretical computer science literature on automated theorem proving. We also
establish a generalization of the Dushnik-Miller theorem, which we use to give
a complete description of the out-of-sample predictions generated by the data
under any such collection of axioms.
