We introduce the novel notion of an abstract numeraire commodity, consisting of a family of self-transformations of an abstract consumption space. We provide necessary and sufficient conditions for such a family to be able to provide a complete and consistent system of measurements of preference intensity for a given collection of preferences. Using measurements of this form, we develop a least squares regression theory for quantifying the predictive accuracy of a wide range of models of preference and individual decision making. Our approach allows for straightforward estimation of a model’s underlying primitives and provides granular insights into the drivers of a model’s predictive success or failure, often at an axiom-by-axiom level. In the presence of stochastic data, we provide a general class of non-parametric statistical tests of rationalizability for a variety of models.