We recover approximate parametric preferences from consistent and inconsistent consumer choices. The procedure seeks to utilize revealed preference information contained in choices by minimizing its ranking inconsistency with the proposed parametric preferences. We prove that the goodness-of-t of such an approximation can be decomposed into measures of inconsistency and misspecication. This provides a reasonable way to test restrictions on parametric models. An application of the method to the
data set constructed by Choi et al. [2007] to study choice under risk suggests more frequent and pronounced non-expected utility preferences than previously suggested.