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A goodness-of-fit index measures the consistency of consumption data with a given model of utility-maximization. We show that for the class of well-behaved (i.e., continuous and increasing) utility functions there is no goodness-of-fit index that is continuous and accurate, where the latter means that a perfect score is obtained if and only if a dataset can be rationalized by a well-behaved utility function. While many standard goodness-of-fit indices are inaccurate we show that these indices are (in a sense we make precise) essentially accurate. Goodness-of-fit indices are typically generated by loss functions and we find that standard loss functions usually do not yield a best-fitting utility function when they are minimized. Nonetheless, welfare comparisons can be made by working out a robust preference relation from the data.

Afriat's Theorem (1967) states that a dataset can be thought of as being generated by a consumer maximizing a continuous and increasing utility function if and only if it is free of revealed preference cycles containing a strict relation. The latter property is often known by its acronym, GARP (for generalized axiom of revealed preference). This paper surveys extensions and applications of Afriat's seminal result. We focus on those results where the consistency of a dataset with the maximization of a utility function satisfying some property can be characterized by a suitably modified version of GARP.

The standard criterion of rationality in economics is the maximization of a utility function that is stable across multiple observations of an agent's choice behavior. In this paper, we discuss two notions of the money pump that characterize two corresponding notions of utility-maximization. We explain the senses in which the amount of money that can be pumped from a consumer is a useful measure of the consumer's departure from utility-maximization.