Revealed preference theory, pioneered by American economist Paul Samuelson, is a method by which it is possible to discern the best possible option on the basis of consumer behavior. Essentially, this means that the preferences of consumers can be revealed by their purchasing habits. Revealed preference theory came about because the theories of consumer demand were based on a diminishing marginal rate of substitution (MRS). This diminishing MRS is based on the assumption that consumers make consumption decisions based on their intent to maximize their utility. While utility maximization was not a controversial assumption, the underlying utility functions could not be measured with great certainty. Revealed preference theory was a means to reconcile demand theory by creating a means to define utility functions by observing behavior.
If a person chooses a certain bundle of goods (ex. 2 apples, 3 bananas) while another bundle of goods is affordable (ex. 3 apples, 2 bananas), then we say that the first bundle is revealed preferred to the second. It is then assumed that the first bundle of goods is always preferred to the second. This means that if the consumer ever purchases the second bundle of goods then it is assumed that the first bundle is unaffordable. This implies that preferences are transitive. In other words if we have bundles A, B, C, …., Z, and A is revealed preferred to B which is revealed preferred to C and so on then it is concluded that A is revealed preferred to C through Z. With this theory economists can chart indifference curves which adhere to already developed models of consumer theory.
The Weak Axiom of Revealed Preference
The Weak Axiom of Revealed Preference (WARP) is a characteristic on the choice behavior of an economic agent. For example, if an individual chooses A and never B when faced with a choice of both alternatives, they should never choose B when faced with a choice of A,B and some additional options. More formally, if A is ever chosen when B is available, then there can be no budget set containing both alternatives for which B is chosen and A is not.
This characteristic can be stated as a characteristic of Walrasian demand functions as seen in the following example. Let pa be the price of apples and pb be the price of bananas, and let the amount of money available be m=5. If pa =1 and pb=1, and if the bundle (2,3) is chosen, it is said that that the bundle (2,3) is revealed preferred to (3,2), as the latter bundle could have been chosen as well at the given prices. More formally, assume a consumer has a demand function x such that they choose bundles x(p,w) and x(p’,w’) when faced with price-wealth situations (p,w) and (p’,w’) respectively. If p·x(p’,w’) ≤ w then the consumer chooses x(p,w) even when x(p’,w’) was available under prices p at wealth w, so x(p,w) must be preferred to x(p’,w’).
If, in a theoretical model, there exist only an apple and an orange, and that an orange is picked, then one can definitely say that an orange is preferred over an apple. In a real world, when it is observed that a consumer purchased an orange, it is impossible to say what good or set of goods or behavioural options were discarded in preference of purchasing an orange. In this sense, preference is not revealed at all in the sense of ordinal utility.  One of the critic state that “Instead of replacing ‘metaphysical’ terms such as ‘desire’ and ‘purpose'” they “used it to legitimize them by giving them operational definitions.” Thus in psychology, as in economics, the initial, quite radical operationalist ideas eventually came to serve as little more than a “reassurance fetish” (Koch 1992, 275) for mainstream methodological practice.”