On the Rationalizability of Observed Consumers’ Choices when Preferences Depend on Budget Sets and (Potentially) on Anything Else

We prove that defining consumers’ preferences over budget sets is both
necessary and sufficient to make every fully informative and finite set
of observed consumption choices rationalizable by a collection of preferences which are transitive, complete, and monotone with respect to
own consumption. Our finding has two important theoretical consequences. First, assuming that preferences depend on budget sets is
illegitimate under the scientific commitments of revealed preference
theory. Second, as long as consumers’ preferences are not defined over
budget sets, we can assume that preferences depend on observable objects other than own consumption without compromising the logical
possibility to reject the model against observation. We however point
out that, despite this logical possibility, in practice it can be almost
impossible to reject a model where preferences are defined over objects
that depend on budget sets. As an example of this we show that if
preferences are defined over consumption choices of other individuals
then rationalization fails only in cases of negligible practical interest.