(Joint with Rahul Deb)

In this paper, we examine how the geometry underlying revealed preference affects the set of preferences that can be revealed by choices. Specifically, given an arbitrary preference relation defined on a finite set of points, we ask whether there exists a data set which can generate the given relation through revealed preference. We first show that there exist data sets which can generate preference relations exhibiting severe irrationality- every choice is revealed preferred to every other. We then prove that the number of goods in the consumption space under study affects the set of revealed preference relations. We show that if the consumption space has enough goods relative to observations, any revealed preference relation could arise. Conversely, if the consumption space has low dimension relative to the number of observations, then there exist preference relations that could never be revealed by choices.

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