The Tree that Hides the Forest: A Note on Revealed Preference

The common interpretation given to choice behavior that satisfies the traditional revealed preference axioms is that it results from the maximization of a single preference. We show that choice data alone does not enable one to rule out the possibility that the choice behavior that satisfies the revealed preference axioms is instead the result of the aggregation of a collection of distinct preferences. In particular, we show that any ordering is observationally equivalent to a majoritarian aggregation of a collection of distinct dichotomous orderings. We also show that any ordering is observationally equivalent to a Borda’s aggregation of a collection of distinct linear orderings.