Can Median-Maximizing Behavior Be Rational?

In this note, we consider a perennial problem in single-person choice theory, that is, characterizing choice under uncertainty. In particular, we consider a hypothesis put forward by Joseph Stiglitz (2005), suggesting that median-maximing behavior may be optimal under certain circumstances, and consider how it might best be rationalized within choice theory as it is currently conceived. As is well known, median-maximizing behavior is not generally optimal in the classical VNM framework. Our main result is that it is possible to rationalize the Stiglitz hypothesis in the Machina-Schmeidler (1992) framework of probabilistic sophistication.