Never Choose the Uniquely Largest: A Characterization.

In this paper we characterize choice behavior that picks the second largest element if there is a uniquely largest: otherwise, the largest elements are picked. Having defined our choice function, we offer a complete characterization of the latter in terms of pure choice function conditions. Similarities to and divergences from conventional choice theory are explained. We discuss the motivations underlying our exercise and provide several examples for the axiomatized choice behaviour.