  I formulate and characterize the following two-stage choice behavior. The
decision maker is endowed with two preferences. She shortlists all maximal
alternatives according to the first preference. If the first preference is
decisive, in the sense that it shortlists a unique alternative, then that
alternative is the choice. If multiple alternatives are shortlisted, then, in a
second stage, the second preference vetoes its minimal alternative in the
shortlist, and the remaining members of the shortlist form the choice set. Only
the final choice set is observable. I assume that the first preference is a
weak order and the second is a linear order. Hence the shortlist is fully
rationalizable but one of its members can drop out in the second stage, leading
to bounded rational behavior. Given the asymmetric roles played by the
underlying binary relations, the consequent behavior exhibits a minimal
compromise between two preferences. To our knowledge it is the first Choice
function that satisfies Sen's $\beta$ axiom of choice,but not $\alpha$.
