Choosing two finalists and the winner

We study a class of boundedly rational choice functions which operate as follows. The decision maker uses two criteria in two stages to make a choice. First, she shortlists the top two alternatives, i.e. two finalists, according to one criterion. Next, she chooses the winner in this binary shortlist using the second criterion. The criteria are linear orders that rank the alternatives. Only the winner is observable. We study the behavior exhibited by this choice procedure and provide an axiomatic characterization of it. We leave as an open question the characterization of a generalization to larger shortlists.