Two-stage majoritarian choice

We propose a class of decisive collective choice rules that rely on a linear ordering to partition the majority relation into two acyclic relations. The first of these relations is used to pare down the set of the feasible alternatives into a shortlist while the second is used to make a final choice from the shortlist. Rules in this class are characterized by four properties: two classical rationality requirements (Sen's expansion consistency and Manzini and Mariotti's weak WARP); and adaptations of two classical collective choice requirements (Arrow's independence of irrelevant alternatives and Saari and Barney's no preference reversal bias). These rules also satisfy some other desirable properties, including an adaptation of May's positive responsiveness.