Compromising on compromise rules

We propose three mechanisms to reach compromise between two opposing parties. They are based on the use of Rules of k Names, whereby one of the parties proposes a shortlist and the other chooses from it. Methods of this class are used in practice to appoint Supreme Court justices and have been recently proposed for arbitration selection processes. Those we suggest are flexible and allow the parties to participate in the endogenous determination of the role of proposer and the shortlist size. They involve few stages, implement the Unanimity Compromise Set, and are robust to the strategic inclusion of candidates.