On the advantages and disadvantages of being the first mover under rules of k names

Rules of k names are methods that allow two potentially conflicting parties to share the power to appoint officers. One of the parties (the proposer) selects k candidates from a larger pool, and then the other party (the chooser) selects the winner from this restricted list. We investigate conditions under which the two parties could agree ex ante on the distributions of roles, one of them preferring to be the chooser and the other preferring to be the proposer. We show that this may not always be possible, and discuss what are the relevant characteristics of the environments where agreement can be reached.