Selecting Winners, Excluding Losers: Duality in Bilateral Multiwinner Compromise

How should two parties with conflicting interests jointly choose a panel of candidates? This question arises in arbitration, judicial appointments, expert committees, and other settings in which neither side should control the selection process on its own. We study two simple ways of sharing influence. In one, parties exercise power by excluding candidates from consideration; in the other, they exercise power by directly appointing members of the panel. We show how these two approaches generate different forms of compromise. One favors candidates who are mutually acceptable to both parties, while the other favors representation of candidates who rank highly for at least one of them. We characterize the equilibrium outcomes of both procedures and relate them to natural multiwinner compromise benchmarks. We also uncover a structural duality between appointment and exclusion: once selected candidates and excluded candidates are interchanged, the two compromise mechanisms become closely related versions of the same underlying procedure.