Adversarial Selection

In many institutional settings, $k$ items are selected with the goal of representing the underlying distribution of claims, opinions, or characteristics in a large population. We study environments with two adversarial parties whose preferences over the selected items are commonly known and opposed. We propose the Quantile Mechanism: one party partitions the population into $k$ disjoint subsets, and the other selects one item from each subset. We show that this procedure is optimally representative among all feasible mechanisms, and illustrate its use in jury selection, multi-district litigation, and committee formation.