Adversarial Selection
This addresses fairness and representation in institutional selection processes for adversarial settings, offering a novel solution with broad applicability.
The paper tackles the problem of selecting k items to represent a population when two adversarial parties have opposing preferences, proposing the Quantile Mechanism where one party partitions the population and the other selects items from each subset. It shows this mechanism is optimally representative and applies it to scenarios like jury selection and committee formation.
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.