Adversarial Selection

TL;DR

This paper introduces the Quantile Mechanism, a method for selecting representative items in adversarial settings, ensuring optimal representation and applicable to various institutional decision-making processes.

Contribution

It proposes the Quantile Mechanism, a novel selection process that is proven to be optimally representative in adversarial environments with known preferences.

Findings

Quantile Mechanism is optimal among feasible mechanisms.

Applicable to jury selection, litigation, and committee formation.

Ensures representative selection in adversarial settings.

Abstract

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.