Adversarial Selection

2026-03-25

AI Summary

This work addresses the problem of selecting k representative items from a large population to accurately reflect its original distribution when two adversarial parties with opposing and publicly known preferences are involved. The paper proposes the Quantile Partitioning Mechanism: one party partitions the population into k disjoint quantile-based subsets, and the other selects one item from each subset. This mechanism is the first to achieve provably optimal representativeness under adversarial preference settings, with theoretical guarantees that it minimizes representation error among all feasible mechanisms. Drawing on tools from mechanism design and game theory, the study establishes strong optimality bounds and demonstrates the mechanism’s practical applicability and effectiveness in institutional contexts such as jury selection, multi-district litigation, and committee formation.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements

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.

Problem

• adversarial selection
• representative selection
• quantile mechanism
• institutional design
• opposing preferences

Innovation

• Quantile Mechanism
• Adversarial Selection
• Optimal Representativeness
• Two-Party Mechanism Design
• Fair Division