The Panel Complexity of Sortition: Is 12 Angry Men Enough?

2025-04-29

AI Summary

This paper addresses the fundamental problem of determining the minimal size of a randomly sampled citizen panel that ensures its decisions reliably generalize to the entire population across three dimensions: social welfare efficiency, group fairness (i.e., core stability), and robustness (i.e., low outlier probability). We formally define a “representative panel” via the Wasserstein distance and develop a novel panel complexity framework. Integrating tools from statistical learning theory, social choice theory, and probabilistic analysis, we derive nearly tight lower bounds on panel size for two canonical participatory democracy settings: participatory budgeting and facility location. Our results establish that panels of this theoretically grounded size simultaneously guarantee group-level efficiency and fairness while provably bounding the probability of deviation from optimal societal decisions. This work provides the first rigorous, theory-backed sizing criterion for democratic experiments.

Technology Category

• Game Theory and Economic Paradigms: Social Choice / Voting
• Reasoning under Uncertainty: Stochastic Optimization
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

Sortition is the practice of delegating public decision-making to randomly selected panels. Recently, it has gained momentum worldwide through its use in citizens' assemblies, sparking growing interest within the computer science community. One key appeal of sortition is that random panels tend to be more representative of the population than elected committees or parliaments. Our main conceptual contribution is a novel definition of representative panels, based on the Wasserstein distance from statistical learning theory. Using this definition, we develop a framework for analyzing the panel complexity problem -- determining the required panel size to ensure desirable properties. We focus on three key desiderata: (1) that efficiency at the panel level extends to the whole population, measured by social welfare; (2) that fairness guarantees for the panel translate to fairness for the population, captured by the core; and (3) that the probability of an outlier panel, for which the decision significantly deviates from the optimal one, remains low. We establish near-tight panel complexity guarantees for these desiderata across two fundamental social choice settings: participatory budgeting and facility location.

Problem

• Determining required panel size for representative decision-making
• Ensuring panel efficiency extends to population welfare
• Guaranteeing fairness and low outlier probability in panels

Innovation

• Novel representative panels definition using Wasserstein distance
• Framework for analyzing panel complexity problem
• Near-tight guarantees for social choice settings