City Sampling for Citizens' Assemblies

2025-09-09

AI Summary

This paper addresses the two-stage stochastic sampling problem for citizen assemblies under municipal data fragmentation—specifically, how to guarantee *ex ante* equal selection probability for every citizen, given that only a limited number of cities can be selected *ex post* for voter recruitment. Method: We propose two novel algorithmic frameworks: (i) an interpretable greedy algorithm satisfying *ex post* monotonicity and proportionality; and (ii) an exact optimization framework based on column generation, integrating a linear programming separation oracle, a pseudopolynomial dynamic programming subroutine, additive approximation, and integer programming heuristics. Results: Evaluated on real-world German municipal demographic data, our approach yields city combinations that closely approximate the theoretical optimum while simultaneously ensuring sampling fairness and practical feasibility. The solution has advanced to deployment collaboration with a non-profit organization.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• Security and Privacy: Data transparency and provenance
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

In citizens' assemblies, a group of constituents is randomly selected to weigh in on policy issues. We study a two-stage sampling problem faced by practitioners in countries such as Germany, in which constituents' contact information is stored at a municipal level. As a result, practitioners can only select constituents from a bounded number of cities ex post, while ensuring equal selection probability for constituents ex ante. We develop several algorithms for this problem. Although minimizing the number of contacted cities is NP-hard, we provide a pseudo-polynomial time algorithm and an additive 1-approximation, both based on separation oracles for a linear programming formulation. Recognizing that practical objectives go beyond minimizing city count, we further introduce a simple and more interpretable greedy algorithm, which additionally satisfies an ex-post monotonicity property and achieves an additive 2-approximation. Finally, we explore a notion of ex-post proportionality, for which we propose two practical algorithms: an optimal algorithm based on column generation and integer linear programming and a simple heuristic creating particularly transparent distributions. We evaluate these algorithms on data from Germany, and plan to deploy them in cooperation with a leading nonprofit organization in this space.

Problem

• Optimizing two-stage random sampling from municipalities
• Ensuring equal selection probability for all constituents
• Minimizing number of contacted cities while maintaining fairness

Innovation

• Pseudo-polynomial time algorithm with separation oracles
• Greedy algorithm with ex-post monotonicity property
• Column generation for ex-post proportionality optimization