Near-Optimal Dropout-Robust Sortition

TL;DR

This paper introduces an efficient algorithm for selecting citizen panels that remain representative and balanced despite unpredictable last-minute dropouts, addressing a key challenge in designing resilient citizens' assemblies.

Contribution

It presents a novel minimax game model and an optimal loss-minimizing algorithm that balances robustness, fairness, and representation in panel selection under dropout uncertainty.

Findings

Algorithm remains optimal across different dropout models.

Addresses the open question of equal probability selection.

Demonstrates effectiveness on real-world datasets.

Abstract

Citizens' assemblies - small panels of citizens that convene to deliberate on policy issues - often face the issue of panelists dropping out at the last-minute. Without intervention, these dropouts compromise the size and representativeness of the panel, prompting the question: Without seeing the dropouts ahead of time, can we choose panelists such that after dropouts, the panel will be representative and appropriately-sized? We model this problem as a minimax game: the minimizer aims to choose a panel that minimizes the loss, i.e., the deviation of the ultimate panel from predefined representation targets. Then, an adversary defines a distribution over dropouts from which the realized dropouts are drawn. Our main contribution is an efficient loss-minimizing algorithm, which remains optimal as we vary the maximizer's power from worst case to average case. Our algorithm - which iteratively plays a projected gradient descent subroutine against an efficient algorithm for computing the best-response dropout distribution - also addresses a key open question in the area: how to manage dropouts while ensuring that each potential panelist is chosen with relatively equal probabilities. Using real-world datasets, we compare our algorithms to existing benchmarks, and we offer the first characterizations of tradeoffs between robustness, loss, and equality in this problem.