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.

翻译：公民议会——由少数公民组成、针对政策议题进行审议的小型小组——常面临成员在最后时刻退出的问题。若不加以干预，这些退出行为将损害小组的规模与代表性，由此引出一个关键问题：在无法提前预知退出情况的前提下，能否通过选择成员的方式，使得退出发生后的最终小组仍保持适当规模并具有代表性？我们将该问题建模为极小极大博弈：极小化方旨在选择能最小化损失（即最终小组与预设代表性目标的偏差）的成员组；随后，对手方定义一个退出概率分布，实际退出情况依此分布产生。我们的核心贡献是提出一种高效的最小化损失算法，该算法在对手方能力从最坏情况到平均情况变化时均保持最优性。该算法通过迭代执行投影梯度下降子程序对抗计算最优响应退出分布的高效算法，同时解决了该领域一个关键开放问题：如何在管理退出行为的同时，确保每位潜在成员被选中的概率相对均衡。基于真实世界数据集，我们将所提算法与现有基准方法进行比较，首次系统刻画了该问题中鲁棒性、损失与公平性之间的权衡关系。