Permanent citizens' assemblies are ongoing deliberative bodies composed of randomly selected citizens, organized into panels that rotate over time. Unlike one-off panels, which represent the population in a single snapshot, permanent assemblies enable shifting participation across multiple rounds. This structure offers a powerful framework for ensuring that different groups of individuals are represented over time across successive panels. In particular, it allows smaller groups of individuals that may not warrant representation in every individual panel to be represented across a sequence of them. We formalize this temporal sortition framework by requiring proportional representation both within each individual panel and across the sequence of panels. Building on the work of Ebadian and Micha (2025), we consider a setting in which the population lies in a metric space, and the goal is to achieve both proportional representation, ensuring that every group of citizens receives adequate representation, and individual fairness, ensuring that each individual has an equal probability of being selected. We extend the notion of representation to a temporal setting by requiring that every initial segment of the panel sequence, viewed as a cumulative whole, proportionally reflects the structure of the population. We present algorithms that provide varying guarantees of proportional representation, both within individual panels and across any sequence of panels, while also maintaining individual fairness over time.

翻译：持续性公民大会是由随机抽选的公民组成的长期审议机构，其成员被编入随时间轮换的小组。与仅代表单一时点人口状况的一次性小组不同，持续性大会允许参与者在多轮审议中动态更替。这种结构为保障不同群体在连续轮次的小组中获得时序性代表提供了有力框架，尤其使得那些可能无法在单个小组中获得代表权的少数群体，能够通过连续小组序列实现代表性。我们通过要求每个独立小组内部及跨小组序列均满足比例代表性，将此时序抽选框架形式化。基于Ebadian和Micha（2025）的研究，我们考虑人口分布于度量空间的场景，其目标在于同时实现比例代表性（确保每个公民群体获得充分代表）与个体公平性（确保每个个体被选中的概率均等）。通过要求将小组序列的每个初始片段视为累积整体时，均能按比例反映人口结构特征，我们将代表性概念扩展至时序场景。本文提出的算法能够在保持个体公平性的同时，为独立小组内部及任意小组序列提供不同程度的比例代表性保证。