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Temporal Panel Selection in Ongoing Citizens' Assemblies

Yusuf Hakan Kalayci, Evi Micha

Abstract

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.

Temporal Panel Selection in Ongoing Citizens' Assemblies

Abstract

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.
Paper Structure (20 sections, 12 theorems, 20 equations, 1 figure, 5 algorithms)

This paper contains 20 sections, 12 theorems, 20 equations, 1 figure, 5 algorithms.

Table of Contents

  1. Introduction
  2. Temporal Sortition.
  3. Technical Challenge and Our Contributions.
  4. Related Work.
  5. Preliminaries
  6. Representation Axioms.
  7. Axioms for Temporal Sortition.
  8. Paper Organization.
  9. Warm-up: Proportional Representation Per Panel and Global Panel
  10. Prefix and Panel Level Representation
  11. Satisfying Property (a) - Panel Representation:
  12. Satisfying Property (b) - Prefix Representation:
  13. Modified Greedy Capture
  14. Proof of Lemma \ref{['lem:hierarchical']}
  15. Proof of Theorem \ref{['thm:exponential']}
  16. ...and 5 more sections

Key Result

Theorem 3.1

Given a population $V$ and panel sizes $k_1$ and $k_2$, let $P_1$ be a panel of size $k_1$ that satisfies $\alpha$-PRF for population $V$, and let $P_2$ be a smaller panel of size $k_2$ that satisfies $\beta$-PRF for population $P_1$. Then,

Figures (1)

  • Figure 1: This figure illustrates the hierarchical group structure built in Phase 1 of NestedBasedRepresentation for eight individuals ($v_1,v_2$ at location 1; $v_3,v_4$ at 2; $v_5$–$v_8$ at 4) with parameters $\ell=2$ and $k=2$. The left-hand side shows two calls to ModifiedGreedyCapture: first with $t=2$, which forms $\mathcal{G}^2=\{G^2_1,G^2_2,G^2_3\}$ (leaving $v_7$ and $v_8$ ungrouped), and then with $t=1$, applied to these groups and the remaining individuals to obtain $\mathcal{G}^1=\{G^1_1,G^1_2\}$. The right-hand side depicts the resulting tree, with groups as internal nodes and individuals as leaves.

Theorems & Definitions (27)

  • Definition 2.1: $\alpha$-Proportionally Fair Clustering ($\alpha$-PFC)chen2019proportionally
  • Definition 2.2: $\beta$-Proportionally Representative Fairness ($\beta$-PRF) aziz-lee-chu-vollen-proportional-clustering
  • Theorem 3.1
  • proof
  • Corollary 3.2
  • Theorem 4.1
  • Lemma 4.2
  • proof : Proof of Lemma \ref{['lem:hierarchical']}
  • Claim 4.3
  • proof : Proof of Claim
  • ...and 17 more