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Federated Assemblies

Daniel Halpern, Ariel D. Procaccia, Ehud Shapiro, Nimrod Talmon

TL;DR

This work introduces federated assemblies, a DAG-based framework where each parent assembly is formed from its child assemblies and members are drawn from descendants to achieve descriptive representation. It formalizes three guarantees—individual representation, ex ante representation of child assemblies, and ex post representation of child assemblies—and develops a progression of algorithms that satisfy these properties in increasingly general settings, from laminar trees to semi-laminar region-topic structures. A column-generation convex programming approach demonstrates practical feasibility for general instances, supported by experiments showing most instances can be resolved with meaningful guarantees; the complexity grows with the number of equivalence classes and federations. The results offer a path toward scalable, organzation-level deliberative democracy with potential resistance to manipulation and sybil attacks, while acknowledging challenges around governance, maintenance, and time-varying changes.

Abstract

A citizens' assembly is a group of people who are randomly selected to represent a larger population in a deliberation. While this approach has successfully strengthened democracy, it has certain limitations that suggest the need for assemblies to form and associate more organically. In response, we propose federated assemblies, where assemblies are interconnected, and each parent assembly is selected from members of its child assemblies. The main technical challenge is to develop random selection algorithms that meet new representation constraints inherent in this hierarchical structure. We design and analyze several algorithms that provide different representation guarantees under various assumptions on the structure of the underlying graph.

Federated Assemblies

TL;DR

This work introduces federated assemblies, a DAG-based framework where each parent assembly is formed from its child assemblies and members are drawn from descendants to achieve descriptive representation. It formalizes three guarantees—individual representation, ex ante representation of child assemblies, and ex post representation of child assemblies—and develops a progression of algorithms that satisfy these properties in increasingly general settings, from laminar trees to semi-laminar region-topic structures. A column-generation convex programming approach demonstrates practical feasibility for general instances, supported by experiments showing most instances can be resolved with meaningful guarantees; the complexity grows with the number of equivalence classes and federations. The results offer a path toward scalable, organzation-level deliberative democracy with potential resistance to manipulation and sybil attacks, while acknowledging challenges around governance, maintenance, and time-varying changes.

Abstract

A citizens' assembly is a group of people who are randomly selected to represent a larger population in a deliberation. While this approach has successfully strengthened democracy, it has certain limitations that suggest the need for assemblies to form and associate more organically. In response, we propose federated assemblies, where assemblies are interconnected, and each parent assembly is selected from members of its child assemblies. The main technical challenge is to develop random selection algorithms that meet new representation constraints inherent in this hierarchical structure. We design and analyze several algorithms that provide different representation guarantees under various assumptions on the structure of the underlying graph.
Paper Structure (16 sections, 4 theorems, 33 equations, 1 figure, 4 algorithms)

This paper contains 16 sections, 4 theorems, 33 equations, 1 figure, 4 algorithms.

Table of Contents

  1. Introduction
  2. Our proposal: Federated assemblies.
  3. Technical challenge and our results.
  4. Related work.
  5. Model
  6. Ex Ante Child Representation
  7. Ex Post Child Representation
  8. Laminar Instances
  9. Semi-Laminar Instances
  10. Experiments
  11. Discussion
  12. Extending \ref{['alg:priority-order']} to Smaller Equivalence Classes
  13. Proof of \ref{['thm:tree']}
  14. Impossibility for Iterative Algorithms
  15. \ref{['alg:region-topic']} Helper Functions
  16. ...and 1 more sections

Key Result

Theorem 1

Assume that each nonempty equivalence class $C^L$ satisfies $|C^L| \ge n$. Then, alg:priority-order satisfies individual representation and ex ante child representation.

Figures (1)

  • Figure 1: Scatter plots showing the time taken and number of panels in the support for each of the instances we ran on. Sub-plots show the same plot, colored by a parameter.

Theorems & Definitions (6)

  • Theorem 1
  • proof
  • Theorem 2
  • Theorem 3
  • Proposition 1
  • proof