Temporal Panel Selection in Ongoing Citizens' Assemblies

Technical Deep Dive: Temporal Panel Selection in Ongoing Citizens' Assemblies

Overview

This work formalizes the problem of temporal sortition, where a sequence of representative panels must be constructed to ensure proportional representation both within each individual panel and across the cumulative selection over time. In ongoing citizens' assemblies, this allows smaller groups that may not qualify for representation in every individual panel to still receive representation over the course of the assembly.

The key contributions are:

• Defining precise representation axioms for individual panels, the global panel, and panel prefixes
• Presenting algorithms that achieve constant-factor approximations to these axioms, while also ensuring individual fairness
• Highlighting the technical challenges and subtle structural issues that arise when extending proportional representation from static to dynamic panel selection

Problem & Context

Permanent citizens' assemblies offer a promising model for community-driven governance, where a randomly selected panel of citizens is empowered to provide input on policy decisions. Unlike one-off panels, permanent assemblies allow participation to shift across multiple rounds over time.

This temporal structure opens up new opportunities to ensure representation for smaller groups that may not warrant a seat in every individual panel. By accumulating seats across a sequence of panels, these groups can still receive proportional representation over the long run.

The key technical challenge is designing a distribution over panel sequences that satisfies three key properties:

1. Individual Panel Representation: Each individual panel satisfies a strong notion of proportional representation, ensuring that every sufficiently large group has at least one representative.
2. Global Panel Representation: The cumulative selection across all panels (the "global panel") also satisfies proportional representation.
3. Prefix Representation: For every prefix of the panel sequence, the cumulative selection up to that point also satisfies proportional representation.

Additionally, the algorithm must ensure Individual Fairness, where each individual has an equal probability of being selected for the overall panel sequence.

Methodology

The paper presents three algorithmic approaches to this problem, each making different tradeoffs between the strength of representation guarantees and the complexity of the solution:

1. Warm-up: Proportional Representation Per Panel and Global Panel
   • Achieves constant-factor approximations to proportionally representative fairness (PRF) for both individual panels and the global panel
   • Relies on existing algorithms for static panel selection
2. Prefix and Panel Level Representation
   • Provides stronger guarantees, ensuring constant-factor approximations to proportionally fair clustering (PFC) for each individual panel and every prefix panel
   • Uses a nested hierarchy of groups to link representation across panel sizes
   • Incurs an exponential blow-up in the approximation factor as the number of panels increases
3. Prefix Level Representation
   • Relaxes the per-panel guarantee, focusing solely on ensuring constant-factor PFC for every prefix panel
   • Constructs a more flexible chain-based structure to link groups across different prefix sizes
   • Achieves a constant-factor approximation independent of the number of panels

The key technical innovations are the nested-group construction in the second approach, and the chain-based linking in the third approach, which allow the algorithms to navigate the subtle challenges of extending proportional representation from static to dynamic panel selection.

Results

The three algorithms presented in the paper provide the following guarantees:

1. Warm-up: There exists a polynomial-time algorithm that returns a distribution over ell panels, where each individual panel and the global panel satisfy 26-approximations to proportionally representative fairness (PRF). Each individual is selected to participate in one of the panels with probability k/n, where k is the panel size and n is the population size.
2. Prefix and Panel Level: There exists a polynomial-time algorithm that returns a distribution over ell panels, where:
   • Each individual panel satisfies O(4^ell)-approximations to proportionally fair clustering (PFC)
   • Each prefix panel (the cumulative selection up to any time t) satisfies O(4^(ell-t))-approximations to PFC
   • Each individual is selected to participate in the overall panel sequence with probability (ell*k)/n
3. Prefix Level: There exists a polynomial-time algorithm that returns a distribution over ell panels, where:
   • Each prefix panel satisfies 19-approximations to PFC
   • Each individual is selected to participate in the overall panel sequence with probability (sum_t k_t)/n, where k_t is the size of panel t

Interpretation

The results demonstrate that it is possible to achieve strong proportional representation guarantees in the context of temporal sortition, where panels are selected over time rather than all at once. The three algorithms presented provide a spectrum of solutions, trading off the strength of the representation axioms against the complexity of the approach.

The key technical insights are:

• Extending proportional representation from static to dynamic panel selection introduces new structural challenges that are not present in the single-shot setting
• Nested group structures and chain-based linking are effective techniques for ensuring representation is maintained across the panel sequence
• There is a fundamental tradeoff between the tightness of the representation guarantees and the scalability/complexity of the algorithms

Limitations & Uncertainties

The paper leaves a few important open questions:

1. Proportionally Representative Fairness (PRF) for Prefixes: Can we design an algorithm that achieves constant-factor approximations to PRF (rather than just PFC) for every prefix panel, in addition to the individual panels?
2. Relaxing Advance Knowledge: The algorithms presented assume the full sequence of panel sizes is known in advance. Can we design algorithms that work without this knowledge?
3. Representation for Arbitrary Subsequences: The current solutions ensure representation for prefixes, but not for arbitrary consecutive subsequences of panels. Can we strengthen the guarantees further?

Addressing these open questions would help expand the applicability and generality of the temporal sortition framework for citizens' assemblies and other domains.

What Comes Next

The proposed temporal sortition framework and the associated algorithmic techniques open up several promising directions for future research, including:

• Exploring relaxations or variants of the representation axioms to better capture real-world desiderata
• Developing efficient distributed/decentralized algorithms for implementing temporal sortition in practice
• Investigating connections to other areas of computer science, such as online and dynamic resource allocation, that may offer relevant tools and insights
• Validating the framework through empirical case studies and user studies with citizens' assembly organizers and participants

By continuing to refine the theoretical foundations and practical considerations around temporal sortition, the computer science community can make important contributions to the design of more equitable and representative democratic institutions.