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Federated Assemblies
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Proposes federated assemblies (hierarchical DAG of citizens' assemblies where parent assemblies are drawn from child assemblies) and gives random selection algorithms satisfying individual, ex ante and ex post child representation under various graph structures, plus a column-generation experiment on 6400 random instances.
Problem
How to randomly select members of hierarchically federated citizens' assemblies (parent assemblies drawn from child assemblies) so that representation constraints (equal individual chance, proportional child representation ex ante and ex post) are met.
Approach
Model federated assemblies as a DAG and design randomized selection that inherits members from child assemblies; uses random orders and dependent rounding (Birkhoff-von Neumann / bihierarchy rounding) to jointly guarantee individual representation and proportional child representation, with exact ex post guarantees on laminar instances and approximate ones on semi-laminar instances.
Key results
- Algorithm for laminar instances achieves individual, ex ante and ex post child representation exactly.
- Semi-laminar algorithm achieves individual and ex ante representation with ex post child representation up to additive error of one under regularity conditions.
- Column generation found feasible distributions satisfying all guarantees on 6400 random instances; algorithm terminated on all but 15 (99.7%), with no infeasible instances found.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the proposed optimization algorithm to find randomized assignments satisfying all ex ante and ex post guarantees | Federated assembly instances · Sampled arbitrary DAG instances | termination rate: Of the 6400 instances, on all but 15, the algorithm terminated, returning an optimal solution; >99.7% | Helped |
| Increase the number of equivalence classes and federations | Column-generation optimization algorithm · Sampled arbitrary DAG instances | computational complexity | Hurt |
| Increase assembly size | Column-generation optimization algorithm · Sampled arbitrary DAG instances | computational complexity | No clear effect |
Surprising findings
- Natural iterative (top-down) algorithms cannot satisfy individual and ex ante child representation simultaneously on some non-laminar or non-tree instances.
Limitations
- Existence of a distribution satisfying all properties in the general (non-laminar, non-semi-laminar) case is not proven.
- Semi-laminar guarantees hold only under regularity conditions and ex post child representation is approximate (additive error one).
- Static, single-shot model; does not address dynamic updates over time.
Experimental setup
Metrics: feasibility of satisfying all guarantees running time number of panels in support
Builds on: citizens' assembly sortition column generation (Flanigan et al.) pipage rounding Birkhoff-von Neumann theorem
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