Constitutional Governance in Metric Spaces

2026-05-13

AI Summary

This work addresses the absence of end-to-end polynomial-time procedures in existing autonomous governance mechanisms, where the core aggregation problem is NP-hard. The authors propose a constitutional governance framework that unifies voting, proposal formation, deliberation, amendment, and consensus into an efficient autonomous process: members submit ideal proposals, which are synthesized—via coalition formation, AI-mediated negotiation, and supermajority support—into public proposals scored and adopted according to constitutional rules. The framework innovatively integrates metric space aggregation centered on the generalized median, reality-aware social choice, supermajority-based constitutional amendment, and self-amending constitutional mechanisms. Theoretically, sincere voting is shown to weakly dominate strategic misreporting; the compromise gap vanishes in one-dimensional settings and remains bounded in general cases. Empirical validation across seven instance types demonstrates the framework’s efficacy, with simulations indicating that proposed heuristics substantially reduce the compromise gap.

Abstract

Computational social choice and algorithmic decision theory offer rich aggregation theory but no end-to-end, polynomial-time process for egalitarian self-governance: prior work treats aggregation, deliberation, amendment, and consensus in isolation, and key metric-space aggregators are NP-hard. We propose constitutional governance in metric spaces, integrating these stages into one polynomial-time process. The constitution assigns, per amendable component, a metric space, aggregation rule, and supermajority threshold. Each member submits an ideal element -- both vote and personal proposal. Any member may then submit a public proposal carrying supermajority public support under the revealed votes -- sourced from coalition deliberation, optimization, or AI mediation. The constitutional rule scores proposals against the status quo, adopting the supported proposal of positive maximal score (else retaining the status quo); the same rule, possibly with a higher threshold, amends the constitution itself. We develop the generalised median as the worked rule, establish framework-level guarantees, prove no misreport weakly dominates sincere voting, and study the compromise gap between best peak and unconstrained optimum -- zero in one dimension, bounded in general, narrowed in simulation by a simple heuristic. We instantiate the framework on seven canonical settings; the mean appears as a utilitarian alternative in the appendix. By unifying metric-space aggregation, reality-aware social choice, supermajority amendment, constitutional consensus, deliberative coalition formation, and AI mediation, this work delivers a comprehensive solution to the constitutional democratic governance of digital communities and organisations.

Problem

• constitutional governance
• metric spaces
• egalitarian self-governance
• social choice
• aggregation

Innovation

• constitutional governance
• metric space aggregation
• generalized median
• supermajority amendment
• AI-mediated deliberation