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.

翻译：计算社会选择与算法决策理论提供了丰富的聚合理论，但缺乏一种端到端、多项式时间内的平等自治治理流程：先前的研究分别处理聚合、商议、修正和共识，且关键的度量空间聚合器为NP难问题。我们提出度量空间中的宪制治理，将这些阶段整合为一个多项式时间流程。宪法为每个可修正的组成部分分配一个度量空间、聚合规则及超级多数门槛。每位成员提交一个理想元素——既作为投票也作为个人提案。任何成员随后可提交一项公开提案，该提案需基于已揭示投票获得超级多数公众支持——这种支持可源自联盟商议、优化或人工智能调解。宪制规则对提案与现状进行评分，采纳具有正最大分数的支持提案（否则保留现状）；同一规则（可能采用更高门槛）用于修正宪法本身。我们开发广义中位数作为具体规则，建立框架层面的保证，证明无虚报弱支配诚实投票，并研究最优峰值与无约束最优之间的妥协差距——在一维中为零，在一般情况下有界，在模拟中通过简单启发式方法缩小。我们在七个经典场景中实例化该框架；均值作为功利主义替代方案出现在附录中。通过统一度量空间聚合、现实感知的社会选择、超级多数修正、宪制共识、商议联盟形成及人工智能调解，本研究为数字社区与组织的宪制民主治理提供了全面解决方案。